Cultivating Computational Thinking Practices and Mathematical Habits of Mind in Lattice Land

ERIC Educational Resources Information Center

Pei, Christina; Weintrop, David; Wilensky, Uri

2018-01-01

There is a great deal of overlap between the set of practices collected under the term "computational thinking" and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the…

The Relationship between Higher Order Thinking Skills and Academic Performance of Student in Mathematics Instruction

ERIC Educational Resources Information Center

Tanujaya, Benidiktus; Mumu, Jeinne; Margono, Gaguk

2017-01-01

Higher order thinking skills (HOTS) is one of important aspects in education. Students with high level of higher order thinking skills tend to be more successful. However, do this phenomenon also happen in the learning of Mathematics? To answer this question, this research aims to study the relationship between HOTS and students' academic…

Teachers' Perceptions of Examining Students' Thinking: Changing Mathematics Instructional Practice

ERIC Educational Resources Information Center

Anderson-Pence, Katie L.

2015-01-01

This paper seeks to illuminate teachers' perceptions of the challenges and benefits of systematically examining students' thinking as part of a professional development program in elementary mathematics education. Using a framework of models of conceptual change and principles of discomfort, three elementary teachers' perceptions of their…

Explicating mathematical thinking in differential equations using a computer algebra system

NASA Astrophysics Data System (ADS)

Zeynivandnezhad, Fereshteh; Bates, Rachel

2018-07-01

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks.

Instructional Reasoning about Interpretations of Student Thinking That Supports Responsive Teaching in Secondary Mathematics

ERIC Educational Resources Information Center

Dyer, Elizabeth B.; Sherin, Miriam Gamoran

2016-01-01

Basing instruction on the substance of student thinking, or responsive teaching, is a critical strategy for supporting student learning. Previous research has documented responsive teaching by identifying observable teaching practices in a broad range of disciplines and classrooms. However, this research has not provided access to the teacher…

Empowering K-12 Students with Disabilities to Learn Computational Thinking and Computer Programming

ERIC Educational Resources Information Center

Israel, Maya; Wherfel, Quentin M.; Pearson, Jamie; Shehab, Saadeddine; Tapia, Tanya

2015-01-01

This article's focus is on including computing and computational thinking in K-12 instruction within science, technology, engineering, and mathematics (STEM) education, and to provide that instruction in ways that promote access for students traditionally underrepresented in the STEM fields, such as students with disabilities. Providing computing…

Improving Student Higher-Order Thinking Skills in Mathematics.

ERIC Educational Resources Information Center

Butkowski, Jean; And Others

This report describes a program for improving higher-order thinking skills in mathematics of (n=17) third-, (n=27) fifth-, and (n=27) sixth-grade students in a middle class community. Three interventions were chosen: (1) cooperative learning to develop student self-confidence and to improve student achievement, (2) the instruction of students in…

Defining Computational Thinking for Mathematics and Science Classrooms

NASA Astrophysics Data System (ADS)

Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri

2016-02-01

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.

An Inquiry Approach to Construct Instructional Trajectories Based on the Use of Digital Technologies

ERIC Educational Resources Information Center

Santos-Trigo, Manuel

2008-01-01

There are diverse ways to construct instructional activities that teachers can use to foster their students' development of mathematical thinking. It is argued that the use of computational tools offers teachers the possibility of designing and exploring mathematical tasks from distinct perspectives that might lead their students to the…

Decentering: A Construct to Analyze and Explain Teacher Actions as They Relate to Student Thinking

ERIC Educational Resources Information Center

Teuscher, Dawn; Moore, Kevin C.; Carlson, Marilyn P.

2016-01-01

Mathematics educators and writers of mathematics education policy documents continue to emphasize the importance of teachers focusing on and using student thinking to inform their instructional decisions and interactions with students. In this paper, we characterize the interactions between a teacher and student(s) that exhibit this focus.…

Using Integer Manipulatives: Representational Determinism

ERIC Educational Resources Information Center

Bossé, Michael J.; Lynch-Davis, Kathleen; Adu-Gyamfi, Kwaku; Chandler, Kayla

2016-01-01

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…

Business Mathematics Curriculum.

ERIC Educational Resources Information Center

EASTCONN Regional Educational Services Center, North Windham, CT.

This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…

NCTM Principles and Standards for Mathematically Talented Students

ERIC Educational Resources Information Center

Deal, Linda J.; Wismer, Michael G.

2010-01-01

The "Principles and Standards for School Mathematics" published in 2000 by the National Council of Teachers of Mathematics (NCTM) created a vision of mathematical concepts and processes to establish core educational guidelines for instruction from grades K to 12. The overall plan does emphasize higher level thinking, problem solving, and…

Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving

ERIC Educational Resources Information Center

Ben-Hur, Meir

2006-01-01

Fact-filled textbooks that stress memorization and drilling are not very good for teaching students how to think mathematically and solve problems. But this is a book that comes to the rescue with an instructional approach that helps students in every grade level truly understand math concepts so they can apply them on high-stakes assessments,…

Promoting middle school students’ abstract-thinking ability through cognitive apprenticeship instruction in mathematics learning

NASA Astrophysics Data System (ADS)

Yusepa, B. G. P.; Kusumah, Y. S.; Kartasasmita, B. G.

2018-01-01

The aim of this study is to get an in-depth understanding of students’ abstract-thinking ability in mathematics learning. This study was an experimental research with pre-test and post-test control group design. The subject of this study was eighth-grade students from two junior high schools in Bandung. In each schools, two parallel groups were selected and assigned into control and experimental groups. The experimental group was exposed to Cognitive Apprenticeship Instruction (CAI) treatment, whereas the control group was exposed to conventional learning. The results showed that abstract-thinking ability of students in experimental group was better than that of those in control group in which it could be observed from the overall and school level. It could be concluded that CAI could be a good alternative learning model to enhance students’ abstract-thinking ability.

Challenging a Teacher's Perceptions of Mathematical Smartness through Reflections on Students' Thinking

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2015-01-01

Creating equitable opportunities so all students can learn and succeed mathematically has been a key focus of mathematics education across several decades. Central to student achievement are students' mathematical identity and their feelings of success during instruction. Researchers (e.g., Boaler & Staples, 2008) have shown that teachers can…

Using Portfolio Assignments to Assess Students' Mathematical Thinking

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy; Buck, Stephen

2010-01-01

Writing in mathematics can improve procedural knowledge and communication skills and may also help students better understand and then remember problems. The majority of mathematics teachers know that they ought to include some writing assignments in their instructional plans, but the challenge of covering the curriculum and the time required to…

Learning to Leverage Children's Multiple Mathematical Knowledge Bases in Mathematics Instruction

ERIC Educational Resources Information Center

Turner, Erin E.; Foote, Mary Q.; Stoehr, Kathleen Jablon; McDuffie, Amy Roth; Aguirre, Julia Maria; Bartell, Tonya Gau; Drake, Corey

2016-01-01

In this article, the authors explore prospective elementary teachers' engagement with and reflection on activities they conducted to learn about a single child from their practicum classroom. Through these activities, prospective teachers learned about their child's mathematical thinking and the interests, competencies, and resources she or he…

Capturing Thinking on the Talk Frame

ERIC Educational Resources Information Center

Casa, Tutita M.

2013-01-01

The National Council of Teachers of Mathematics (NCTM 1991, 2000) recommends that students be positioned as sense makers who weigh one another's ideas and judge their mathematical validity. The instructional tool discussed in this article helps students engage in discussions that foster student reasoning, then settle on correct mathematics.…

Evaluating the Effects of Lesson Study as a Way to Help Student Teachers Learn How to Use Student Thinking when Planning and Revising Mathematics Lesson Plans

ERIC Educational Resources Information Center

Sisofo, Eric Joseph

2010-01-01

The use of student thinking in teaching has been linked to improved instruction and learning. It is reasonable to assume that the University of Delaware's undergraduate program might be interested in figuring out ways to develop this skill in its mathematics specialist pre-service teachers. Currently, the student teaching experience at the…

Scaffolded Inquiry-Based Instruction with Technology: A Signature Pedagogy for STEM Education

ERIC Educational Resources Information Center

Crippen, Kent J.; Archambault, Leanna

2012-01-01

Inquiry-based instruction has become a hallmark of science education and increasingly of integrated content areas, including science, technology, engineering, and mathematics (STEM) education. Because inquiry-based instruction very clearly contains surface, deep, and implicit structures as well as engages students to think and act like scientists,…

Designing Spaces for Creativity and Divergent Thinking: Pre-Service Teachers Creating Stop Motion Animation on Tablets

ERIC Educational Resources Information Center

O'Byrne, W. Ian; Radakovic, Nenad; Hunter-Doniger, Tracey; Fox, Madison; Kern, Reggie; Parnell, Stephanie

2018-01-01

In recent years, tablets have been shown to serve as incredible teaching tools in classrooms around the world. In mathematics education, divergent thinking, creativity, and play may play a key role in formation of adaptive thinking and math achievement. This qualitative, participatory action research investigated the use of an instructional model…

The Nature of Scaffolding in Undergraduate Students' Transition to Mathematical Proof

ERIC Educational Resources Information Center

Blanton, Maria L.; Stylianou, Despina A.; David, Maria Manuela

2003-01-01

This paper explores the role of instructional scaffolding in the development of undergraduate students' understanding of mathematical proof during a one-year discrete mathematics course. We describe here the framework adapted for the analysis of whole-class discussion and examine how the teacher scaffolded students' thinking. Results suggest that…

Informal Content and Student Note-Taking in Advanced Mathematics Classes

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy; Weber, Keith; Mejía-Ramos, Juan Pablo

2017-01-01

This study investigates 3 hypotheses about proof-based mathematics instruction: (a) that lectures include informal content (ways of thinking and reasoning about advanced mathematics that are not captured by formal symbolic statements), (b) that informal content is usually presented orally but not written on the board, and (c) that students do not…

Teacher Professionalism--An Innovative Programme for Teaching Mathematics to Foundation Level Learners with Limited Language Proficiency.

ERIC Educational Resources Information Center

Naude, H.; Pretorius, E.; Vandeyar, S.

2003-01-01

Details a study of the ways that limited language proficiency affected learners' readiness for mathematics instruction among disadvantaged preschoolers within a Griqua community in South Africa. Notes a link between limited language proficiency and nonreadiness for foundation level mathematics due to limited thinking skills, which constitute…

Developing Mathematical Thinking: Changing Teachers' Knowledge and Instruction

ERIC Educational Resources Information Center

Brendefur, Jonathan L.; Thiede, Keith; Strother, Sam; Bunning, Kim; Peck, Duane

2013-01-01

In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and…

Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction. Studies in Mathematical Thinking and Learning Series

ERIC Educational Resources Information Center

Remillard, Janine T., Ed.; Herbel-Eisenmann, Beth A., Ed.; Lloyd, Gwendolyn M., Ed.

2011-01-01

This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on--but not restricted to--those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite…

Making 10 My Way

ERIC Educational Resources Information Center

Bofferding, Laura; Kemmerle, Melissa; Murata, Aki

2012-01-01

Young students, new to formal mathematics, come to school with various number experiences. To meet their needs, teachers must understand each student's thinking and tailor instruction appropriately. Differentiation is a vehicle for making this possible. According to Tomlinson (2001), differentiated instruction is student-centered; rooted in…

Can goal-free problems facilitating students' flexible thinking?

NASA Astrophysics Data System (ADS)

Maulidya, Sity Rahmy; Hasanah, Rusi Ulfa; Retnowati, Endah

2017-08-01

Problem solving is the key of doing and also learning mathematics. It takes also the fundamental role of developing mathematical knowledge. Responding to the current reform movement in mathematics, students are expected to learn to be a flexible thinker. The ability to think flexible is challenged by the globalisation, hence influence mathematics education. A flexible thinking includes ability to apply knowledge in different contexts rather than simply use it in similar context when it is studied. Arguably problem solving activities can contribute to the development of the ability to apply skills to unfamiliar situations. Accordingly, an appropriate classroom instructional strategy must be developed. A cognitive load theory suggests that by reducing extraneous cognitive load during learning could enhance transfer learning. A goal-free problem strategy that is developed based in cognitive load theory have been showed to be effective for transfer learning. This strategy enables students to learn a large numbers of problem solving moves from a mathematics problem. The instruction in a goal-free problem directs students to `calculate as many solution as you can' rather than to calculate a single given goal. Many experiment research evident goal-free problem enhance learning. This literature review will discuss evidence goal-free problem facilitate students to solve problems flexibly and thus enhance their problem solving skills, including how its implication in the classroom.

Learning from the Unknown Student

ERIC Educational Resources Information Center

Barlow, Angela T.; Gerstenschlager, Natasha E.; Harmon, Shannon E.

2016-01-01

In this article, three instructional situations demonstrate the value of using an "unknown" student's work to allow the advancement of students' mathematical thinking as well as their engagement in the mathematical practice of critiquing the reasoning of others: (1) introducing alternative solution strategies; (2) critiquing inaccuracies…

Catalyzing Genetic Thinking in Undergraduate Mathematics Education

ERIC Educational Resources Information Center

King, Samuel Olugbenga

2016-01-01

In undergraduate mathematics education, atypical problem solving approaches are usually discouraged because they are not adaptive to systematic deduction on which undergraduate instructional systems are predicated. I present preliminary qualitative research evidence that indicates that these atypical approaches, such as genetic guessing, which…

Instructional design in mathematics for undergraduate students based on learning by mistakes approach utilizing scilab assistance

NASA Astrophysics Data System (ADS)

Kartika, H.

2018-03-01

The issue related to making mistake while learning such as negative emotion is found while students learn mathematics with the aid of a computer. When the computer output showed a mistake message, the students considered it as a computer software malfunction. Based on this issue, the writer designs an instructional model based on learning by mistake approach and which is Scilab assisted. The method used in this research is research design involving undergraduate students in matrix algebra courses. The data collected throught survey with questionnaire to gain feedback about the approach implemented. The data analyzed using quantitative descriptive. The instructional design proposed is the student act as a mistake corrector while the teacher acts as a mistake maker. Teacher deliberately makes mistakes with the help of Scilab software. On the other hand, students correct, analyze and explain errors resulting from Scilab software. The result of this research is an ICT based instructional design which is expected to be applicable as an alternative learning in directing students to think positively about mistakes in learning. Furthermore, students are also expected to improve their ability in understanding and thinking critically while solving problems and improving themselves in learning mathematics.

Gesture Supports Spatial Thinking in STEM

ERIC Educational Resources Information Center

Stieff, Mike; Lira, Matthew E.; Scopelitis, Stephanie A.

2016-01-01

The present article describes two studies that examine the impact of teaching students to use gesture to support spatial thinking in the Science, Technology, Engineering, and Mathematics (STEM) discipline of chemistry. In Study 1 we compared the effectiveness of instruction that involved either watching gesture, reproducing gesture, or reading…

Ready, Aim, Fire Your Cannons!

ERIC Educational Resources Information Center

Enderson, Mary C.

2015-01-01

This article presents a science, technology, engineering, and mathematics (STEM) activity, building an air cannon, in a mathematics classroom. It describes an investigation grounded in STEM concepts that elementary and middle school teachers carried out to think about ways of implementing STEM activities into their instruction. This particular…

Thinking the Unthinkable: The Story of Complex Numbers (with a Moral).

ERIC Educational Resources Information Center

Kleiner, Israel

1988-01-01

The evolution of complex numbers is described, followed by discussion of some lessons that can be learned from this story, as with other stories from the history of mathematics. Suggestions for teachers about incorporating history into mathematics instruction are included. (MNS)

Targeting Instruction with Formative Assessment Probes

ERIC Educational Resources Information Center

Fagan, Emily R.; Tobey, Cheryl Rose; Brodesky, Amy R.

2016-01-01

This article introduces the formative assessment probe--a powerful tool for collecting focused, actionable information about student thinking and potential misconceptions--along with a process for targeting instruction in response to probe results. Drawing on research about common student mathematical misconceptions as well as the former work of…

Preservice Teachers' Conceptions and Enactments of Project-Based Instruction

ERIC Educational Resources Information Center

Marshall, Jill A.; Petrosino, Anthony J.; Martin, Taylor

2010-01-01

We present results of an investigation of preservice secondary mathematics and science teachers' conceptions of project-based instruction (PBI) and their enactments of PBI in apprentice (student) teaching. We evaluated their thinking and implementations within a composite framework based on the work of education researchers. We analyzed survey…

Silent method for mathematics instruction: An overview of teaching subsets

NASA Astrophysics Data System (ADS)

Sugiman, Apino, Ezi

2017-05-01

Generally, teachers use oral communication for teaching mathematics. Taking an opposite perspective, this paper describes how instructional practices for mathematics can be carried out namely a silent method. Silent method uses body language, written, and oral communication for classroom interaction. This research uses a design research approach consisting of four phases: preliminary, prototyping and developing the instruction, and assessment. There are four stages of silent method. The first stage is conditioning stage in which the teacher introduces the method and makes agreement about the `rule of the game'. It is followed by the second one, elaborating stage, where students guess and explore alternative answers. The third stage is developing mathematical thinking by structuring and symbolizing. Finally, the method is ended by reinforcing stage which aims at strengthening and reflecting student's understanding. In this paper, every stage is described on the basis of practical experiences in a real mathematics classroom setting.

An Experimental Text in Transformational Geometry, Student Text; Cambridge Conference on School Mathematics Feasibility Study No. 43a.

ERIC Educational Resources Information Center

Cambridge Conference on School Mathematics, Newton, MA.

This is part of a student text which was written with the aim of reflecting the thinking of The Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for mathematics. The instructional materials were developed for teaching geometry in the secondary schools. This document is chapter six and titled Motions and…

Examining the Impact of a Framework to Support Prospective Secondary Teachers' Transition from 'Doer' to 'Teacher' of Mathematics

ERIC Educational Resources Information Center

Lee, Hea-Jin; Özgün-Koca, S. Asli; Meagher, Michael; Edwards, Michael Todd

2018-01-01

A transition from "doer" to "teacher" for prospective teachers requires them to reorient from thinking about how they do mathematics to engaging with students and their work, understanding student representations, and planning instruction accordingly. To scaffold a transition, we developed a five-step mathematics as teacher…

An Examination of the Role of Technological Tools in Relation to the Cognitive Demand of Mathematical Tasks in Secondary Classrooms

ERIC Educational Resources Information Center

Sherman, Milan

2011-01-01

This study investigates the role of digital cognitive technologies in supporting students' mathematical thinking while engaging with instructional tasks. Specifically, the study sought to better understand how the use of technology is related to the cognitive demand of tasks. Data were collected in four secondary mathematics classrooms via…

Development and Evaluation of a Case-Based Digital Learning Tool about Children's Mathematical Thinking for Elementary School Teachers (L-TEST)

ERIC Educational Resources Information Center

Olkun, Sinan; Altun, Arif; Deryakulu, Deniz

2009-01-01

It is important for teachers of mathematics to know how pupils react to certain mathematical situations and what these reactions imply, in order to design more effective instructional environments based on their learning needs. This study reports the development processes of a digital learning tool (Learning Tool for Elementary School Teachers…

The Impact of a Professional Development Program on Teachers' Mathematical Knowledge for Teaching, Instruction, and Student Achievement

ERIC Educational Resources Information Center

Jacob, Robin; Hill, Heather; Corey, Doug

2017-01-01

In this paper, we describe findings from a three-year evaluation of a well-developed mathematics professional development program that is commercially available on a wide scale. The professional development is designed to improve teachers' mathematical knowledge for teaching and to enable them to elicit more student thinking and reasoning during…

Using Virtual Manipulative Instruction to Teach the Concepts of Area and Perimeter to Secondary Students with Learning Disabilities

ERIC Educational Resources Information Center

Satsangi, Rajiv; Bouck, Emily C.

2015-01-01

Secondary students with a learning disability in mathematics often struggle with the academic demands presented in advanced mathematics courses, such as algebra and geometry. With greater emphasis placed on problem solving and higher level thinking skills in these subject areas, students with a learning disability in mathematics often fail to keep…

A Mathematical Private Eye

ERIC Educational Resources Information Center

Lee, Ji-Eun; Kim, Kyoung-Tae

2007-01-01

This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…

The Challenge of Formative Assessment in Mathematics Education: Children's Minds, Teachers' Minds

ERIC Educational Resources Information Center

Ginsburg, Herbert P.

2009-01-01

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

Enhancing Thinking Skills in the Sciences and Mathematics.

ERIC Educational Resources Information Center

Halpern, Diane F., Ed.

The need to provide an improved science and mathematics curriculum is imperative. Over recent years cognitive psychologists and educators have responded to this need by designing instructional programs that are more compatible with our knowledge of how people acquire, use, and retain knowledge. This book contains many of the guiding principles…

Expanding Competence: Supporting Students to Engage with Each Other's Mathematical Ideas

ERIC Educational Resources Information Center

Johnson, Nicholas Charles

2017-01-01

This case study examined competence in two third-grade classrooms where teachers centered children's mathematical thinking in instructional decision-making. Offering a synthesis of sociocultural characterizations of competence, and drawing from a variety of data sources including classroom video, student work and assessments, and teacher…

Characterizing Teacher Attention to Student Thinking: A Role for Epistemological Messages

ERIC Educational Resources Information Center

Russ, Rosemary S.

2018-01-01

Although research and policy suggest science and mathematics teachers should attend to their student's thinking during instruction, our field has inadequately defined what that means in relation to our ultimate goals for the practice. Here I present a theoretical argument that, in making their definitions, researchers should leverage the ways…

Technology, the Columbus Effect, and the Third Revolution in Learning

DTIC Science & Technology

2001-03-01

comprehension-fostering and comprehension-monitoring activities. Cognition and Instruction , 1, 117–-175. Rogoff, B. (1990). Apprenticeship in thinking ...elementary school mathematics (Suppes, Fletcher, and Zanotti, 1975). Instructional approaches used in these early programs required computers that cost $2–3...supported by considerations of pace: the speed with which students learn material and reach instructional objectives. Easily adjusted pacing is a

Instructional Objectives for a Junior College Course in Introduction to Mathematical Thinking.

ERIC Educational Resources Information Center

Starkweather, Ann, Comp.

These instructional objectives have been selected from materials submitted to the Curriculum Laboratory of the Graduate School of Education at UCLA. Arranged by major course goals, these objectives are offered simply as samples that may be used where they correspond to the skills, abilities, and attitudes instructors want their students to…

Mathematics Instruction and the Common Core: Where Do We Go from Here? Q&A with William Schmidt, Ph.D. REL Mid-Atlantic Webinar

ERIC Educational Resources Information Center

Regional Educational Laboratory Mid-Atlantic, 2015

2015-01-01

In this webinar, Dr. William Schmidt of Michigan State University discussed helpful instructional tools for promoting the higher order conceptual thinking found in the Common Core Standards. The PowerPoint presentation and webinar recording are also available.

Teaching Mathematics by Comparison: Analog Visibility as a Double-Edged Sword

ERIC Educational Resources Information Center

Begolli, Kreshnik Nasi; Richland, Lindsey Engle

2016-01-01

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or…

Transposing reform pedagogy into new contexts: complex instruction in remote Australia

NASA Astrophysics Data System (ADS)

Sullivan, Peter; Jorgensen, Robyn; Boaler, Jo; Lerman, Steve

2013-03-01

This article draws on the outcomes of a 4-year project where complex instruction was used as the basis for a reform in mathematics teaching in remote Aboriginal communities in Australia. The article describes the overall project in terms of the goals and aspirations for learning mathematics among remote Indigenous Australians. Knowing that the approach had been successful in a diverse setting in California, the project team sought to implement and evaluate the possibilities of such reform in a context in which the need for a culturally responsive pedagogy was critical. Elements of complex instruction offered considerable possibilities in aligning with the cultures of the remote communities, but with recognition of the possibility that some elements may not be workable in these contexts. Complex instruction also valued deep knowledge of mathematics rather than a tokenistic, impoverished mathematics. The strategies within complex instruction allowed for mathematical and cultural scaffolding to promote deep learning in mathematics. Such an approach was in line with current reforms in Indigenous education in Australia where there are high expectations of learners in order to break away from the deficit thinking that has permeated much education in remote Australia. The overall intent is to demonstrate what pedagogies are possible within the constraints of the remote context.

Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education

ERIC Educational Resources Information Center

Fonger, Nicole L.; Stephens, Ana; Blanton, Maria; Isler, Isil; Knuth, Eric; Gardiner, Angela Murphy

2018-01-01

Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked…

The role of local theories: teacher knowledge and its impact on engaging students with challenging tasks

NASA Astrophysics Data System (ADS)

Choppin, Jeffrey

2011-03-01

This study explores the extent to which a teacher elicited students' mathematical reasoning through the use of challenging tasks and the role her knowledge played in doing so. I characterised the teacher's knowledge in terms of a local theory of instruction, a form of pedagogical content knowledge that involves an empirically tested set of conjectures situated within a mathematical domain. Video data were collected and analysed and used to stimulate the teacher's reflection on her enactments of an instructional sequence. The teacher, chosen for how she consistently elicited student reasoning, showed evidence of possessing a local theory in that she articulated the ways student thinking developed over time, the processes by which that thinking developed, and the resources that facilitated the development of student thinking. Her knowledge informed how she revised and enacted challenging tasks in ways that elicited and refined student thinking around integer addition and subtraction. Furthermore, her knowledge and practices emphasised the progressive formalisation of students' ideas as a key learning process. A key implication of this study is that teachers are able to develop robust knowledge from enacting challenging tasks, knowledge that organises how they elicit and refine student reasoning from those tasks.

Professional development in statistics, technology, and cognitively demanding tasks: classroom implementation and obstacles

NASA Astrophysics Data System (ADS)

Foley, Gregory D.; Bakr Khoshaim, Heba; Alsaeed, Maha; Nihan Er, S.

2012-03-01

Attending professional development programmes can support teachers in applying new strategies for teaching mathematics and statistics. This study investigated (a) the extent to which the participants in a professional development programme subsequently used the techniques they had learned when teaching mathematics and statistics and (b) the obstacles they encountered in enacting cognitively demanding instructional tasks in their classrooms. The programme created an intellectual learning community among the participants and helped them gain confidence as teachers of statistics, and the students of participating teachers became actively engaged in deep mathematical thinking. The participants indicated, however, that time, availability of resources and students' prior achievement critically affected the implementation of cognitively demanding instructional activities.

Using Inquiry-Based Instructional Strategies to Increase Student Achievement in 3rd Grade Social Studies

ERIC Educational Resources Information Center

McRae-Jones, Wanda Joycelyn

2017-01-01

21st Century skills such as critical-thinking and problem-solving skills are very important when it comes to Science Technology Engineering and Mathematics or STEM. But those same skills should be integrated in social studies. The impact of students' learning in social studies as a result of implementing inquiry-based instructional strategies was…

Journeys of Transformation: A Statewide Effort by Mathematics and Science Professors To Improve Student Understanding. Case Reports from Participants in the Maryland Collaborative for Teacher Preparation.

ERIC Educational Resources Information Center

Gardner, Maureen B., Ed.

This document presents the Maryland Collaborative for Teacher Preparation (MCTP) faculty's reviews on instructional issues of different disciplines. Contents include: (1) "The Maryland Collaborative for Teacher Preparation"; (2) "Guiding Principles: New Thinking in Mathematics and Science Teaching"; (3) "Introduction: Parallel Journeys of Risk and…

A preliminary study on the integral relationship between critical thinking and mathematical thinking among practicing civil engineers

NASA Astrophysics Data System (ADS)

Osman, Sharifah; Mohammad, Shahrin; Abu, Mohd Salleh

2015-05-01

Mathematics and engineering are inexorably and significantly linked and essentially required in analyzing and accessing thought to make good judgment when dealing in complex and varied engineering problems. A study in the current engineering education curriculum to explore how the critical thinking and mathematical thinking relates to one another, is therefore timely crucial. Unfortunately, there is not much information available explicating about the link. This paper aims to report findings of a critical review as well as to provide brief description of an on-going research aimed to investigate the dispositions of critical thinking and the relationship and integration between critical thinking and mathematical thinking during the execution of civil engineering tasks. The first part of the paper reports an in-depth review on these matters based on rather limited resources. The review showed a considerable form of congruency between these two perspectives of thinking, with some prevalent trends of engineering workplace tasks, problems and challenges. The second part describes an on-going research to be conducted by the researcher to investigate rigorously the relationship and integration between these two types of thinking within the perspective of civil engineering tasks. A reasonably close non-participant observations and semi-structured interviews will be executed for the pilot and main stages of the study. The data will be analyzed using constant comparative analysis in which the grounded theory methodology will be adopted. The findings will serve as a useful grounding for constructing a substantive theory revealing the integral relationship between critical thinking and mathematical thinking in the real civil engineering practice context. The substantive theory, from an angle of view, is expected to contribute some additional useful information to the engineering program outcomes and engineering education instructions, aligns with the expectations of engineering program outcomes set by the Engineering Accreditation Council.

Cognitive Psychology and Design Paradigms in the Development of Multimedia Courseware

DTIC Science & Technology

1993-09-01

Cognitive Apprenticeship : Teaching the Crafts of Reading, Writing, and Mathematics ". In Resnick, Lauren B. (Editor) Knowing, Learning , and Instruction , pp... thinking are cognitive processes the designers of interactive learning systems must consider the connection between cognition and the ability of an...should be based on instructional design theory, human factors, and cognitive learning theories. If these elements are not included in a

Teachers' Understanding of Algebraic Generalization

NASA Astrophysics Data System (ADS)

Hawthorne, Casey Wayne

Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby teachers respond to and build upon the ideas that arise from students' explorations of these activities. Although more and more teachers are engaging their students in such generalizing tasks, little is known about teachers' understanding of generalization and their understanding of students' mathematical thinking in this domain. In this work, I addressed this gap, exploring the understanding of algebraic generalization of 4 exemplary 8th-grade teachers from multiple perspectives. A significant feature of this investigation is an examination of teachers' understanding of the generalization process, including the use of algebraic symbols. The research consisted of two phases. Phase I was an examination of the teachers' understandings of the underlying quantities and quantitative relationships represented by algebraic notation. In Phase II, I observed the instruction of 2 of these teachers. Using the lens of professional noticing of students' mathematical thinking, I explored the teachers' enacted knowledge of algebraic generalization, characterizing how it supported them to effectively respond to the needs and queries of their students. Results indicated that teachers predominantly see these figural patterns as enrichment activities, disconnected from course content. Furthermore, in my analysis, I identified conceptual difficulties teachers experienced when solving generalization tasks, in particular, connecting multiple symbolic representations with the quantities in the figures. Moreover, while the teachers strived to overcome the challenges of connecting different representations, they invoked both productive and unproductive conceptualizations of the symbols. Finally, by comparing two teachers' understandings of student thinking in the classroom, I developed an instructional trajectory to describe steps along students' generalization processes. This emergent framework serves as an instructional tool for teachers' use in identifying significant connections in supporting students to develop understanding of algebraic symbols as representations that communicate the quantities perceived in the figure.

Lily Pad Doubling: Proportional Reasoning Development

ERIC Educational Resources Information Center

Robichaux-Davis, Rebecca R.

2017-01-01

Progressing from additive to multiplicative thinking is critical for the development of middle school students' proportional reasoning abilities. Yet, many middle school mathematics teachers lack a thorough understanding of additive versus multiplicative situations. This article describes a sequence of instructional activities used to develop the…

Performance-based classrooms: A case study of two elementary teachers of mathematics and science

NASA Astrophysics Data System (ADS)

Jones, Kenneth W.

This case study depicts how two elementary teachers develop classrooms devoted to performance-based instruction in mathematics and science. The purpose is to develop empirical evidence of classroom practices that leads to a conceptual framework about the nature of performance-based instruction. Performance-based assessment and instruction are defined from the literature to entail involving students in tasks that are complex and engaging, requiring them to apply knowledge and skills in authentic contexts. In elementary mathematics and science, such an approach emphasizes problem solving, exploration, inquiry, and reasoning. The body of the work examines teacher beliefs, curricular orientations, instructional strategies, assessment approaches, management and organizational skills, and interpersonal relationships. The focus throughout is on those aspects that foster student performance in elementary mathematics and science. The resulting framework describes five characteristics that contribute to performance-based classrooms: a caring classroom community, a connectionist learning theory, a thinking and doing curriculum, diverse opportunities for learning, and ongoing assessment, feedback, and adjustment. The conclusion analyzes factors external to the classroom that support or constrain the development of performance-based classrooms and discusses the implications for educational policy and further research.

Higher Order Thinking in the Australian Army Suite of Logistic Officer Courses

DTIC Science & Technology

2006-12-15

normal curriculum. They can target subject-specific learning such as science, mathematics, geography ; or they can be infused across the curriculum by...some form of didactic , explicit, or direct instruction. On the other hand, if the focus is on procedural knowledge, it is likely that modeling and...socialization and the teaching method of cooperative learning. Learning the process of critical thinking might be best facilitated by a combination of didactic

The Expert Mathematician. Revised. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2006

2006-01-01

"The Expert Mathematician" is designed to help middle school students develop the thinking processes for mathematical applications and communication. A three-year program of instruction, "The Expert Mathematician" uses a software and consumable print materials package with 196 lessons that teach the "Logo" programming…

Data Modeling for Preservice Teachers and Everyone Else

ERIC Educational Resources Information Center

Petrosino, Anthony J.; Mann, Michele J.

2018-01-01

Although data modeling, the employment of statistical reasoning for the purpose of investigating questions about the world, is central to both mathematics and science, it is rarely emphasized in K-16 instruction. The current work focuses on developing thinking about data modeling with undergraduates in general and preservice teachers in…

Learning to Think in a Math Lab.

ERIC Educational Resources Information Center

Charbonneau, Manon P.

This document begins with a discussion of the author's approach to instruction in a mathematics laboratory. This discussion includes an enumeration of types of desirable or necessary equipment and advice on the management of a laboratory. The author examines issues related to achievement and readiness for more traditional school experiences in…

Professional Noticing: Learning to Teach Responsively

ERIC Educational Resources Information Center

Thomas, Jonathan; Fisher, Molly H.; Jong, Cindy; Schack, Edna O.; Krause, Lisa R.; Kasten, Sarah

2015-01-01

In the buzzing activity of the mathematics classroom, teaching in a way that effectively responds to and furthers students' thinking can be quite challenging. Given that teachers' instructional decisions will directly influence students' learning, it is extremely important to develop the sorts of practices that lead to productive in-the-moment…

Focus group discussion in mathematical physics learning

NASA Astrophysics Data System (ADS)

Ellianawati; Rudiana, D.; Sabandar, J.; Subali, B.

2018-03-01

The Focus Group Discussion (FGD) activity in Mathematical Physics learning has helped students perform the stages of problem solving reflectively. The FGD implementation was conducted to explore the problems and find the right strategy to improve the students' ability to solve the problem accurately which is one of reflective thinking component that has been difficult to improve. The research method used is descriptive qualitative by using single subject response in Physics student. During the FGD process, one student was observed of her reflective thinking development in solving the physics problem. The strategy chosen in the discussion activity was the Cognitive Apprenticeship-Instruction (CA-I) syntax. Based on the results of this study, it is obtained the information that after going through a series of stages of discussion, the students' reflective thinking skills is increased significantly. The scaffolding stage in the CA-I model plays an important role in the process of solving physics problems accurately. Students are able to recognize and formulate problems by describing problem sketches, identifying the variables involved, applying mathematical equations that accord to physics concepts, executing accurately, and applying evaluation by explaining the solution to various contexts.

The Effects of Schema-Based Instruction on the Proportional Thinking of Students With Mathematics Difficulties With and Without Reading Difficulties.

PubMed

Jitendra, Asha K; Dupuis, Danielle N; Star, Jon R; Rodriguez, Michael C

2016-07-01

This study examined the effect of schema-based instruction (SBI) on the proportional problem-solving performance of students with mathematics difficulties only (MD) and students with mathematics and reading difficulties (MDRD). Specifically, we examined the responsiveness of 260 seventh grade students identified as MD or MDRD to a 6-week treatment (SBI) on measures of proportional problem solving. Results indicated that students in the SBI condition significantly outperformed students in the control condition on a measure of proportional problem solving administered at posttest (g = 0.40) and again 6 weeks later (g = 0.42). The interaction between treatment group and students' difficulty status was not significant, which indicates that SBI was equally effective for both students with MD and those with MDRD. Further analyses revealed that SBI was particularly effective at improving students' performance on items related to percents. Finally, students with MD significantly outperformed students with MDRD on all measures of proportional problem solving. These findings suggest that interventions designed to include effective instructional features (e.g., SBI) promote student understanding of mathematical ideas. © Hammill Institute on Disabilities 2014.

National Science Resources Center Project to Improve Science Teaching in Elementary Schools with Special Emphasis on Department of Defense Dependents Schools and Other Schools Serving Children of Military Personnel

DTIC Science & Technology

1992-10-01

science and mathematics education: • DOD Apprenticeship Programs * DOD Teacher Internship Programs * DOD Partnership Programs * DOD Dependents Schools ...corporate sponsors. curriculum and instruction in school mathematics For further information about the project or for were developed in a comprehensive... students develop critical thinking skills and to enhance their ability to solve problems through hands-on activities. The staff and participants were most

Responsive Teaching from the Inside Out: Teaching Base Ten to Young Children

ERIC Educational Resources Information Center

Empson, Susan B.

2014-01-01

Decision making during instruction that is responsive to children's mathematical thinking is examined reflexively by the researcher in the context of teaching second graders. Focus is on exploring how the research base on learning informs teaching decisions that are oriented to building on children's sound conceptions. The development of four…

GRID[subscript C] Renewable Energy Data Streaming into Classrooms

ERIC Educational Resources Information Center

DeLuca, V. William; Carpenter, Pam; Lari, Nasim

2010-01-01

For years, researchers have shown the value of using real-world data to enhance instruction in mathematics, science, and social studies. In an effort to help develop students' higher-order thinking skills in a data-rich learning environment, Green Research for Incorporating Data in the Classroom (GRID[subscript C]), a National Science…

Differentiating Assessment in Middle and High School Mathematics and Science

ERIC Educational Resources Information Center

Waterman, Sheryn Spencer

2009-01-01

This book by Sheryn Spencer Waterman follows the bestselling "Handbook on Differentiated Instruction for Middle and High Schools." With numerous examples and strategies, it is an all-inclusive manual on assessing student readiness, interests, learning and thinking styles. It includes examples of: (1) Pre-, Formative and Summative assessments; (2)…

Integrating Science and Mathematics Curricula Using Computer Mediated Communications: A Vygotskian Perspective.

ERIC Educational Resources Information Center

Charnitski, Christina Wotell; Harvey, Francis A.

This paper presents the theories of L.S. Vygotsky as a conceptual framework for implementing instruction that supports concept development and promotes higher level thinking skills in students. Three major components (i.e., language, scientific and spontaneous concepts, and the zone of proximal development) of Vygotsky's socio-cultural-historical…

Self-Grading: A Simple Strategy for Formative Assessment in Activity-Based Instruction.

ERIC Educational Resources Information Center

Ulmer, M. B.

This paper discusses the author's personal experiences in developing and implementing a problem-based college mathematics course for liberal arts majors. This project was initiated in response to the realization that most students are dependent on "patterning" learning algorithms and have no expectation that self-initiated thinking is a…

Research and Teaching: WikiED--Using Web 2.0 Tools to Teach Content and Critical Thinking

ERIC Educational Resources Information Center

Frisch, Jennifer K.; Jackson, Paula C.; Murray, Meg C.

2013-01-01

WIKIed Biology is a National Science Foundation Transforming Undergraduate Education in Science, Technology, Engineering, and Mathematics interdisciplinary project in which the authors developed and implemented a model for student centered, inquiry-driven instruction using Web 2.0 technologies to increase inquiry and conceptual understanding in…

Reflections on Language and Mathematics Problem Solving: A Case Study of a Bilingual First-Grade Teacher

ERIC Educational Resources Information Center

Musanti, Sandra I.; Celedon-Pattichis, Sylvia; Marshall, Mary E.

2009-01-01

This case study investigates a professional development initiative in which a first-grade bilingual teacher engages in learning and teaching Cognitively Guided Instruction, a framework for understanding student thinking through context-rich word-problem lessons. The study explores (a) the impact of classroom-based professional development on a…

The Development of Children's Algebraic Thinking: The Impact of a Comprehensive Early Algebra Intervention in Third Grade

ERIC Educational Resources Information Center

Blanton, Maria; Stephens, Ana; Knuth, Eric; Gardiner, Angela Murphy; Isler, Isil; Kim, Jee-Seon

2015-01-01

This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written…

What If Your ABCs Were Your 123s?: Building Connections Between Literacy and Numeracy

ERIC Educational Resources Information Center

Minton, Leslie

2007-01-01

Designed for the primary and elementary levels, this book helps teachers transform the way they think about and teach mathematics. While many teachers feel confident about their preparation and strategic repertoire for literacy instruction, some are less confident about their preparation and content depth for teaching math. This book makes visible…

Grade 11 Students' Interconnected Use of Conceptual Knowledge, Procedural Skills, and Strategic Competence in Algebra: A Mixed Method Study of Error Analysis

ERIC Educational Resources Information Center

Egodawatte, Gunawardena; Stoilescu, Dorian

2015-01-01

The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students' difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly…

Developing geogebra-assisted reciprocal teaching strategy to improve junior high school students’ abstraction ability, lateral thinking and mathematical persistence

NASA Astrophysics Data System (ADS)

Priatna, N.; Martadiputra, B. A. P.; Wibisono, Y.

2018-05-01

The development of science and technology requires reform in the utilization of various resources for mathematics teaching and learning process. One of the efforts that can be made is the implementation of GeoGebra-assisted Reciprocal Teaching strategy in mathematics instruction as an effective strategy in improving students’ cognitive, affective, and psychomotor abilities. This research is intended to implement GeoGebra-assisted Reciprocal Teaching strategy in improving abstraction ability, lateral thinking, and mathematical persistence of junior high school students. It employed quasi-experimental method with non-random pre-test and post-test control design. More specifically, it used the 2x3 factorial design, namely the learning factors that included GeoGebra-assisted Reciprocal Teaching and conventional teaching learning, and levels of early mathematical ability (high, middle, and low). The subjects in this research were the eighth grade students of junior high school, taken with purposive sampling. The results of this research show: Abstraction and lateral abilities of students who were taught with GeoGebra-assisted Reciprocal Teaching strategy were significantly higher than those of students who received conventional learning. Mathematical persistence of students taught with GeoGebra-assisted Reciprocal Teaching strategy was also significantly higher than of those taught with conventional learning.

Mathematization in introductory physics

NASA Astrophysics Data System (ADS)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in doing physics. It contrasts with their more common experience with mathematics as the practice of specified procedures to improve efficiency. This paper describes new curricular materials based on invention instruction provide students with opportunities to generate mathematical relationships in physics, and the paper presents preliminary evidence of the effectiveness of this method with mathematically underprepared engineering students.

Improving students’ mathematical critical thinking through rigorous teaching and learning model with informal argument

NASA Astrophysics Data System (ADS)

Hamid, H.

2018-01-01

The purpose of this study is to analyze an improvement of students’ mathematical critical thinking (CT) ability in Real Analysis course by using Rigorous Teaching and Learning (RTL) model with informal argument. In addition, this research also attempted to understand students’ CT on their initial mathematical ability (IMA). This study was conducted at a private university in academic year 2015/2016. The study employed the quasi-experimental method with pretest-posttest control group design. The participants of the study were 83 students in which 43 students were in the experimental group and 40 students were in the control group. The finding of the study showed that students in experimental group outperformed students in control group on mathematical CT ability based on their IMA (high, medium, low) in learning Real Analysis. In addition, based on medium IMA the improvement of mathematical CT ability of students who were exposed to RTL model with informal argument was greater than that of students who were exposed to CI (conventional instruction). There was also no effect of interaction between RTL model and CI model with both (high, medium, and low) IMA increased mathematical CT ability. Finally, based on (high, medium, and low) IMA there was a significant improvement in the achievement of all indicators of mathematical CT ability of students who were exposed to RTL model with informal argument than that of students who were exposed to CI.

Instructional Quality Features in Videotaped Biology Lessons: Content-Independent Description of Characteristics

NASA Astrophysics Data System (ADS)

Dorfner, Tobias; Förtsch, Christian; Boone, William; Neuhaus, Birgit J.

2017-09-01

A number of studies on single instructional quality features have been reported for mathematics and science instruction. For summarizing single instructional quality features, researchers have created a model of three basic dimensions (classroom management, supportive climate, and cognitive activation) of instructional quality mainly through observing mathematics instruction. Considering this model as valid for all subjects and as usable for describing instruction, we used it in this study which aimed to analyze characteristics of instructional quality in biology lessons of high-achieving and low-achieving classes, independently of content. Therefore, we used the data of three different previous video studies of biology instruction conducted in Germany. From each video study, we selected three high-achieving and three low-achieving classes (N = 18 teachers; 35 videos) for our multiple-case study, in which conspicuous characteristics of instructional quality features were qualitatively identified and qualitatively analyzed. The amount of these characteristics was counted in a quantitative way in all the videos. The characteristics we found could be categorized using the model of three basic dimensions of instructional quality despite some subject-specific differences for biology instruction. Our results revealed that many more characteristics were observable in high-achieving classes than in low-achieving classes. Thus, we believe that this model could be used to describe biology instruction independently of the content. We also make the claims about the qualities for biology instruction—working with concentration in a content-structured environment, getting challenged in higher order thinking, and getting praised for performance—that could have positive influence on students' achievement.

The impact of computer-based versus "traditional" textbook science instruction on selected student learning outcomes

NASA Astrophysics Data System (ADS)

Rothman, Alan H.

This study reports the results of research designed to examine the impact of computer-based science instruction on elementary school level students' science content achievement, their attitude about science learning, their level of critical thinking-inquiry skills, and their level of cognitive and English language development. The study compared these learning outcomes resulting from a computer-based approach compared to the learning outcomes from a traditional, textbook-based approach to science instruction. The computer-based approach was inherent in a curriculum titled The Voyage of the Mimi , published by The Bank Street College Project in Science and Mathematics (1984). The study sample included 209 fifth-grade students enrolled in three schools in a suburban school district. This sample was divided into three groups, each receiving one of the following instructional treatments: (a) Mixed-instruction primarily based on the use of a hardcopy textbook in conjunction with computer-based instructional materials as one component of the science course; (b) Non-Traditional, Technology-Based -instruction fully utilizing computer-based material; and (c) Traditional, Textbook-Based-instruction utilizing only the textbook as the basis for instruction. Pre-test, or pre-treatment, data related to each of the student learning outcomes was collected at the beginning of the school year and post-test data was collected at the end of the school year. Statistical analyses of pre-test data were used as a covariate to account for possible pre-existing differences with regard to the variables examined among the three student groups. This study concluded that non-traditional, computer-based instruction in science significantly improved students' attitudes toward science learning and their level of English language development. Non-significant, positive trends were found for the following student learning outcomes: overall science achievement and development of critical thinking-inquiry skills. These conclusions support the value of a non-traditional, computer-based approach to instruction, such as exemplified by The Voyage of the Mimi curriculum, and a recommendation for reform in science teaching that has recommended the use of computer technology to enhance learning outcomes from science instruction to assist in reversing the trend toward what has been perceived to be relatively poor science performance by American students, as documented by the 1996 Third International Mathematics and Science Study (TIMSS).

Higher-order thinking skill problem on data representation in primary school: A case study

NASA Astrophysics Data System (ADS)

Putri, R. I. I.; Zulkardi, Z.

2018-01-01

This article aimed at reporting research result on a case study of a lesson using a HOTS problem. The task was about data representation using baby growth context. The study used a design research method consisting of three stages: preparing for an experiment, experiment in the classroom (pilot and teaching), and retrospective analysis. Participants were sixth grade students who were learning data representations in a Primary School in Palembang Indonesia. A set of instructional activities were designed using Indonesian version of Realistic Mathematics Education (PMRI) approach. The result showed that students were able to solve the problem and present their solution in front of the classroom. The conclusion indicated that that HOTS problem using the growth of a child as the context could lead students to use their mathematical thinking. During the learning activities along with teacher orchestra’s guidance, and discussion, students were able to solve the problem using line graph although some of them used a bar graph. In the future, teachers are necessary to focus on the role of real-world figure in mathematics learning.

The Effect of Critical Thinking Instruction on Verbal Descriptions of Music

ERIC Educational Resources Information Center

Johnson, Daniel C.

2011-01-01

The purpose of this study was to determine the effect of critical thinking instruction on music listening skills of fifth-grade students as measured by written responses to music listening. The researcher compared instruction that included opportunities for critical thinking (Critical Thinking Instruction, CTI) with parallel instruction without…

The effects of critical thinking instruction on training complex decision making.

PubMed

Helsdingen, Anne S; van den Bosch, Karel; van Gog, Tamara; van Merriënboer, Jeroen J G

2010-08-01

Two field studies assessed the effects of critical thinking instruction on training and transfer of a complex decision-making skill. Critical thinking instruction is based on studies of how experienced decision makers approach complex problems. Participants conducted scenario-based exercises in both simplified (Study I) and high-fidelity (Study 2) training environments. In both studies, half of the participants received instruction in critical thinking. The other half conducted the same exercises but without critical thinking instruction. After the training, test scenarios were administered to both groups. The first study showed that critical thinking instruction enhanced decision outcomes during both training and the test. In the second study, critical thinking instruction benefited both decision outcomes and processes, specifically on the transfer to untrained problems. The results suggest that critical thinking instruction improves decision strategy and enhances understanding of the general principles of the domain. The results of this study warrant the implementation of critical thinking instruction in training programs for professional decision makers that have to operate in complex and highly interactive, dynamic environments.

Noticing numeracy now! Examining changes in preservice teachers' noticing, knowledge, and attitudes

NASA Astrophysics Data System (ADS)

Fisher, Molly H.; Thomas, Jonathan; Schack, Edna O.; Jong, Cindy; Tassell, Janet

2018-06-01

This study examined the impact of an intervention, focused on professional noticing of children's conceptual development in whole number and arithmetic reasoning, on preservice elementary teachers' (PSETs') professional noticing skills, attitudes toward mathematics, and mathematical knowledge for teaching mathematics. A video-based professional noticing module, situated in the pedagogies of practice framework, was used with 224 PSETs from five universities. Comparison data was also collected with similar groups not participating in the instructional module. Through pre- and post-assessments, findings indicated that PSETs can develop sound professional noticing skills as a result of participation in a video-based module. The impact on attitudes toward mathematics was less convincing as significant changes were revealed in intervention as well as comparison groups. We hypothesized the potential for professional noticing of children's mathematical thinking to serve as a mechanism for increasing the capabilities of PSETs to negotiate the complexities of mathematics teaching and learning; however, mathematics knowledge for teaching showed no significant increase for either group.

Investigation of the Effects of Mathematical Thinking States of Form Teachers on Their Mathematics Teaching Anxieties

ERIC Educational Resources Information Center

Yorulmaz, Alper; Altintas, Sedat; Sidekli, Sabri

2017-01-01

The state of mathematical thinking is considered to have an effect on the formation of anxiety regarding teaching mathematics. It is hypothesized that with the formation of mathematical thinking, the anxiety in teachers regarding teaching mathematics will be reduced. Since mathematical thinking is a skill acquired starting from the early years of…

Factors Considered by Elementary Teachers When Developing and Modifying Mathematical Tasks to Support Children's Mathematical Thinking

NASA Astrophysics Data System (ADS)

Fredenberg, Michael Duane

The idea that problems and tasks play a pivotal role in a mathematics lesson has a long standing in mathematics education research. Recent calls for teaching reform appeal for training teachers to better understand how students learn mathematics and to employ students' mathematical thinking as the basis for pedagogy (CCSSM, 2010; NCTM, 2000; NRC 1999). The teaching practices of (a) developing a task for a mathematics lesson and, (b) modifying the task for students while enacting the lesson fit within the scope of supporting students' mathematical thinking. Surprisingly, an extensive search of the literature did not yield any research aimed to identify and refine the constituent parts of the aforementioned teaching practices in the manner called for by Grossman and xiii colleagues (2009). Consequently, my research addresses the two questions: (a) what factors do exemplary elementary teachers consider when developing a task for a mathematics lesson? (b) what factors do they consider when they modify a task for a student when enacting a lesson? I conducted a multiple case study involving three elementary teachers, each with extensive training in the area of Cognitively Guided Instruction (CGI), as well as several years experience teaching mathematics following the principles of CGI (Carpenter et al., 1999). I recorded video of three mathematics lessons with each participant and after each lesson I conducted a semi-structured stimulated recall interview. A subsequent follow-up clinical interview was conducted soon thereafter to further explore the teacher's thoughts (Ginsberg, 1997). In addition, my methodology included interjecting myself at select times during a lesson to ask the teacher to explain her reasoning. Qualitative analysis led to a framework that identified four categories of influencing factors and seven categories of supporting objectives for the development of a task. Subsets of these factors and objectives emerged as particularly relevant when the teachers decided to modify a task. Moreover, relationships between and among the various factors were identified. The emergent framework from this study offers insight into decompositions of the two teaching practices of interest, and, in particular, the utility of the number choices made by the teachers.

The relationships between spatial ability, logical thinking, mathematics performance and kinematics graph interpretation skills of 12th grade physics students

NASA Astrophysics Data System (ADS)

Bektasli, Behzat

Graphs have a broad use in science classrooms, especially in physics. In physics, kinematics is probably the topic for which graphs are most widely used. The participants in this study were from two different grade-12 physics classrooms, advanced placement and calculus-based physics. The main purpose of this study was to search for the relationships between student spatial ability, logical thinking, mathematical achievement, and kinematics graphs interpretation skills. The Purdue Spatial Visualization Test, the Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom observations were made to acquire ideas about classroom environment and instructional techniques. Factor analysis, simple linear correlation, multiple linear regression, and descriptive statistics were used to analyze the quantitative data. Each instrument has two principal components. The selection and calculation of the slope and of the area were the two principal components of TUG-K. MIPT was composed of a component based upon processing text and a second component based upon processing symbolic information. The Purdue Spatial Visualization Test was composed of a component based upon one-step processing and a second component based upon two-step processing of information. Student ability to determine the slope in a kinematics graph was significantly correlated with spatial ability, logical thinking, and mathematics aptitude and achievement. However, student ability to determine the area in a kinematics graph was only significantly correlated with student pre-calculus semester 2 grades. Male students performed significantly better than female students on the slope items of TUG-K. Also, male students performed significantly better than female students on the PSAT mathematics assessment and spatial ability. This study found that students have different levels of spatial ability, logical thinking, and mathematics aptitude and achievement levels. These different levels were related to student learning of kinematics and they need to be considered when kinematics is being taught. It might be easier for students to understand the kinematics graphs if curriculum developers include more activities related to spatial ability and logical thinking.

Characteristic of critical and creative thinking of students of mathematics education study program

NASA Astrophysics Data System (ADS)

Rochmad; Agoestanto, A.; Kharis, M.

2018-03-01

Critical and creative thinking give important role in learning matematics for mathematics education students. This research to explored the characteristic of critical and creative thinking of students of mathematics study program in mathematics department. Critical thinking and creative thinking can be illustrated as two sides of a coin, which one is associated to the other. In elementary linear algebra courses, however, critical thinking can be seen as a foundation to build students’ creative thinking.

Instructional Design Models and Teacher Thinking: Toward a New Conceptual Model for Research and Development.

ERIC Educational Resources Information Center

Moallem, Mahnaz; Earle, Rodney S.

1998-01-01

In an effort to connect current research findings on teacher thinking with components of instructional design models and principles, this article discusses a new contextual model for thinking about teaching and considers the implications of the model for instructional development of research in instructional design and teacher thinking. (Author)

Beyond Critical Thinking Skills: Investigating the Relationship between Critical Thinking Skills and Dispositions through Different Online Instructional Strategies

ERIC Educational Resources Information Center

Yang, Ya-Ting C.; Chou, Heng-An

2008-01-01

The purpose of this study was to investigate (1) the relationship between critical thinking skills (CTS) and critical thinking dispositions (CTD), and (2) the effectiveness of different levels of instructional strategy (asynchronous online discussions (AODs), CTS instruction via AODs, and CTS instruction with CTD cultivation via AODs) in improving…

The Effect of Concept Attainment Model on Mathematically Critical Thinking Ability of The University Students

NASA Astrophysics Data System (ADS)

Angraini, L. M.; Kartasasmita, B.; Dasari, D.

2017-02-01

This study examined the university students’ mathematically critical thinking ability through Concept Attainment Model learning. The Kolmogorov-Smirnov test, Levene test, t test, ANOVA one and two ways were used to analyse the data. The results of this study showed that (1) there is no difference grade on the student’s mathematical critical thinking ability between experimental group and conventional group as a whole, (2) there is no difference on the students’ mathematical critical thinking ability of experimental classes based on their mathematical early ability (3) there is no interaction between the learning that is used with the students’ mathematical early ability on the students’ mathematical critical thinking ability.

Thinking Skills Instruction: Concepts and Techniques. Building Students' Thinking Skills Series.

ERIC Educational Resources Information Center

Heiman, Marcia, Ed.; Slomianko, Joshua, Ed.

This book is a collection of essays on thinking skills instruction and includes the following chapters and their authors: "Encounter with Thinking" (H. Anderson); "Thinking Skills: Neither an Add-on nor a Quick Fix" (A. Costa); "Teaching for Thinking, of Thinking, and about Thinking" (J. McTighe); "Thinking and…

Construction of the mathematical concept of pseudo thinking students

NASA Astrophysics Data System (ADS)

Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.

2018-05-01

Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.

Profile of male-field dependent (FD) prospective teacher's reflective thinking in solving contextual mathematical problem

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

Rigorous Mathematical Thinking Approach to Enhance Students’ Mathematical Creative and Critical Thinking Abilities

NASA Astrophysics Data System (ADS)

Hidayat, D.; Nurlaelah, E.; Dahlan, J. A.

2017-09-01

The ability of mathematical creative and critical thinking are two abilities that need to be developed in the learning of mathematics. Therefore, efforts need to be made in the design of learning that is capable of developing both capabilities. The purpose of this research is to examine the mathematical creative and critical thinking ability of students who get rigorous mathematical thinking (RMT) approach and students who get expository approach. This research was quasi experiment with control group pretest-posttest design. The population were all of students grade 11th in one of the senior high school in Bandung. The result showed that: the achievement of mathematical creative and critical thinking abilities of student who obtain RMT is better than students who obtain expository approach. The use of Psychological tools and mediation with criteria of intentionality, reciprocity, and mediated of meaning on RMT helps students in developing condition in critical and creative processes. This achievement contributes to the development of integrated learning design on students’ critical and creative thinking processes.

A Conceptual Model for the Design and Delivery of Explicit Thinking Skills Instruction

ERIC Educational Resources Information Center

Kassem, Cherrie L.

2005-01-01

Developing student thinking skills is an important goal for most educators. However, due to time constraints and weighty content standards, thinking skills instruction is often embedded in subject matter, implicit and incidental. For best results, thinking skills instruction requires a systematic design and explicit teaching strategies. The…

Extending Students' Mathematical Thinking during Whole-Group Discussions

ERIC Educational Resources Information Center

Cengiz, Nesrin; Kline, Kate; Grant, Theresa J.

2011-01-01

Studies show that extending students' mathematical thinking during whole-group discussions is a challenging undertaking. To better understand what extending student thinking looks like and how teachers' mathematical knowledge for teaching (MKT) supports teachers in their efforts to extend student thinking, the teaching of six experienced…

Conversations about curriculum change: mathematical thinking and team-based learning in a discrete mathematics course

NASA Astrophysics Data System (ADS)

Paterson, Judy; Sneddon, Jamie

2011-10-01

This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused on what he calls the 'unspoken curriculum': mathematical thinking. We consider the ways in which the TBL model promoted and enabled this in the light of literature on mathematical thinking, sense-making and behaviours, and strongly suggest that this approach warrants more attention from the mathematics teaching community. We also discuss shifts in the mathematician's thinking about task construction as he refined the tasks to encourage students to think and behave like mathematicians.

Intuitive vs Analytical Thinking: Four Perspectives

ERIC Educational Resources Information Center

Leron, Uri; Hazzan, Orit

2009-01-01

This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives--mathematics, mathematics education, cognitive psychology, and evolutionary psychology--each offering a different view on mathematical thinking and learning and, in particular, on the…

Explicit Mathematics Instruction: What Teachers Can Do for Teaching Students With Mathematics Difficulties

ERIC Educational Resources Information Center

Doabler, Christian T.; Fien, Hank

2013-01-01

This article describes the essential instructional elements necessary for delivering explicit mathematics instruction to students with mathematics difficulties. Mathematics intervention research indicates that explicit instruction is one of the most effective instructional approaches for teaching students with or at risk for math difficulties.…

Integrating Direct and Inquiry-Based Instruction in the Teaching of Critical Thinking: An Intervention Study

ERIC Educational Resources Information Center

Ku, Kelly Y. L.; Ho, Irene T.; Hau, Kit-Tai; Lai, Eva C. M.

2014-01-01

Critical thinking is a unifying goal of modern education. While past research has mostly examined the efficacy of a single instructional approach to teaching critical thinking, recent literature has begun discussing mixed teaching approaches. The present study examines three modes of instruction, featuring the direct instruction approach and the…

Instructional Design as Critical and Creative Thinking: A Journey through a Jamestown-Era Native American Village

ERIC Educational Resources Information Center

Baum, Liesl M.; Newbill, Phyllis Leary

2010-01-01

The role of critical and creative thinking has been debated within the field of instructional design. Through an instructional design and development project we have identified how critical and creative thinking are essential to the instructional design process. This paper highlights a recent project focused on a virtual Native American village…

Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition

ERIC Educational Resources Information Center

Su, Hui Fang Huang; Ricci, Frederick A.; Mnatsakanian, Mamikon

2016-01-01

A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…

Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)

NASA Astrophysics Data System (ADS)

Winda, A.; Sufyani, P.; Elah, N.

2018-05-01

Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.

Case study of a successful learner's epistemological framings of quantum mechanics

NASA Astrophysics Data System (ADS)

Dini, Vesal; Hammer, David

2017-06-01

Research on student epistemologies in introductory courses has highlighted the importance of understanding physics as "a refinement of everyday thinking" [A. Einstein, J. Franklin Inst. 221, 349 (1936), 10.1016/S0016-0032(36)91047-5]. That view is difficult to sustain in quantum mechanics, for students as for physicists. How might students manage the transition? In this article, we present a case study of a graduate student's approaches and reflections on learning over two semesters of quantum mechanics, based on a series of nine interviews. We recount his explicit grappling with the shift in epistemology from classical to quantum, and we argue that his success in learning largely involved his framing mathematics as expressing physical meaning. At the same time, we show he was not entirely stable in these framings, shifting away from them in particular during his study of scattering. The case speaks to literature on students' epistemologies, with respect to the roles of everyday thinking and mathematics. We discuss what this case suggests for further research, with possible implications for instruction.

The Relationships between Teachers' Instructional Practices and Their Learners' Level of Geometrical Thinking

ERIC Educational Resources Information Center

Bleeker, Cheryl; Stols, Gerrit; Van Putten, Sonja

2013-01-01

This case study describes and investigates the instructional practices of Grades 1 to 5 teachers and the levels of geometry thinking of the learners, according to the Van Hiele model, with a view to determining whether there is a match between the instructional practice and the learners' level of thinking. The instructional practices of the…

EDUCATION ENHANCES THE ACUITY OF THE NON-VERBAL APPROXIMATE NUMBER SYSTEM

PubMed Central

Piazza, Manuela; Pica, Pierre; Izard, Véronique; Spelke, Elizabeth; Dehaene, Stanislas

2015-01-01

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the number of objects in sets with ratio-limited precision. Inter-individual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucu, who have a very restricted numerical lexicon and highly variable access to mathematical education. By comparing Mundurucu subjects with or without access to schooling, we demonstrate that education significantly enhances the acuity with which sets of concrete objects are estimated. These results speak in favor of an important effect of culture and education on basic number perception. We hypothesize that symbolic and non-symbolic numerical thinking mutually enhance one another over the course of mathematics instruction. PMID:23625879

Mathematics lecturing in the digital age

NASA Astrophysics Data System (ADS)

Trenholm, Sven; Alcock, Lara; Robinson, Carol L.

2012-09-01

In this article, we consider the transformation of tertiary mathematics lecture practice. We undertake a focused examination of the related research with two goals in mind. First, we document this research, reviewing the findings of key studies and noting that reflective pieces on individual practice as well as surveys are more prevalent than empirical studies. Second, we investigate issues related to the transformation of lecture practice by the emergence of e-lectures. We discuss the latter in terms of claims about the efficiencies offered by new technologies and contrast these with possible disadvantages in terms of student engagement in a learning community. Overall findings indicate that while survey results appear to trumpet the value of e-lecture provision, empirical study results appear to call that value into question. Two explanatory theoretical frameworks are presented. Issues concerning the instructional context (e.g. the nature of mathematical thinking), inherent complexities and recommendations for implementation are discussed.

Mathematics creative thinking levels based on interpersonal intelligence

NASA Astrophysics Data System (ADS)

Kuncorowati, R. H.; Mardiyana; Saputro, D. R. S.

2017-12-01

Creative thinking ability was one of student’s ability to determine various alternative solutions toward mathematics problem. One of indicators related to creative thinking ability was interpersonal intelligence. Student’s interpersonal intelligence would influence to student’s creativity. This research aimed to analyze creative thinking ability level of junior high school students in Karanganyar using descriptive method. Data was collected by test, questionnaire, interview, and documentation. The result showed that students with high interpersonal intelligence achieved third and fourth level in creative thinking ability. Students with moderate interpersonal intelligence achieved second level in creative thinking ability and students with low interpersonal intelligence achieved first and zero level in creative thinking ability. Hence, students with high, moderate, and low interpersonal intelligence could solve mathematics problem based on their mathematics creative thinking ability.

An Analysis of the Reasoning Skills of Pre-Service Teachers in the Context of Mathematical Thinking

ERIC Educational Resources Information Center

Yavuz Mumcu, Hayal; Aktürk, Tolga

2017-01-01

The aim of this study is to address and analyse pre-service teachers' mathematical reasoning skills in relation to mathematical thinking processes. For these purposes, pre-service teachers' mathematical reasoning skills namely generalising/abstraction/modelling, ratiocination, development and creative thinking skills and the relationships among…

Holistic School Leadership: Systems Thinking as an Instructional Leadership Enabler

ERIC Educational Resources Information Center

Shaked, Haim; Schechter, Chen

2016-01-01

As instructional leadership involves attempts to understand and improve complex systems, this study explored principals' perceptions regarding possible contributions of systems thinking to instructional leadership. Based on a qualitative analysis, systems thinking was perceived by middle and high school principals to contribute to the following…

Critical Thinking and Online Supplemental Instruction: A Case Study

ERIC Educational Resources Information Center

Shaw, Cassandra S.; Holmes, Karen E.

2014-01-01

A wealth of research is available regarding supplemental instruction; however, a dearth exists regarding online supplemental instruction and critical thinking. This case study explored what was assumed to be known of critical thinking and investigated the extent to which critical thought was promoted within a university's online supplemental…

Scrutiny of the Bounty or Teaching Critical Thinking in

ERIC Educational Resources Information Center

Cash, D. Michele

This paper, presented at the Indiana Library Association Meeting, discusses critical thinking in general terms and then briefly discusses why it is important to include critical thinking skills in bibliographic instruction sessions at the higher education level. A discussion of the instructional design of bibliographic instruction in relation to…

Mathematics in Finance and Economics: Importance of Teaching Higher Order Mathematical Thinking Skills in Finance

ERIC Educational Resources Information Center

Tularam, Gurudeo Anand

2013-01-01

This paper addresses the importance of teaching mathematics in business and finance schools of tertiary institutions of Australia. The paper explores the nature of thinking and reasoning required for advancement financial or economic studies involves the use of higher order thinking and creativity skills (HOTS) for teaching in mathematics classes.…

Preschoolers' Thinking during Block Play

ERIC Educational Resources Information Center

Piccolo, Diana L.; Test, Joan

2010-01-01

Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages…

Investigating and analyzing prospective teacher's reflective thinking in solving mathematical problem: A case study of female-field dependent (FD) prospective teacher

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-05-01

In the last few years, reflective thinking becomes very popular term in the world of education, especially in professional education of teachers. One of goals of the educational personnel and teacher institutions create responsible prospective teachers and they are able reflective thinking. Reflective thinking is a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. Reflective thinking can be applied in mathematics becauseby reflective thinking, students can improve theircuriosity to solve mathematical problem. In solving mathematical problem is assumed that cognitive style has an impact on prospective teacher's mental activity. As a consequence, reflective thinking and cognitive style are important things in solving mathematical problem. The subject, in this research paper, isa female-prospective teacher who has fielddependent cognitive style. The purpose of this research paperis to investigate the ability of prospective teachers' reflective thinking in solving mathematical problem. This research paper is a descriptive by using qualitativeapproach. To analyze the data related to prospectiveteacher's reflective thinking in solving contextual mathematicalproblem, the researchers focus in four main categories which describe prospective teacher's activities in using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

Creative Thinking Ability to Increase Student Mathematical of Junior High School by Applying Models Numbered Heads Together

ERIC Educational Resources Information Center

Lince, Ranak

2016-01-01

Mathematical ability of students creative thinking is a component that must be mastered by the student. Mathematical creative thinking plays an important role, both in solving the problem and well, even in high school students. Therefore, efforts are needed to convey ideas in mathematics. But the reality is not yet developed the ability to…

Authentic Instruction for 21st Century Learning: Higher Order Thinking in an Inclusive School

ERIC Educational Resources Information Center

Preus, Betty

2012-01-01

The author studied a public junior high school identified as successfully implementing authentic instruction. Such instruction emphasizes higher order thinking, deep knowledge, substantive conversation, and value beyond school. To determine in what ways higher order thinking was fostered both for students with and without disabilities, the author…

Teaching by Open-Approach Method in Japanese Mathematics Classroom.

ERIC Educational Resources Information Center

Nohda, Nobuhiko

Mathematics educators in Japan have traditionally emphasized mathematical perspectives in research and practice. This paper features an account of changes in mathematics education in Japan that focus on the possibilities of individual students as well as their mathematical ways of thinking. Students' mathematical thinking, mathematical…

SPELT (Strategies Program for Effective Learning/Thinking): A Description and Analysis of Instructional Procedures.

ERIC Educational Resources Information Center

Peat, D.; And Others

1989-01-01

Describes an instructional model, Strategies Program for Effective Learning/Thinking (SPELT), that was developed to translate cognitive psychological theory and research into a practical instructional program. The extent to which SPELT conforms to current instructional design principles is examined, and macro versus micro instructional sequencing…

Advanced Mathematical Thinking

ERIC Educational Resources Information Center

Dubinsky, Ed; McDonald, Michael A.; Edwards, Barbara S.

2005-01-01

In this article we propose the following definition for advanced mathematical thinking: Thinking that requires deductive and rigorous reasoning about mathematical notions that are not entirely accessible to us through our five senses. We argue that this definition is not necessarily tied to a particular kind of educational experience; nor is it…

Refractive Thinking Profile In Solving Mathematical Problem Reviewed from Students Math Capability

NASA Astrophysics Data System (ADS)

Maslukha, M.; Lukito, A.; Ekawati, R.

2018-01-01

Refraction is a mental activity experienced by a person to make a decision through reflective thinking and critical thinking. Differences in mathematical capability have an influence on the difference of student’s refractive thinking processes in solving math problems. This descriptive research aims to generate a picture of refractive thinking of students in solving mathematical problems in terms of students’ math skill. Subjects in this study consisted of three students, namely students with high, medium, and low math skills based on mathematics capability test. Data collection methods used are test-based methods and interviews. After collected data is analyzed through three stages that are, condensing and displaying data, data display, and drawing and verifying conclusion. Results showed refractive thinking profiles of three subjects is different. This difference occurs at the planning and execution stage of the problem. This difference is influenced by mathematical capability and experience of each subject.

Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication

ERIC Educational Resources Information Center

Kaya, Defne; Aydin, Hasan

2016-01-01

Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…

The Influence of Building Block Play on Mathematics Achievement and Logical and Divergent Thinking in Italian Primary School Mathematics Classes

ERIC Educational Resources Information Center

Pirrone, Concetta; Tienken, Christopher H.; Pagano, Tatiana; Di Nuovo, Santo

2018-01-01

In an experimental study to explain the effect of structured Building Block Play with LEGO™ bricks on 6-year-old student mathematics achievement and in the areas of logical thinking, divergent thinking, nonverbal reasoning, and mental imagery, students in the experimental group scored significantly higher (p = 0.05) in mathematics achievement and…

Mathematical Modeling and Computational Thinking

ERIC Educational Resources Information Center

Sanford, John F.; Naidu, Jaideep T.

2017-01-01

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

Students' Exploratory Thinking about a Nonroutine Calculus Task

ERIC Educational Resources Information Center

Nabb, Keith

2013-01-01

In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…

Unraveling the Effects of Critical Thinking Instructions, Practice, and Self-Explanation on Students' Reasoning Performance

ERIC Educational Resources Information Center

Heijltjes, Anita; van Gog, Tamara; Leppink, Jimmie; Paas, Fred

2015-01-01

Acquisition of critical thinking skills is considered an important goal in higher education, but it is still unclear which specific instructional techniques are effective for fostering it. The main aim of this study was to unravel the impact of critical thinking instructions, practice, and self-explanation prompts during practice, on students'…

Measuring the Mathematical Quality of Instruction

ERIC Educational Resources Information Center

Journal of Mathematics Teacher Education, 2011

2011-01-01

In this article, we describe a framework and instrument for measuring the mathematical quality of mathematics instruction. In describing this framework, we argue for the separation of the "mathematical quality of instruction" (MQI), such as the absence of mathematical errors and the presence of sound mathematical reasoning, from pedagogical…

The Transition to Formal Thinking in Mathematics

ERIC Educational Resources Information Center

Tall, David

2008-01-01

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

The transition to formal thinking in mathematics

NASA Astrophysics Data System (ADS)

Tall, David

2008-09-01

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts towards a formal framework of axiomatic systems and mathematical proof. In this paper, the transition in thinking is formulated within a framework of `three worlds of mathematics'- the `conceptual-embodied' world based on perception, action and thought experiment, the `proceptual-symbolic' world of calculation and algebraic manipulation compressing processes such as counting into concepts such as number, and the `axiomatic-formal' world of set-theoretic concept definitions and mathematical proof. Each `world' has its own sequence of development and its own forms of proof that may be blended together to give a rich variety of ways of thinking mathematically. This reveals mathematical thinking as a blend of differing knowledge structures; for instance, the real numbers blend together the embodied number line, symbolic decimal arithmetic and the formal theory of a complete ordered field. Theoretical constructs are introduced to describe how genetic structures set before birth enable the development of mathematical thinking, and how experiences that the individual has met before affect their personal growth. These constructs are used to consider how students negotiate the transition from school to university mathematics as embodiment and symbolism are blended with formalism. At a higher level, structure theorems proved in axiomatic theories link back to more sophisticated forms of embodiment and symbolism, revealing the intimate relationship between the three worlds.

Promoting Scientific Thinking and Conceptual Change about Alternative Explanations of Climate Change and Other Controversial Socio-scientific Topics

NASA Astrophysics Data System (ADS)

Lombardi, D.; Sinatra, G. M.

2013-12-01

Critical evaluation and plausibility reappraisal of scientific explanations have been underemphasized in many science classrooms (NRC, 2012). Deep science learning demands that students increase their ability to critically evaluate the quality of scientific knowledge, weigh alternative explanations, and explicitly reappraise their plausibility judgments. Therefore, this lack of instruction about critical evaluation and plausibility reappraisal has, in part, contributed to diminished understanding about complex and controversial topics, such as global climate change. The Model-Evidence Link (MEL) diagram (originally developed by researchers at Rutgers University under an NSF-supported project; Chinn & Buckland, 2012) is an instructional scaffold that promotes students to critically evaluate alternative explanations. We recently developed a climate change MEL and found that the students who used the MEL experienced a significant shift in their plausibility judgments toward the scientifically accepted model of human-induced climate change. Using the MEL for instruction also resulted in conceptual change about the causes of global warming that reflected greater understanding of fundamental scientific principles. Furthermore, students sustained this conceptual change six months after MEL instruction (Lombardi, Sinatra, & Nussbaum, 2013). This presentation will discuss recent educational research that supports use of the MEL to promote critical evaluation, plausibility reappraisal, and conceptual change, and also, how the MEL may be particularly effective for learning about global climate change and other socio-scientific topics. Such instruction to develop these fundamental thinking skills (e.g., critical evaluation and plausibility reappraisal) is demanded by both the Next Generation Science Standards (Achieve, 2013) and the Common Core State Standards for English Language Arts and Mathematics (CCSS Initiative-ELA, 2010; CCSS Initiative-Math, 2010), as well as a society that is equipped to deal with challenges in a way that is beneficial to our national and global community.

Instructional Systems Design and Preservice Teachers' Processes of Thinking, Teaching and Planning: What Do They Learn and How Do They Change?

ERIC Educational Resources Information Center

Moallem, Mahnaz; Applefield, James

This study explored the development and processes of thinking, planning, and decision making of two preservice teachers as they progressed through their teacher education program. The effects of training in the systems approach on two preservice teachers' thinking about instruction and on their actual instructional planning documents were…

Integrating E-Learning into the Direct-Instruction Model to Enhance the Effectiveness of Critical-Thinking Instruction

ERIC Educational Resources Information Center

Yeh, Yu-Chu

2009-01-01

The "Direct-instruction Model" favors the use of teacher explanations and modeling combined with student practice and feedback to teach thinking skills. Using this paradigm, this study incorporates e-learning during an 18-week experimental instruction period that includes 48 preservice teachers. The instructional design in this study emphasizes…

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

ERIC Educational Resources Information Center

Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

2016-01-01

This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

Middle School Mathematics Instruction in Instructionally Focused Urban Districts

ERIC Educational Resources Information Center

Boston, Melissa D.; Wilhelm, Anne Garrison

2017-01-01

Direct assessments of instructional practice (e.g., classroom observations) are necessary to identify and eliminate opportunity gaps in students' learning of mathematics. This study examined 114 middle school mathematics classrooms in four instructionally focused urban districts. Results from the Instructional Quality Assessment identified high…

Teachers' Integration of Scientific and Engineering Practices in Primary Classrooms

NASA Astrophysics Data System (ADS)

Merritt, Eileen G.; Chiu, Jennie; Peters-Burton, Erin; Bell, Randy

2017-06-01

The Next-Generation Science Standards (NGSS) challenge primary teachers and students to work and think like scientists and engineers as they strive to understand complex concepts. Teachers and teacher educators can leverage what is already known about inquiry teaching as they plan instruction to help students meet the new standards. This cross-case analysis of a multiple case study examined teacher practices in the context of a semester-long professional development course for elementary teachers. We reviewed lessons and teacher reflections, examining how kindergarten and first grade teachers incorporated NGSS scientific and engineering practices during inquiry-based instruction. We found that most of the teachers worked with their students on asking questions; planning and carrying out investigations; analyzing and interpreting data, using mathematics and computational thinking; and obtaining, evaluating and communicating information. Teachers faced challenges in supporting students in developing their own questions that could be investigated and using data collection strategies that aligned with students' development of number sense concepts. Also, some teachers overemphasized the scientific method and lacked clarity in how they elicited and responded to student predictions. Discussion focuses on teacher supports that will be needed as states transition to NGSS.

Instructional Designers as Reflective Practitioners: Developing Professional Identity through Reflection

ERIC Educational Resources Information Center

Tracey, Monica W.; Hutchinson, Alisa; Grzebyk, Tamme Quinn

2014-01-01

As the design thinking approach becomes more established in the instructional design (ID) discourse, the field will have to reconsider the professional identity of instructional designers. Rather than passively following models or processes, a professional identity rooted in design thinking calls for instructional designers to be dynamic agents of…

Implementing a reform-oriented pedagogy: challenges for novice secondary mathematics teachers

NASA Astrophysics Data System (ADS)

Lewis, Gary M.

2014-06-01

Novice secondary mathematics teachers attempting teaching consonant with the National Council of Teachers of Mathematics (1991, 2007) Professional Standards for Teaching Mathematics experience many stresses related to their attempts at student-centered instruction; prominent among those were novices' challenges when orchestrating whole-class mathematical discussions with students taking a central, substantive role. During such discussions, students offer conjectures, ideas, and solutions and use mathematical argumentation and verification processes. Such teaching can create uncertainty and stress as teachers occupy a revised teaching role. They avoid evaluating student ideas during class; instead, they ask questions to move students' thinking forward, pose problems that deepen students' mathematical understanding, and choose between competing directions the discussion may take. Ultimately, teachers decide whether to continue pursuing such teaching goals or revert back to more familiar, teacher-centered methods. Supportive networks showed promise at helping novices navigate their first few years of teaching; organized networks helped novices meet their teaching goals while limiting the impact of their challenges on their well-being and teaching goals. The results of this study may inform teacher educators, administrators, and colleagues on how to support novices in pursuing teaching better aligned with novices' teaching ideals and reformer's visions.

Examining the Association between Explicit Mathematics Instruction and Student Mathematics Achievement

ERIC Educational Resources Information Center

Doabler, Christian T.; Baker, Scott K.; Kosty, Derek B.; Smolkowski, Keith; Clarke, Ben; Miller, Saralyn J.; Fien, Hank

2015-01-01

Explicit instruction is a systematic instructional approach that facilitates frequent and meaningful instructional interactions between teachers and students around critical academic content. This study examined the relationship between student mathematics outcomes and the rate and quality of explicit instructional interactions that occur during…

Improving Student Critical Thinking and Perceptions of Critical Thinking through Direct Instruction in Rhetorical Analysis

ERIC Educational Resources Information Center

McGuire, Lauren A.

2010-01-01

This study investigated the effect of direct instruction in rhetorical analysis on students' critical thinking abilities, including knowledge, skills, and dispositions. The researcher investigated student perceptions of the effectiveness of argument mapping; Thinker's Guides, based on Paul's model of critical thinking; and Socratic questioning.…

Pedagogy for Developing Critical Thinking in Adolescents: Explicit Instruction Produces Greatest Gains

ERIC Educational Resources Information Center

Marin, Lisa M.; Halpern, Diane F.

2011-01-01

Although the development and transfer of critical thinking skills are recognized as primary goals for education, there is little empirical evidence to help educators decide how to teach in ways that enhance critical thinking. In two studies, we compared explicit and imbedded instructional modes and assessed critical thinking with the Halpern…

Reflection as a Means of Developing Expertise in Problem Solving, Decision Making, and Complex Thinking of Designers.

ERIC Educational Resources Information Center

Moallem, Mahnaz

This paper focuses on reflection and reflective thinking as a means of developing expertise in instructional designers. The need for the reflective instructional designer is discussed, and reflective thinking is examined from several perspectives, i.e., controlled thinking, tacit knowledge, epistemic assumption, abductive reasoning, willingness to…

Analysis of critical thinking ability of VII grade students based on the mathematical anxiety level through learning cycle 7E model

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Widyaningsih, E.; Waluya, S. B.; Kurniasih, A. W.

2018-03-01

This study aims to know mastery learning of students’ critical thinking ability with learning cycle 7E, determine whether the critical thinking ability of the students with learning cycle 7E is better than students’ critical thinking ability with expository model, and describe the students’ critical thinking phases based on the mathematical anxiety level. The method is mixed method with concurrent embedded. The population is VII grade students of SMP Negeri 3 Kebumen academic year 2016/2017. Subjects are determined by purposive sampling, selected two students from each level of mathematical anxiety. Data collection techniques include test, questionnaire, interview, and documentation. Quantitative data analysis techniques include mean test, proportion test, difference test of two means, difference test of two proportions and for qualitative data used Miles and Huberman model. The results show that: (1) students’ critical thinking ability with learning cycle 7E achieve mastery learning; (2) students’ critical thinking ability with learning cycle 7E is better than students’ critical thinking ability with expository model; (3) description of students’ critical thinking phases based on the mathematical anxiety level that is the lower the mathematical anxiety level, the subjects have been able to fulfil all of the indicators of clarification, assessment, inference, and strategies phases.

Attributes of Instances of Student Mathematical Thinking That Are Worth Building on in Whole-Class Discussion

ERIC Educational Resources Information Center

Van Zoest, Laura R.; Stockero, Shari L.; Leatham, Keith R.; Peterson, Blake E.; Atanga, Napthalin A.; Ochieng, Mary A.

2017-01-01

This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners' understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative…

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

Blurring Boundaries within Mathematics Education: Prospective K-8 Teachers Interrogating Intersectional Identities, Narratives, and Positionings in Out-of-School Contexts

ERIC Educational Resources Information Center

Guzman, Lynette DeAun

2017-01-01

Mathematics teacher noticing as a pedagogical practice--attending to, interpreting, and responding to children's mathematical thinking--is growing within mathematics education communities. Much of the research literature primarily focuses on supporting teacher noticing of children's mathematical thinking within classroom contexts, such as…

Diagnosis and Evaluation in Mathematics Instruction: Making Contact with Students' Mental Representations.

ERIC Educational Resources Information Center

Davis, Robert B.

Research on mathematics instruction is reviewed in order to respond to two questions: (1) Has the influx of talented people who have entered the mathematics instruction field over the last three decades changed anything? and (2) Will any of the work being done actually improve mathematics instruction? The different ways in which parents, students,…

Focusing of Students' Mathematical Thinking

ERIC Educational Resources Information Center

Breyfogle, M. Lynn; Herbel-Eisenmann, Beth A.

2004-01-01

Suggestions and ideas that enable teachers to take a closer look at students' thinking are discussed. A teacher should periodically reflect on his or her own classroom practices in order to increase attention on students' mathematical thinking.

The DREME Network: Research and Interventions in Early Childhood Mathematics.

PubMed

Day-Hess, Crystal; Clements, Douglas H

2017-01-01

The DREME Network was created to advance the field of early mathematics research and improves the opportunities to develop math competencies offered to children birth through age 8 years, with an emphasis on the preschool years. All four main Network projects will have implications for interventions. Section 1 introduces the Network and its four projects. The remainder of the chapter focuses on one of these four projects, Making More of Math (MMM), in depth. MMM is directly developing an intervention for children, based on selecting high-quality instructional activities culled from the burgeoning curriculum resources. We first report a review of 457 activities from 6 research-based curricula, which describes the number of activities by content focus, type (nature), and setting of each activity. Given the interest in higher-order thinking skills and self-regulation, we then identified activities that had the potential to, develop both mathematics and executive function (EF) proficiencies. We rated these, selecting the top 10 for extensive coding by mathematics content and EF processes addressed. We find a wide divergence across curricula in all these categories and provide comprehensive reports for those interested in selecting, using, or developing early mathematics curricula. © 2017 Elsevier Inc. All rights reserved.

The Enhancement of Mathematical Critical Thinking Ability of Aliyah Madrasas Student Model Using Gorontalo by Interactive Learning Setting Cooperative Model

ERIC Educational Resources Information Center

Husnaeni

2016-01-01

Critical thinking ability of students' mathematical is a component that must be mastered by the student. Learn to think critically means using mental processes, such as attention, categorize, selection, and rate/decide. Critical thinking ability in giving proper guidance in thinking and working, and assist in determining the relationship between…

New Directions for Mathematics Instruction. 1989 Yearbook.

ERIC Educational Resources Information Center

Blume, Glendon W., Ed.; Heid, M. Kathleen, Ed.

This yearbook discusses instructional approaches that are consistent with the reformulation of the school mathematics curriculum by the National Council of Teachers of Mathematics (NCTM). Articles included cover: (1) Pennsylvania standards for mathematics programs (including goals, curriculum, instruction, evaluation, teachers, and…

Putting Research into Practice in the Elementary Grades: Readings from Journals of the National Council of Teachers of Mathematics.

ERIC Educational Resources Information Center

Chambers, Donald L., Ed.

This book describes children's mathematical thinking to guide and support teachers in their reflection upon student thinking and teaching and learning. It is organized into five parts: (1) reasoning, student thinking, and invented strategies independent of the mathematics content domain which addresses the role of discourse in helping students…

Exploring Prospective Secondary Mathematics Teachers' Interpretation of Student Thinking through Analysing Students' Work in Modelling

ERIC Educational Resources Information Center

Didis, Makbule Gozde; Erbas, Ayhan Kursat; Cetinkaya, Bulent; Cakiroglu, Erdinc; Alacaci, Cengiz

2016-01-01

Researchers point out the importance of teachers' knowledge of student thinking and the role of examining student work in various contexts to develop a knowledge base regarding students' ways of thinking. This study investigated prospective secondary mathematics teachers' interpretations of students' thinking as manifested in students' work that…

Visible Thinking in High School Mathematics

ERIC Educational Resources Information Center

Sliman, Emily

2013-01-01

If a teacher asked their students what thinking looks like, what would they say? Would they just look at the teacher quizzically? The question is challenging because thinking is largely an invisible endeavor, and developing thoughtful students can be a daunting task. However, the job of mathematics teachers is to develop students who think about…

Leveling Students' Creative Thinking in Solving and Posing Mathematical Problem

ERIC Educational Resources Information Center

Siswono, Tatag Yuli Eko

2010-01-01

Many researchers assume that people are creative, but their degree of creativity is different. The notion of creative thinking level has been discussed .by experts. The perspective of mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking…

An Expert Teacher's Thinking and Teaching and Instructional Design Models and Principles: An Ethnographic Study.

ERIC Educational Resources Information Center

Moallem, Mahnaz

1998-01-01

Examines an expert teacher's thinking and teaching processes in order to link them to instructional-design procedures. Findings suggest that there were fundamental differences between the teacher's thinking and teaching processes and microinstructional design models. (Author/AEF)

A study of rural preschool practitioners' views on young children's mathematical thinking

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Hunting, Robert P.; Mousley, Judith A.; Perry, Bob

2012-03-01

The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian states. The questions focused on five broad themes: children's mathematics learning, support for mathematics teaching, technology and computers, attitudes and feelings, and assessment and record keeping. We review results from the interview data for each of these themes, discuss their importance, and outline recommendations related to teacher education as well as resource development and research.

The Mathematics and Mathematical Thinking of Seamstresses.

ERIC Educational Resources Information Center

Hancock, Sabrina J. C.

This study documents the mathematics practiced by four women in the context of sewing. The study describes the mathematics recognized in the skills, thinking and strategies used by the seamstresses. Through their work, the seamstresses exhibited an understanding of the concepts of angles, direction, parallel, reflection, symmetry, proportion,…

Student’s thinking process in solving word problems in geometry

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Khasanah, V. N.; Usodo, B.; Subanti, S.

2018-05-01

This research aims to find out the thinking process of seventh grade of Junior High School in solve word problem solving of geometry. This research was descriptive qualitative research. The subject of the research was selected based on sex and differences in mathematical ability. Data collection was done based on student’s work test, interview, and observation. The result of the research showed that there was no difference of thinking process between male and female with high mathematical ability, and there were differences of thinking process between male and female with moderate and low mathematical ability. Also, it was found that male with moderate mathematical ability took a long time in the step of making problem solving plans. While female with moderate mathematical ability took a long time in the step of understanding the problems. The importance of knowing the thinking process of students in solving word problem solving were that the teacher knows the difficulties faced by students and to minimize the occurrence of the same error in problem solving. Teacher could prepare the right learning strategies which more appropriate with student’s thinking process.

Documenting and Interpreting Ways to Engage Students in `Thinking Like a Physicist'

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van Zee, Emily; Manogue, Corinne

2010-10-01

The Paradigms in Physics Program at Oregon State University has adapted a variety of interactive pedagogies to engage students in `thinking like a physicist.' Video recordings of class sessions document what the students and instructor say and do. This paper discusses development of narrative interpretations of such videos. Examples are drawn from two detailed narratives of activities during which the main ideas emerged during the wrap-up discussions rather than during the tasks that the students had been doing in their small groups. The goal of these `compare and contrast' wrap-up discussions was to help the students envision connections among geometric and algebraic representations of the mathematics they would be using during the coming weeks of instruction in quantum mechanics. The purpose of the narratives is to provide examples of wrap-up discussions with commentary about ways in which the instructor was choosing to guide this process.

Lower-Order Mathematical Thinking Skills in Finance, from the Viewpoint of Financial Employees in the Iranian Bank of Industry and Mine

ERIC Educational Resources Information Center

Kumleh, Seyedeh Zahra Aboalhasani; Roodposhti, Fereydon Rahnamay; Shahvarani, Ahmad; Lotfi, Farhad Hosseinzadeh

2017-01-01

In this paper, lower-order mathematical thinking skills within finance were studied from the viewpoint of financial employees in the Iranian Bank of Industry and Mine. To conduct this research, a questionnaire was developed after reviewing lower-order mathematical thinking skills in finance. In accordance with the revised Bloom's taxonomy, the…

The Increase of Critical Thinking Skills through Mathematical Investigation Approach

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Sumarna, N.; Wahyudin; Herman, T.

2017-02-01

Some research findings on critical thinking skills of prospective elementary teachers, showed a response that is not optimal. On the other hand, critical thinking skills will lead a student in the process of analysis, evaluation and synthesis in solving a mathematical problem. This study attempts to perform an alternative solution with a focus on mathematics learning conditions that is held in the lecture room through mathematical investigation approach. This research method was Quasi-Experimental design with pre-test post-test design. Data analysis using a mixed method with Embedded design. Subjects were regular students enrolled in 2014 at the study program of education of primary school teachers. The number of research subjects were 111 students consisting of 56 students in the experimental group and 55 students in the control group. The results of the study showed that (1) there is a significant difference in the improvement of critical thinking ability of students who receive learning through mathematical investigation approach when compared with students studying through expository approach, and (2) there is no interaction effect between prior knowledge of mathematics and learning factors (mathematical investigation and expository) to increase of critical thinking skills of students.

Teachers' Experiences with Middle-Level Mathematics Coaches

ERIC Educational Resources Information Center

Frost, Bernard Emmanuel

2013-01-01

Many school districts have provided support to middle school mathematics teachers who face challenges involving delivery of instruction by hiring instructional mathematics coaches. The purpose of this qualitative case study was to explore the experiences between classroom mathematics middle school teachers and their instructional coach, and to…

Equity and Access: All Students Are Mathematical Problem Solvers

ERIC Educational Resources Information Center

Franz, Dana Pompkyl; Ivy, Jessica; McKissick, Bethany R.

2016-01-01

Often mathematical instruction for students with disabilities, especially those with learning disabilities, includes an overabundance of instruction on mathematical computation and does not include high-quality instruction on mathematical reasoning and problem solving. In fact, it is a common misconception that students with learning disabilities…

Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

An investigation of mathematics and science instruction in English and Spanish for English language learners

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Rodriguez-Esquivel, Marina

The contextual demands of language in content area are difficult for ELLS. Content in the native language furthers students' academic development and native language skills, while they are learning English. Content in English integrates pedagogical strategies for English acquisition with subject area instruction. The following models of curriculum content are provided in most Miami Dade County Public Schools: (a) mathematics instruction in the native language with science instruction in English or (b) science instruction in the native language with mathematics instruction in English. The purpose of this study was to investigate which model of instruction is more contextually supportive for mathematics and science achievement. A pretest and posttest, nonequivalent group design was used with 94 fifth grade ELLs who received instruction in curriculum model (a) or (b). This allowed for statistical analysis that detected a difference in the means of .5 standard deviations with a power of .80 at the .05 level of significance. Pretreatment and post-treatment assessments of mathematics, reading, and science achievement were obtained through the administration of Aprenda-Segunda Edicion and the Florida Comprehensive Achievement Test. The results indicated that students receiving mathematics in English and Science in Spanish scored higher on achievement tests in both Mathematics and Science than the students who received Mathematics in Spanish and Science in English. In addition, the mean score of students on the FCAT mathematics examination was higher than their mean score on the FCAT science examination regardless of the language of instruction.

How Much English Language Arts and Mathematics Instruction Do Students Receive? Investigating Variation in Instructional Time

ERIC Educational Resources Information Center

Phelps, Geoffrey; Corey, Douglas; DeMonte, Jenny; Harrison, Delena; Loewenberg Ball, Deborah

2012-01-01

The amount of instruction students receive has long been viewed as a foundational educational resource. This article presents an analysis of the time students spend in elementary English language arts (ELA) and mathematics instruction. In mathematics, the average student received about 140 hr of instruction, but students in the top sixth of…

Developing Contextual Mathematical Thinking Learning Model to Enhance Higher-Order Thinking Ability for Middle School Students

ERIC Educational Resources Information Center

Samo, Damianus D.; Darhim; Kartasasmita, Bana

2017-01-01

The purpose of this research is to develop contextual mathematical thinking learning model which is valid, practical and effective based on the theoretical reviews and its support to enhance higher-order thinking ability. This study is a research and development (R & D) with three main phases: investigation, development, and implementation.…

Level of Student's Creative Thinking in Classroom Mathematics

ERIC Educational Resources Information Center

Siswono, Tatag Yuli Eko

2011-01-01

It is reasonable to assume that people are creative, but the degree of creativity is different. The Idea of the level of student's creative thinking has been expressed by experts, such as Gotoh (2004), and Krulik and Rudnick (1999). The perspective of the mathematics creative thinking refers to a combination of logical and divergent thinking which…

An Analysis of Mathematics Teacher Candidates' Critical Thinking Dispositions and Their Logical Thinking Skills

ERIC Educational Resources Information Center

Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri

2013-01-01

This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…

Forces and Issues Related to Curriculum and Instruction, K-6

ERIC Educational Resources Information Center

DeVault, M. Vere; Weaver, J. Fred

1970-01-01

Traces the development of elementary mathematics curriculum and instruction from colonial times to the present. Each section emphasizes four major issues: Why teach mathematics? What mathematics should be taught? How should the mathematics we teach be organized? How should we organize and implement instruction? Also included are several items…

Preservice Mathematics Teachers' Perceptions of Drama Based Instruction

ERIC Educational Resources Information Center

Bulut, Neslihan

2016-01-01

The purpose of this study was to determine the perceptions of pre-service mathematics teachers related to drama-based instruction. For this purpose, effects of a drama-based mathematics course on senior class pre-service mathematics teachers' knowledge about drama-based instruction and teacher candidates' competencies for developing and…

Effects of Gender-Based Instruction on Fifth Graders' Attitudes toward Mathematics

ERIC Educational Resources Information Center

Oswald, Deborah R.

2009-01-01

Differences in male and female brains may impact the way girls and boys process mathematics and underscores the need for research that examines modification of mathematics instruction according to gender differences. Based in constructivist theory, this mixed-methods study investigated the effect of mathematics instruction modified according to…

The Construction of a Square through Multiple Approaches to Foster Learners' Mathematical Thinking

ERIC Educational Resources Information Center

Reyes-Rodriguez, Aaron; Santos-Trigo, Manuel; Barrera-Mora, Fernando

2017-01-01

The task of constructing a square is used to argue that looking for and pursuing several solution routes is a powerful principle to identify and analyse properties of mathematical objects, to understand problem statements and to engage in mathematical thinking activities. Developing mathematical understanding requires that students delve into…

Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving

ERIC Educational Resources Information Center

Rasiman

2015-01-01

This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…

Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

ERIC Educational Resources Information Center

Bal, Aytgen Pinar; Doganay, Ahmet

2014-01-01

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

Metaphorical Thinking Learning and Junior High School Teachers' Mathematical Questioning Ability

ERIC Educational Resources Information Center

Hendriana, Heris; Rohaeti, Euis Eti; Hidayat, Wahyu

2017-01-01

This control-group posttest-only experimental design study aims to investigate the role of learning that teaches metaphorical thinking in mathematical questioning ability of junior high school teachers. The population of this study was mathematics junior high school teachers in West Java province. The samples were 82 mathematics junior high school…

Analysis of Mathematics Critical Thinking Students in Junior High School Based on Cognitive Style

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Agoestanto, A.; Sukestiyarno, YL; Rochmad

2017-04-01

The purpose of this research was to determine the critical thinking ability of mathematics from junior high school students based on FI and FD cognitive style. Data of this research were taken from students grade VIII at SMPN 2 Ambarawa. The research method used a descriptive qualitative approach. Data was taken with a testing method; the critical thinking was measured with WGCTA which is modified with mathematical problems, the cognitive style was measured with GEFT. The student’s test result was analysed, then four students were selected, the two of them are FI cognitive style, and the others are FD cognitive style, for qualitative analysis. The result showed that the ability of mathematics critical thinking students with FI cognitive style is better than FD cognitive style on the ability of inference, assumption, deduction, and interpretation. While on the aspect of argument evaluation, mathematics critical thinking ability of students with FD cognitive style is a little better than students with FI cognitive style.

Do Instructional Interventions Influence College Students' Critical Thinking Skills? A Meta-Analysis

ERIC Educational Resources Information Center

Niu, Lian; Behar-Horenstein, Linda S.; Garvan, Cyndi W.

2013-01-01

Promoting students' critical thinking skills is an important task of higher education. Colleges and universities have designed various instructional interventions to enhance students' critical thinking skills. Empirical studies have yielded inconsistent results in terms of the effects of such interventions. This meta-analysis presents a synthesis…

Implementation of a School-Wide Approach to Critical Thinking Instruction.

ERIC Educational Resources Information Center

Kassem, Cherrie L.

2000-01-01

To improve students' critical-thinking skills, an interdisciplinary team of educators collaborated with a specialist. The result: a new model for infusing thinking-skills instruction. This paper describes the change process, the CRTA model's evolution, derivation of its acronym, and early qualitative results. (Contains 31 references.) (MLH)

Inhibition and interference in the think/no-think task.

PubMed

Racsmány, Mihály; Conway, Martin A; Keresztes, Attila; Krajcsi, Attila

2012-02-01

Five experiments using the think/no-think (TNT) procedure investigated the effect of the no-think and substitute instructions on cued recall. In Experiment 1, when unrelated A-B paired associates were studied and cued for recall with A items, recall rates were reliably enhanced in the think condition and reliably impaired below baseline in the no-think condition. In Experiments 2 and 5, final recall was cued with B items, leading to reliably higher recall rates, as compared with baseline, in both the think and no-think conditions. This pattern indicates backward priming of no-think items. In Experiments 3 and 4, the no-think instruction was replaced with a thought substitution instruction, and participants were asked to think of another word instead of the studied one when they saw the no-think cued items. As in Experiments 1 and 2, the same amount of forgetting of B items was observed when A items were the cues, but in contrast to Experiment 2, there was no increase in the recall performance of A items when B items were the cues. These results suggest that not thinking of studied items or, alternatively, thinking of a substitute item to avoid a target item may involve different processes: the former featuring inhibition and the latter interference.

Supporting Mathematical Thinking

ERIC Educational Resources Information Center

Houssart, Jenny; Roaf, Caroline; Watson, Anne

2005-01-01

This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…

A Research on Mathematical Thinking Skills: Mathematical Thinking Skills of Athletes in Individual and Team Sports

ERIC Educational Resources Information Center

Onal, Halil; Inan, Mehmet; Bozkurt, Sinan

2017-01-01

The aim of this research is to examine the mathematical thinking skills of licensed athletes engaged in individual and team sports. The research is designed as a survey model. The sample of the research is composed of 59 female and 170 male licensed athletes (n = 229) and (aged 14 to 52) licensed who do the sports of shooting, billiards, archery,…

The Development of Learning Devices Based Guided Discovery Model to Improve Understanding Concept and Critical Thinking Mathematically Ability of Students at Islamic Junior High School of Medan

ERIC Educational Resources Information Center

Yuliani, Kiki; Saragih, Sahat

2015-01-01

The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…

How to begin a new topic in mathematics: does it matter to students' performance in mathematics?

PubMed

Ma, Xin; Papanastasiou, Constantinos

2006-08-01

The authors use Canadian data from the Third International Mathematics and Science Study to examine six instructional methods that mathematics teachers use to introduce new topics in mathematics on performance of eighth-grade students in six mathematical areas (mathematics as a whole, algebra, data analysis, fraction, geometry, and measurement). Results of multilevel analysis with students nested within schools show that the instructional methods of having the teacher explain the rules and definitions and looking at the textbook while the teacher talks about it had little instructional effects on student performance in any mathematical area. In contrast, the instructional method in which teachers try to solve an example related to the new topic was effective in promoting student performance across all mathematical areas.

Analyzing Preservice Mathematics Teachers' Professional Noticing

ERIC Educational Resources Information Center

Amador, Julie M.; Carter, Ingrid; Hudson, Rick A.

2016-01-01

Recent research in mathematics education has highlighted the importance of teachers' abilities to professionally notice students' thinking. This study examined what preservice teachers professionally notice during lesson study to further describe their attention to students' mathematical thinking, their interpretations about students' reasoning,…

Effects of Experiential Learning Approach on Students' Mathematical Creativity among Secondary School Students of Kericho East Sub-County, Kenya

ERIC Educational Resources Information Center

Chesimet, M. C.; Githua, B. N.; Ng'eno, J. K.

2016-01-01

Mathematics is a subject which seeks to understand patterns that permeate both the world around us and the mind within us. There are many ways of thinking and the kind of thinking one learns in mathematics is an ability to handle abstraction and solve problems that require knowledge of mathematics. Mathematical creativity is essential for…

A life skills approach to mathematics instruction: preparing students with learning disabilities for the real-life math demands of adulthood.

PubMed

Patton, J R; Cronin, M E; Bassett, D S; Koppel, A E

1997-01-01

Current mathematics instruction does not address the day-to-day needs of many students with learning disabilities. Although the vast majority of students with learning disabilities are not college bound, much of mathematics instruction provides college preparation. Too often, classes in mathematics ignore the skills needed in home and community and on the job. The present article examines the ways in which general mathematics instruction, focused on daily living skills, can easily be integrated into the classrooms of students with learning disabilities.

Examining Relations between Mathematics Teachers' Instructional Vision and Knowledge and Change in Practice

ERIC Educational Resources Information Center

Munter, Charles; Correnti, Richard

2017-01-01

This article provides a longitudinal examination of how changes in more than 200 middle-grades mathematics teachers' instructional practices related to their (a) mathematical knowledge for teaching (MKT) and (b) instructional vision. Results of this multilevel regression analysis suggest that MKT and instructional vision are related to instruction…

The Efficacy of Sheltered Instruction Observation Protocol (SIOP) in Mathematics Instruction on English Language Learner Students

ERIC Educational Resources Information Center

Vidot, Jose L.

2011-01-01

Studies by the National Association for Educational Progress found that English Language Learner (ELL) students perform poorly compared to other students on standardized mathematics exams. The research problem addressed how Sheltered Instruction Observation Protocol (SIOP) affected the instructional practices of high school mathematics teachers.…

Enhancing Core Mathematics Instruction for Students at Risk for Mathematics Disabilities

ERIC Educational Resources Information Center

Doabler, Christian T.; Cary, Mari Strand; Jungjohann, Kathleen; Clarke, Ben; Fien, Hank; Baker, Scott; Smolkowski, Keith; Chard, David

2012-01-01

This paper presents eight practical guidelines that teachers can use to make core instruction more systematic and explicit for students with or at-risk for mathematics disabilities. In the paper, we use the notion of explicit and systematic instruction as a foundation for intensifying core math instruction. Explicit and systematic core instruction…

Promoting the teaching of critical thinking skills through faculty development.

PubMed

Behar-Horenstein, Linda S; Schneider-Mitchell, Gail; Graff, Randy

2009-06-01

Practical and effective faculty development programs are vital to individual and institutional success. However, there is little evidence that program outcomes result in instructional changes. The purpose of this study was to determine if and how faculty development would enhance participants' use of critical thinking skills in instruction. Seven faculty members from the University of Florida College of Dentistry and one faculty member from another health science college participated in six weekly two-hour faculty development sessions in spring 2007 that focused on enhancing critical thinking skills in instruction. Kaufman's and Rachal's principles of andragogy (adult learning) were used to design the sessions. Participants used learning journals to respond to four instructor-assigned prompts and provided one presentation to peers. With the use of qualitative methods, eight themes emerged across the learning journals: teaching goals, critical thinking, awareness of learners, planned instructional change, teaching efficacy, self-doubt, external challenges, and changes made. Five of eight participants incorporated critical thinking skills into their presentations at a mean level of 2.4 or higher on a 5-point scale using Paul and Elder's behavioral definition of critical thinking skills. Faculty development opportunities that cause participants to reason through learning journals, peer presentations, and group discussion demonstrated the incorporation of critical thinking concepts in 63 percent of this cohort group's presentations, suggesting that if evidence-based pedagogies are followed, instructional changes can result from faculty development.

Instructional Model and Thinking Skill in Chemistry Class

NASA Astrophysics Data System (ADS)

Langkudi, H. H.

2018-02-01

Chemistry course are considered a difficult lesson for students as evidenced by low learning outcomes on daily tests, mid-semester tests as well as final semester tests. This research intended to investigate the effect of instructional model, thinking skill and the interaction of these variables on students’ achievement in chemistry. Experimental method was applying used 2 x 2 factorial design. The results showed that the use of instructional model with thinking skill influences student’s learning outcomes, so that the chemistry teacher is recommended to pay attention to the learning model, and adjusted to the student’s skill thinking on the chemistry material being taught. The conclusion of this research is that discovery model is suitable for students who have formal thinking skill and conventional model is fit for the students that have concrete thinking skill.

Visual Thinking and Gender Differences in High School Calculus

ERIC Educational Resources Information Center

Haciomeroglu, Erhan Selcuk; Chicken, Eric

2012-01-01

This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…

The ubuntu paradigm in curriculum work, language of instruction and assessment

NASA Astrophysics Data System (ADS)

Brock-Utne, Birgit

2016-02-01

This article discusses the concept " ubuntu", an African worldview rooted in the communal character of African life. Some of the same thinking can, however, be found in various Eurasian and Latin-American philosophies. The concept " ubuntu" is also used in language planning: here, the question of language of instruction is discussed through an ubuntu paradigm. The article focuses on policies regarding language in education, both at the micro-level, where translanguaging and code-switching are central, and at the macro-level, where Prestige Planning is discussed. The assessment practices taking place in schools are also looked at through an ubuntu lens. How far is it possible for developing countries to adhere to an education policy based on their own values when they have to participate in tests like Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Assessment (PISA) for Development?

Middle School Mathematics: 2006-07 to 2008-09. Impact Evaluation. E&R Report No. 10.11

ERIC Educational Resources Information Center

Paeplow, Colleen

2010-01-01

In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

Patterns and Punctuation: Learning to Question Language

ERIC Educational Resources Information Center

Schlessman, Elizabeth

2011-01-01

As teachers plan instruction--even instruction about punctuation--they have the opportunity to engage students' minds and create new labels: question-asking, problem-solving. How teachers teach embeds a vision of who they think kids are and what they think kids are capable of. Are they destined for a future of critical thinking, questioning,…

Critical Thinking Handbook: High School. A Guide for Redesigning Instruction.

ERIC Educational Resources Information Center

Paul, Richard; And Others

This handbook, designed to help high school teachers remodel their lesson plans, has one basic objective: to demonstrate that it is possible and practical to integrate instruction for critical thinking into the teaching of all subjects. The handbook discusses the concept of critical thinking and the principles that underlie it and shows how…

From Ability to Action: Designing Instruction for Critical Thinking Dispositions.

ERIC Educational Resources Information Center

Leader, Lars F.; Middleton, James A.

This paper explains the importance of disposition as an essential aspect of critical thinking and suggests how instruction can be designed to promote learners' development of the dispositional side of critical thinking. Topics addressed include: (1) the dispositional bottleneck between opportunity and action, i.e., sensitivity to occasion; (2)…

Higher Order Thinking Skills: Challenging All Students to Achieve

ERIC Educational Resources Information Center

Williams, R. Bruce

2007-01-01

Explicit instruction in thinking skills must be a priority goal of all teachers. In this book, the author presents a framework of the five Rs: Relevancy, Richness, Relatedness, Rigor, and Recursiveness. The framework serves to illuminate instruction in critical and creative thinking skills for K-12 teachers across content areas. Each chapter…

New Teaching Techniques to Improve Critical Thinking. The Diaprove Methodology

ERIC Educational Resources Information Center

Saiz, Carlos; Rivas, Silvia F.

2016-01-01

The objective of this research is to ascertain whether new instructional techniques can improve critical thinking. To achieve this goal, two different instruction techniques (ARDESOS--group 1--and DIAPROVE--group 2--) were studied and a pre-post assessment of critical thinking in various dimensions such as argumentation, inductive reasoning,…

Fostering 21st-Century Evolutionary Reasoning: Teaching Tree Thinking to Introductory Biology Students

PubMed Central

Novick, Laura R.; Catley, Kefyn M.

2016-01-01

The ability to interpret and reason from Tree of Life (ToL) diagrams has become a vital component of science literacy in the 21st century. This article reports on the effectiveness of a research-based curriculum, including an instructional booklet, laboratory, and lectures, to teach the fundamentals of such tree thinking in an introductory biology class for science majors. We present the results of a study involving 117 undergraduates who received either our new research-based tree-thinking curriculum or business-as-usual instruction. We found greater gains in tree-thinking abilities for the experimental instruction group than for the business-as-usual group, as measured by performance on our novel assessment instrument. This was a medium size effect. These gains were observed on an unannounced test that was administered ∼5–6 weeks after the primary instruction in tree thinking. The nature of students’ postinstruction difficulties with tree thinking suggests that the critical underlying concept for acquiring expert-level competence in this area is understanding that any specific phylogenetic tree is a subset of the complete, unimaginably large ToL. PMID:27881445

Multiplicative Thinking: Much More than Knowing Multiplication Facts and Procedures

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is accepted as a "big idea" of mathematics that underpins important mathematical concepts such as fraction understanding, proportional reasoning, and algebraic thinking. It is characterised by understandings such as the multiplicative relationship between places in the number system, basic and extended number…

Status Report: Mathematics Curriculum-Development Projects Today

ERIC Educational Resources Information Center

Arithmetic Teacher, 1972

1972-01-01

Brief reports on the Cambridge Conference on School Mathematics, Comprehensive School Mathematics Program, Computer-Assisted Instruction Projects at Stanford, Individually Prescribed Instruction Project, The Madison Project, Mathematics/Science Learning System, MINNEMAST, and School Mathematics Study Group. (MM)

Using assessment to individualize early mathematics instruction.

PubMed

Connor, Carol McDonald; Mazzocco, Michèle M M; Kurz, Terri; Crowe, Elizabeth C; Tighe, Elizabeth L; Wood, Taffeta S; Morrison, Frederick J

2018-02-01

Accumulating evidence suggests that assessment-informed personalized instruction, tailored to students' individual skills and abilities, is more effective than more one-size-fits-all approaches. In this study, we evaluate the efficacy of Individualizing Student Instruction in Mathematics (ISI-Math) compared to Reading (ISI-Reading) where classrooms were randomly assigned to ISI-Math or ISI-Reading. The literature on child characteristics X instruction or skill X treatment interaction effects point to the complexities of tailoring instruction for individual students who present with constellations of skills. Second graders received mathematics instruction in small flexible learning groups based on their assessed learning needs. Results of the study (n=32 teachers, 370 students) revealed significant treatment effects on standardized mathematics assessments. With effect sizes (d) of 0.41-0.60, we show that we can significantly improve 2nd graders' mathematics achievement, including for children living in poverty, by using assessment data to individualize the mathematics instruction they receive. The instructional regime, ISI-Math, was implemented by regular classroom teachers and it led to about a 4-month achievement advantage on standardized mathematics tests when compared to students in control classrooms. These results were realized within one school year. Moreover, treatment effects were the same regardless of school-level poverty and students' gender, initial mathematics or vocabulary scores. Copyright © 2017 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

Mathematics beliefs and instructional strategies in achievement of elementary-school students in Japan: results from the TIMSS 2003 assessment.

PubMed

House, J Daniel

2007-04-01

Recent findings concerning mathematics assessment indicate that students in Japan consistently score above international averages. Researchers have examined specific mathematics beliefs and instructional strategies associated with mathematics achievement for students in Japan. This study examined relationships among self-beliefs, classroom instructional strategies, and mathematics achievement for a large national sample of students (N=4,207) from the TIMSS 2003 international sample of fourth graders in Japan. Several significant relationships between mathematics beliefs and test scores were found; a number of classroom teaching strategies were also significantly associated with test scores. However, multiple regression using the complete set of five mathematics beliefs and five instructional strategies explained only 25.1% of the variance in mathematics achievement test scores.

Students' Thinking and the Depth of the Mathematics Curriculum

ERIC Educational Resources Information Center

Kent, Laura B.

2014-01-01

This article explores the impact of students' thinking centered professional development on mathematics teaching and learning. Purposeful pedagogy and problem posing are examined as mechanisms by which teachers can potentially deepen students' understanding of mathematics. A classroom example comparing student generated strategies versus…

Children's Mathematical Reasoning: Opportunities for Developing Understanding and Creative Thinking

ERIC Educational Resources Information Center

Vale, Colleen; Bragg, Leicha A.; Widjaja, Wanty; Herbert, Sandra; Loong, Esther Yook-Kin

2017-01-01

Reasoning underpins students' mathematical understanding and promotes creative thinking. It is regarded as a key mathematical proficiency. This article discusses the reasoning actions that primary children employed and teachers noticed for the "What else belongs?" task focused on forming and testing conjectures.

Discovery learning model with geogebra assisted for improvement mathematical visual thinking ability

NASA Astrophysics Data System (ADS)

Juandi, D.; Priatna, N.

2018-05-01

The main goal of this study is to improve the mathematical visual thinking ability of high school student through implementation the Discovery Learning Model with Geogebra Assisted. This objective can be achieved through study used quasi-experimental method, with non-random pretest-posttest control design. The sample subject of this research consist of 62 senior school student grade XI in one of school in Bandung district. The required data will be collected through documentation, observation, written tests, interviews, daily journals, and student worksheets. The results of this study are: 1) Improvement students Mathematical Visual Thinking Ability who obtain learning with applied the Discovery Learning Model with Geogebra assisted is significantly higher than students who obtain conventional learning; 2) There is a difference in the improvement of students’ Mathematical Visual Thinking ability between groups based on prior knowledge mathematical abilities (high, medium, and low) who obtained the treatment. 3) The Mathematical Visual Thinking Ability improvement of the high group is significantly higher than in the medium and low groups. 4) The quality of improvement ability of high and low prior knowledge is moderate category, in while the quality of improvement ability in the high category achieved by student with medium prior knowledge.

Critical Thinking Skills of Students through Mathematics Learning with ASSURE Model Assisted by Software Autograph

NASA Astrophysics Data System (ADS)

Kristianti, Y.; Prabawanto, S.; Suhendra, S.

2017-09-01

This study aims to examine the ability of critical thinking and students who attain learning mathematics with learning model ASSURE assisted Autograph software. The design of this study was experimental group with pre-test and post-test control group. The experimental group obtained a mathematics learning with ASSURE-assisted model Autograph software and the control group acquired the mathematics learning with the conventional model. The data are obtained from the research results through critical thinking skills tests. This research was conducted at junior high school level with research population in one of junior high school student in Subang Regency of Lesson Year 2016/2017 and research sample of class VIII student in one of junior high school in Subang Regency for 2 classes. Analysis of research data is administered quantitatively. Quantitative data analysis was performed on the normalized gain level between the two sample groups using a one-way anova test. The results show that mathematics learning with ASSURE assisted model Autograph software can improve the critical thinking ability of junior high school students. Mathematical learning using ASSURE-assisted model Autograph software is significantly better in improving the critical thinking skills of junior high school students compared with conventional models.

Upgrading geometry conceptual understanding and strategic competence through implementing rigorous mathematical thinking (RMT)

NASA Astrophysics Data System (ADS)

Nugraheni, Z.; Budiyono, B.; Slamet, I.

2018-03-01

To reach higher order thinking skill, needed to be mastered the conceptual understanding and strategic competence as they are two basic parts of high order thinking skill (HOTS). RMT is a unique realization of the cognitive conceptual construction approach based on Feurstein with his theory of Mediated Learning Experience (MLE) and Vygotsky’s sociocultural theory. This was quasi-experimental research which compared the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and the control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning model toward conceptual understanding and strategic competence of Junior High School Students. The data was analyzed by using Multivariate Analysis of Variance (MANOVA) and obtained a significant difference between experimental and control class when considered jointly on the mathematics conceptual understanding and strategic competence (shown by Wilk’s Λ = 0.84). Further, by independent t-test is known that there was significant difference between two classes both on mathematical conceptual understanding and strategic competence. By this result is known that Rigorous Mathematical Thinking (RMT) had positive impact toward Mathematics conceptual understanding and strategic competence.

Analysis of creative mathematic thinking ability in problem based learning model based on self-regulation learning

NASA Astrophysics Data System (ADS)

Munahefi, D. N.; Waluya, S. B.; Rochmad

2018-03-01

The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.

Mathematics for the Technical Student: The Use of the Computer in the Systems Approach to Instruction.

ERIC Educational Resources Information Center

Capps, Joan P.

An instructional method using flow-chart symbols to make mathematical abstractions more concrete was implemented for a year in a technical mathematics course. Students received instruction in computer applications and programming in the BASIC language in order to increase motivation and firm the mathematical skills and problem-solving approaches…

Investigating Students' Level of Critical Thinking across Instructional Strategies in Online Discussions

ERIC Educational Resources Information Center

Richardson, Jennifer C.; Ice, Phil

2010-01-01

Online discussion questions, which reflect differing instructional strategies, can take many forms and it is important for designers and instructors to understand how the various strategies can impact students' critical thinking levels. For the purpose of the study three instructional strategies used in the development and implementation of online…

Applying Piaget's Theory to Reading Instruction.

ERIC Educational Resources Information Center

Heatherly, Anna L.

This paper discusses beginning reading instruction in the light of Piaget's theory, which demands that we think more broadly about the term "where the child is" in terms of his level of thinking, not simply his reading level or reading skill level. Using Piaget's four major developmental stages as the basis, the task of instruction in…

Sliding into Multiplicative Thinking: The Power of the "Marvellous Multiplier"

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…

Assessing Children's Multiplicative Thinking

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is a "big idea" of mathematics that underpins much of the mathematics learned beyond the early primary school years. This paper reports on a current study that utilises an interview tool and a written quiz to gather data about children's multiplicative thinking. The development of the tools and some of the…

Our Prospective Mathematic Teachers Are Not Critical Thinkers Yet

ERIC Educational Resources Information Center

As'ari, Abdur Rahman; Mahmudi, Ali; Nuerlaelah, Elah

2017-01-01

In order to help students develop their critical thinking skills, teachers need to model the critical thinking skills and dispositions in front of their students. Unfortunately, very rare studies investigating prospective teachers' readiness in critical thinking dispositions are available in the field of mathematics education. This study was…

National Center for Mathematics and Science - what we do

Science.gov Websites

. teachers need more substantive professional development about student thinking and subject matter student thinking is a cornerstone of professional development. In our work with teachers, we have observed the ways that teachers examined student thinking about important mathematics and science ideas, and

Mathematics Pedagogical Standards: A Suggested Model of Instruction in Enhancing the Mathematics Teacher’s Quality of Instruction

NASA Astrophysics Data System (ADS)

Saad, N. S.; Jemali, M.; Zakaria, Z. Hj; Yusof, Q.

2018-01-01

The paper aims at identifying the standards for teaching and learning of mathematics based on National Council of Teacher of Mathematics (NCTM, 2000), The Australian Association of Mathematics Teachers (AAMT, 2006) and Training and Development Agency for School (TDA, 2007). These known standards were used as a guide in identifying the constructs of the mathematics teacher’s instruction in the classroom. The survey method used in which a questionnaire instrument encompassed on the four identified constructs on the standards for teaching and learning of mathematics, namely professional practices, professional attributes, professional knowledge, and professional instructional processes. The instrument was tested during a pilot study and a Cronbach’s Alpha reliability index of greater than 0.85 was obtained. The actual research was carried out in Peninsular Malaysia involving 224 secondary schools with 1.120 mathematics teachers and 108 primary schools with 540 mathematics teachers. From the selected schools, only 820 secondary mathematics teachers (73.2%) and 361 primary teachers (66.9%) gave a response to the mailed questionnaires. The findings of the study revealed that the secondary and primary mathematics teachers strongly agreed on three constructs; professional practices, professional attributes and professional instructional processes.

Reflective thinking in solving an algebra problem: a case study of field independent-prospective teacher

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Yuli Eko Siswono, Tatag

2017-10-01

Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

A Mathematical Mystery Tour: Higher-Thinking Math Tasks.

ERIC Educational Resources Information Center

Wahl, Mark

This book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…

Defining Computational Thinking for Mathematics and Science Classrooms

ERIC Educational Resources Information Center

Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri

2016-01-01

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new…

"This Is the First Time I've Done This": Exploring Secondary Prospective Mathematics Teachers' Noticing of Students' Mathematical Thinking

ERIC Educational Resources Information Center

Simpson, Amber; Haltiwanger, Leigh

2017-01-01

This mixed methods study investigates the ways in which secondary mathematics prospective teachers acquire skills needed to attend to, interpret, and respond to students' mathematical thinking and the ways in which their perceived strengths and weaknesses influence their skills when this type of formalized training is not part of their program.…

Rethinking biology instruction: The application of DNR-based instruction to the learning and teaching of biology

NASA Astrophysics Data System (ADS)

Maskiewicz, April Lee

Educational studies report that secondary and college level students have developed only limited understandings of the most basic biological processes and their interrelationships from typical classroom experiences. Furthermore, students have developed undesirable reasoning schemes and beliefs that directly affect how they make sense of and account for biological phenomena. For these reasons, there exists a need to rethink instructional practices in biology. This dissertation discusses how the principles of Harel's (1998, 2001) DNR-based instruction in mathematics could be applied to the teaching and learning of biology. DNR is an acronym for the three foundational principles of the system: Duality, Necessity, and Repeated-reasoning. This study examines the application of these three principles to ecology instruction. Through clinical and teaching interviews, I developed models of students' existing ways of understanding in ecology and inferred their ways of thinking. From these models a hypothetical learning trajectory was developed for 16 college level freshmen enrolled in a 10-week ecology teaching experiment. Through cyclical, interpretive analysis I documented and analyzed the evolution of the participants' progress. The results provide empirical evidence to support the claim that the DNR principles are applicable to ecology instruction. With respect to the Duality Principle, helping students develop specific ways of understanding led to the development of model-based reasoning---a way of thinking and the cognitive objective guiding instruction. Through carefully structured problem solving tasks, the students developed a biological understanding of the relationship between matter cycling, energy flow, and cellular processes such as photosynthesis and respiration, and used this understanding to account for observable phenomena in nature. In the case of intellectual necessity, the results illuminate how problem situations can be developed for biology learners that create cognitive disequilibrium-equilibrium phases and thus lead to modification or refinement of existing schemes. Elements that contributed to creating intellectual need include (a) problem tasks that built on students' existing knowledge; (b) problem tasks that challenged students; (c) a routine in which students presented their group's solution to the class; and (d) the didactical contract (Brousseau, 1997) established in the classroom.

Mathematical knowledge for teaching: Making the tacit more explicit in mathematics teacher education

NASA Astrophysics Data System (ADS)

Abdullah, Mohd Faizal Nizam Lee; Vimalanandan, Lena

2017-05-01

Teaching practice during school based experiences, afford an opportunity for pre service teachers to put into practice their knowledge for teaching mathematics. Like all knowledge, Mathematical Knowledge for Teaching (MKT) is held in both tacit and explicit form, making it especially difficult to study and map during instruction. This study investigates the tacit and explicit nature of MKT held by pre service teachers in a Malaysian Teacher Education Program and how it impacts the Mathematical Quality of their instruction (MQI). This study of three mathematics pre-service teachers (PSTs), utilised videos of mathematics lessons, reflective debriefs and interviews. The findings suggest that factors such as reflecting, peer-sharing, conferencing with mentors and observing support in making tacit knowledge more explicit during planning and instruction. Implications for preparation of mathematics teachers capable of high Mathematical Quality of Instruction are also discussed.

Critical Thinking Outcomes of Computer-Assisted Instruction versus Written Nursing Process.

ERIC Educational Resources Information Center

Saucier, Bonnie L.; Stevens, Kathleen R.; Williams, Gail B.

2000-01-01

Nursing students (n=43) who used clinical case studies via computer-assisted instruction (CAI) were compared with 37 who used the written nursing process (WNP). California Critical Thinking Skills Test results did not show significant increases in critical thinking. The WNP method was more time consuming; the CAI group was more satisfied. Use of…

Theory into Practice: Best Practices for a School-Wide Approach to Critical Thinking Instruction.

ERIC Educational Resources Information Center

Kassem, Cherrie L.

Educators at one Georgia high school identified improved student proficiency in critical thinking as a major school goal. In order to infuse thinking skills instruction across the curriculum, a nine-member interdisciplinary team of teachers worked with a learning consultant for 1 year. Collaboration resulted in the development of a new model for…

Entering into dialogue about the mathematical value of contextual mathematising tasks

NASA Astrophysics Data System (ADS)

Yoon, Caroline; Chin, Sze Looi; Moala, John Griffith; Choy, Ban Heng

2018-03-01

Our project seeks to draw attention to the rich mathematical thinking that is generated when students work on contextual mathematising tasks. We use a design-based research approach to create ways of reporting that raise the visibility of this rich mathematical thinking while retaining and respecting its complexity. These reports will be aimed for three classroom stakeholders: (1) students, who wish to reflect on and enhance their mathematical learning; (2) teachers, who wish to integrate contextual mathematising tasks into their teaching practice and (3) researchers, who seek rich tasks for generating observable instances of mathematical thinking and learning. We anticipate that these reports and the underlying theoretical framework for creating them will contribute to greater awareness of and appreciation for the mathematical value of contextual mathematising tasks in learning, teaching and research.

Mathematics Word Problem Solving: An Investigation into Schema-Based Instruction in a Computer-Mediated Setting and a Teacher-Mediated Setting with Mathematically Low-Performing Students

ERIC Educational Resources Information Center

Leh, Jayne

2011-01-01

Substantial evidence indicates that teacher-delivered schema-based instruction (SBI) facilitates significant increases in mathematics word problem solving (WPS) skills for diverse students; however research is unclear whether technology affordances facilitate superior gains in computer-mediated (CM) instruction in mathematics WPS when compared to…

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

Understanding and responding the students in learning mathematics through the differentiated instruction

NASA Astrophysics Data System (ADS)

Hapsari, T.; Darhim; Dahlan, J. A.

2018-05-01

This research discusses the differentiated instruction, a mathematic learning which is as expected by the students in connection with the differentiated instruction itself, its implementation, and the students’ responses. This research employs a survey method which involves 62 students as the research respondents. The mathematics learning types required by the students and their responses to the differentiated instruction are examined through questionnaire and interview. The mathematics learning types in orderly required by the students, from the highest frequency cover the easily understood instructions, slowly/not rushing teaching, fun, not complicated, interspersed with humour, various question practices, not too serious, and conducive class atmosphere for the instructions. Implementing the differentiated instruction is not easy. The teacher should be able to constantly assess the students, s/he should have good knowledge of relevant materials and instructions, and properly prepare the instructions, although it is time-consuming. The differentiated instruction is implemented on the instructions of numerical pattern materials. The strategies implemented are flexible grouping, tiered assignment, and compacting. The students positively respond the differentiated learning instruction that they become more motivated and involved in the instruction.

Strategy Instruction in Mathematics.

ERIC Educational Resources Information Center

Goldman, Susan R.

1989-01-01

Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…

Enhancing divergent thinking in visual arts education: Effects of explicit instruction of meta-cognition.

PubMed

van de Kamp, Marie-Thérèse; Admiraal, Wilfried; van Drie, Jannet; Rijlaarsdam, Gert

2015-03-01

The main purposes of visual arts education concern the enhancement of students' creative processes and the originality of their art products. Divergent thinking is crucial for finding original ideas in the initial phase of a creative process that aims to result in an original product. This study aims to examine the effects of explicit instruction of meta-cognition on students' divergent thinking. A quasi-experimental design was implemented with 147 secondary school students in visual arts education. In the experimental condition, students attended a series of regular lessons with assignments on art reception and production, and they attended one intervention lesson with explicit instruction of meta-cognition. In the control condition, students attended a series of regular lessons only. Pre-test and post-test instances tests measured fluency, flexibility, and originality as indicators of divergent thinking. Explicit instruction of meta-cognitive knowledge had a positive effect on fluency and flexibility, but not on originality. This study implies that in the domain of visual arts, instructional support in building up meta-cognitive knowledge about divergent thinking may improve students' creative processes. This study also discusses possible reasons for the demonstrated lack of effect for originality. © 2014 The British Psychological Society.

Mathematics Instruction: Do Classrooms Matter?

ERIC Educational Resources Information Center

Desoete, Annemie; Stock, Pieter

2013-01-01

Counting abilities have been described as determinative precursors for a good development of later mathematical abilities. However, an important part of variance in mathematical achievement has also been associated with differences between instruction methods given in schools. In this study counting and instruction as predictors for mathematical…

Representations in Problem Solving: A Case Study with Optimization Problems

ERIC Educational Resources Information Center

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

Inhibiting Intuitive Thinking in Mathematics Education

ERIC Educational Resources Information Center

Thomas, Michael O. J.

2015-01-01

The papers in this issue describe recent collaborative research into the role of inhibition of intuitive thinking in mathematics education. This commentary reflects on this research from a mathematics education perspective and draws attention to some of the challenges that arise in collaboration between research fields with different cultures,…

Reading the News: The Statistical Preparation of Pre-Service Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Chesler, Joshua

2015-01-01

Undergraduate mathematics programs must prepare teachers for the challenges of teaching statistical thinking as advocated in standards documents and statistics education literature. This study investigates the statistical thinking of pre-service secondary mathematics teachers at the end of their undergraduate educations. Although all had completed…

Gestures and Insight in Advanced Mathematical Thinking

ERIC Educational Resources Information Center

Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy

2011-01-01

What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…

Thinking Like a Mathematician

ERIC Educational Resources Information Center

Weiss, Michael K.; Moore-Russo, Deborah

2012-01-01

What does it mean to think like a mathematician? One of the great paradoxes of mathematics education is that, although mathematics teachers are immersed in mathematical work every day of their professional lives, most of them nevertheless have little experience with the kind of work that research mathematicians do. Their ideas of what doing…

Preparing Beginning Teachers to Elicit and Interpret Students' Mathematical Thinking

ERIC Educational Resources Information Center

Sleep, Laurie; Boerst, Timothy A.

2012-01-01

This study investigated how teacher education assignments can be designed to support beginning teachers in learning to do the work of teaching. We examined beginners' formative assessment practices--in particular, their eliciting and interpreting of students' mathematical thinking--in the context of an elementary mathematics methods assignment,…

Cognitive Psychology and Mathematical Thinking.

ERIC Educational Resources Information Center

Greer, Brian

1981-01-01

This review illustrates aspects of cognitive psychology relevant to the understanding of how people think mathematically. Developments in memory research, artificial intelligence, visually mediated processes, and problem-solving research are discussed. (MP)

Computer Game Development: An Instructional Strategy to Promote Higher Order Thinking Skills

ERIC Educational Resources Information Center

Prayaga, Lakshmi; Coffey, John W.

2008-01-01

Several studies have demonstrated that games have been effectively used as an instructional strategy to motivate and engage students. This paper presents the use of the process of game development as an instructional strategy to promote higher order thinking skills. An analysis of the various aspects of game development including graphics,…

Differentiating Literacy Instruction for Digital Learners: The Effect of Multimedia Think-Aloud Worked Examples on Adolescent Analytical Reading Comprehension

ERIC Educational Resources Information Center

Neebe, Diana Combs

2017-01-01

Learning by example is nothing new to the education landscape. Research into think-aloud protocols, though often used as a form of assessment rather than instruction, provided practical, content-specific literacy strategies for crafting the instructional intervention in this study. Additionally, research into worked examples--from the earliest…

Developing the Mathematics Learning Management Model for Improving Creative Thinking in Thailand

ERIC Educational Resources Information Center

Sriwongchai, Arunee; Jantharajit, Nirat; Chookhampaeng, Sumalee

2015-01-01

The study purposes were: 1) To study current states and problems of relevant secondary students in developing mathematics learning management model for improving creative thinking, 2) To evaluate the effectiveness of model about: a) efficiency of learning process, b) comparisons of pretest and posttest on creative thinking and achievement of…

Investigating Children's Multiplicative Thinking: Implications for Teaching

ERIC Educational Resources Information Center

Hurst, Chris; Hurrell, Derek

2016-01-01

Multiplicative thinking is a "big idea" of mathematics that underpins much of the mathematics learned beyond the early primary school years. This article reports on a recent study that utilised an interview tool and a written quiz to gather data about children's multiplicative thinking. Our research has so far revealed that many primary…

Connecting Research to Teaching: Lenses for Examining Students' Mathematical Thinking

ERIC Educational Resources Information Center

Linsenmeier, Katherine A.; Sherin, Miriam; Walkoe, Janet; Mulligan, Martha

2014-01-01

The authors present three strategies for making sense of students' mathematical thinking. These lenses make the abstract idea of "making sense of student thinking" more manageable and concrete. We start by taking an initial look at a student's idea, going deeper, and finally looking across several ideas.

Children Have the Capacity to Think Multiplicatively, as Long as …

ERIC Educational Resources Information Center

Hurst, Chris

2017-01-01

Multiplicative thinking has been widely accepted as a critically important "big idea" of mathematics and one which underpins much mathematical understanding beyond the primary years of schooling. It is therefore of importance to consider the capacity of children to think multiplicatively but also to consider the capacity of their…

Critical thinking instruction and technology enhanced learning from the student perspective: A mixed methods research study.

PubMed

Swart, Ruth

2017-03-01

Critical thinking is acclaimed as a valuable asset for graduates from higher education programs. Technology has advanced in quantity and quality; recognized as a requirement of 21st century learners. A mixed methods research study was undertaken, examining undergraduate nursing student engagement with critical thinking instruction, platformed on two technology-enhanced learning environments: a classroom response system face-to-face in-class and an online discussion forum out-of-class. The Community of Inquiry framed the study capturing constructivist collaborative inquiry to support learning, and facilitate critical thinking capability. Inclusion of quantitative and qualitative data sources aimed to gather a comprehensive understanding of students' development of critical thinking and engagement with technology-enhanced learning. The findings from the students' perspectives were positive toward the inclusion of technology-enhanced learning, and use in supporting their development of critical thinking. Students considered the use of two forms of technology beneficial in meeting different needs and preferences, offering varied means to actively participate in learning. They valued critical thinking instruction being intentionally aligned with subject-specific content facilitating understanding, application, and relevance of course material. While the findings are limited to student participants, the instructional strategies and technology-enhanced learning identified as beneficial can inform course design for the development of critical thinking. Copyright © 2017 Elsevier Ltd. All rights reserved.

Open-Ended Approach: An Effort in Cultivating Students' Mathematical Creative Thinking Ability and Self-Esteem in Mathematics

ERIC Educational Resources Information Center

Fatah, Abdul; Suryadi, Didi; Sabandar, Jozua; Turmudi

2016-01-01

The present study aims at examining the use of open-ended approach in cultivating senior high school students' mathematical creative thinking ability (MCTA) and self-esteem (SE) in mathematics viewed from school category. The subjects of this research were the students grade XI at three schools; high, middle and low category in Kota Serang, Banten…

Students' Critical Mathematical Thinking Skills and Character: Experiments for Junior High School Students through Realistic Mathematics Education Culture-Based

ERIC Educational Resources Information Center

Palinussa, Anderson L.

2013-01-01

This paper presents the findings of a quasi-experimental with pre-test-post-test design and control group that aims to assess students' critical mathematical thinking skills and character through realistic mathematics education (RME) culture-based. Subjects of this study were 106 junior high school students from two low and medium schools level in…

Critical Thinking Instruction in English for Academic Purposes Writing Courses: A Dialectical Thinking Approach

ERIC Educational Resources Information Center

Tanaka, Jay; Gilliland, Betsy

2017-01-01

Critical thinking (CT) is usually taught as a list of practical skills for students to master. In this article, the authors argue that CT instruction should go beyond skills to engage students with issues of identifying their own biases and understanding multiple perspectives on issues. This explicit attention to one's own bias is essential for…

Future thinking instructions improve prospective memory performance in adolescents.

PubMed

Altgassen, Mareike; Kretschmer, Anett; Schnitzspahn, Katharina Marlene

2017-07-01

Studies on prospective memory (PM) development in adolescents point to age-related increases through to adulthood. The goal of the present study was to examine whether instructing adolescents to engage in an episodic prospection of themselves executing future actions (i.e., future thinking) when forming an intention would improve their PM performance and reduce age-related differences. Further, we set out to explore whether future thinking instructions result in stronger memory traces and/or stronger cue-context associations by evaluating retrospective memory for the PM cues after task completion and monitoring costs during PM task processing. Adolescents and young adults were allocated to either the future thinking, repeated-encoding or standard condition. As expected, adolescents had fewer correct PM responses than young adults. Across age groups, PM performance in the standard condition was lower than in the other encoding conditions. Importantly, the results indicate a significant interaction of age by encoding condition. While adolescents benefited most from future thinking instructions, young adults performed best in the repeated-encoding condition. The results also indicate that the beneficial effects of future thinking may result from deeper intention-encoding through the simulation of future task performance.

Preliminary Findings from a Multi-Year Scale-Up Effectiveness Trial of Everyday Mathematics

ERIC Educational Resources Information Center

Vaden-Kiernan, Michael; Borman, Geoffrey; Caverly, Sarah; Bell, Nance; Ruiz de Castilla, Veronica; Sullivan, Kate

2015-01-01

Given the importance of early mathematics instruction and curricula for preventing mathematics difficulties in later grades, it is necessary to identify effective mathematics curricula and instruction to ensure that children become proficient in early mathematics content and procedures. Everyday Mathematics (EM), was reviewed by the What Works…

Secondary School Mathematics Teachers' and Students' Views on Computer Assisted Mathematics Instruction in Turkey: Mathematica Example

ERIC Educational Resources Information Center

Ardiç, Mehmet Alper; Isleyen, Tevfik

2017-01-01

This study aimed at determining the secondary school mathematics teachers' and students' views on computer-assisted mathematics instruction (CAMI) conducted via Mathematica. Accordingly, three mathematics teachers in Adiyaman and nine 10th-grade students participated in the research. Firstly, the researchers trained the mathematics teachers in the…

Factors Associated with Alignment between Teacher Survey Reports and Classroom Observation Ratings of Mathematics Instruction

ERIC Educational Resources Information Center

Kaufman, Julia Heath; Stein, Mary Kay; Junker, Brian

2016-01-01

We investigated the alignment between a teacher survey self-report measure and classroom observation measure of ambitious mathematics instructional practice among teachers in two urban school districts using two different standards-based mathematics curricula. Survey reports suggested mild differences in teachers' instructional practices between…

Professional Vision: Elementary School Principals' Perceptions of Mathematics Instruction

ERIC Educational Resources Information Center

Schoen, Robert C.

2010-01-01

This study explored 78 elementary school principals' perceptions of classroom mathematics instruction in an effort to build understanding of the professional vision (Goodwin, 1994) of elementary school principals as it relates to mathematics instruction. This study also tested the theory of Leadership Content Knowledge (Stein & Nelson, 2003)…

Beliefs and Instructional Practices of Four Community College Remedial Mathematics Instructors

ERIC Educational Resources Information Center

Wucherer, Robin M.

2011-01-01

In an extension of research linking teachers' beliefs about mathematics and their instructional practices at the Prek-12 level, the present study examined and documented both the beliefs and instructional practices of four community college instructors who teach remedial mathematics. Data was collected through survey, observations, interviews, and…

Reflective Learning and Prospective Teachers' Conceptual Understanding, Critical Thinking, Problem Solving, and Mathematical Communication Skills

ERIC Educational Resources Information Center

Junsay, Merle L.

2016-01-01

This is a quasi-experimental study that explored the effects of reflective learning on prospective teachers' conceptual understanding, critical thinking, problem solving, and mathematical communication skills and the relationship of these variables. It involved 60 prospective teachers from two basic mathematics classes of an institution of higher…

What Secondary Teachers Think and Do about Student Engagement in Mathematics

ERIC Educational Resources Information Center

Skilling, Karen; Bobis, Janette; Martin, Andrew J.; Anderson, Judy; Way, Jennifer

2016-01-01

What teachers' think about student engagement influences the teaching practices they adopt, their responses to students and the efforts they make in the classroom. Interviews were conducted with 31 mathematics teachers from ten high schools to investigate their perceptions and beliefs about student engagement in mathematics. Teachers also reported…

Action-Based Digital Tools: Mathematics Learning in 6-Year-Old Children

ERIC Educational Resources Information Center

Dejonckheere, Peter J. N.; Desoete, Annemie; Fonck, Nathalie; Roderiguez, Dave; Six, Leen; Vermeersch, Tine; Vermeulen, Lies

2014-01-01

Introduction: In the present study we used a metaphorical representation in order to stimulate the numerical competences of six-year-olds. It was expected that when properties of physical action are used for mathematical thinking or when abstract mathematical thinking is grounded in sensorimotor processes, learning gains should be more pronounced…

Designing and Developing Assessments of Complex Thinking in Mathematics for the Middle Grades

ERIC Educational Resources Information Center

Graf, Edith Aurora; Arieli-Attali, Meirav

2015-01-01

Designing an assessment system for complex thinking in mathematics involves decisions at every stage, from how to represent the target competencies to how to interpret evidence from student performances. Beyond learning to solve particular problems in a particular area, learning mathematics with understanding involves comprehending connections…

Convergent and Divergent Thinking in Task Modification: A Case of Korean Prospective Mathematics Teachers' Exploration

ERIC Educational Resources Information Center

Lee, Kyeong-Hwa

2017-01-01

This study investigated how 38 secondary mathematics prospective teachers modified textbook tasks for convergent and divergent thinking while learning to teach mathematics during university coursework. The coursework focused prospective teachers' attention on their analyses of textbook tasks in terms of potential affordances and constraints for…

How Middle Grade Teachers Think about Algebraic Reasoning

ERIC Educational Resources Information Center

Glassmeyer, David; Edwards, Belinda

2016-01-01

Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a…

Student’s rigorous mathematical thinking based on cognitive style

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Fitriyani, H.; Khasanah, U.

2017-12-01

The purpose of this research was to determine the rigorous mathematical thinking (RMT) of mathematics education students in solving math problems in terms of reflective and impulsive cognitive styles. The research used descriptive qualitative approach. Subjects in this research were 4 students of the reflective and impulsive cognitive style which was each consisting male and female subjects. Data collection techniques used problem-solving test and interview. Analysis of research data used Miles and Huberman model that was reduction of data, presentation of data, and conclusion. The results showed that impulsive male subjects used three levels of the cognitive function required for RMT that were qualitative thinking, quantitative thinking with precision, and relational thinking completely while the other three subjects were only able to use cognitive function at qualitative thinking level of RMT. Therefore the subject of impulsive male has a better RMT ability than the other three research subjects.

The Effect of Instructing Critical Thinking through Debate on Male and Female EFL Learners' Reading Comprehension

ERIC Educational Resources Information Center

Tous, Maryam Danaye; Tahriri, Abdorreza; Haghighi, Sara

2015-01-01

The purpose of the present study was to examine the effect of instruction through debate on male and female EFL learners' reading comprehension. Also, their perception of critical thinking (CT) instruction was investigated. A quantitative research method with experimental pre-and post-tests design was conducted to collect the data. Eighty-eight…

Math Thinking Motivators. A Good Apple Math Activity Book for Grades 2-7.

ERIC Educational Resources Information Center

Bernstein, Bob

In this booklet are 43 mathematical games and activities to stimulate creative thinking in grades 2-7. The goal of teaching divergent thinking is stressed, as well as the need to encourage positive self-image, motivation, and creativity. For each activity, the mathematical skills addressed in the activity are listed; topics span the elementary…

Students’ Mathematical Creative Thinking through Problem Posing Learning

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Ulfah, U.; Prabawanto, S.; Jupri, A.

2017-09-01

The research aims to investigate the differences in enhancement of students’ mathematical creative thinking ability of those who received problem posing approach assisted by manipulative media and students who received problem posing approach without manipulative media. This study was a quasi experimental research with non-equivalent control group design. Population of this research was third-grade students of a primary school in Bandung city in 2016/2017 academic year. Sample of this research was two classes as experiment class and control class. The instrument used is a test of mathematical creative thinking ability. Based on the results of the research, it is known that the enhancement of the students’ mathematical creative thinking ability of those who received problem posing approach with manipulative media aid is higher than the ability of those who received problem posing approach without manipulative media aid. Students who get learning problem posing learning accustomed in arranging mathematical sentence become matter of story so it can facilitate students to comprehend about story

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2017-01-01

This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

Contrasting two models of academic self-efficacy--domain-specific versus cross-domain--in children receiving and not receiving special instruction in mathematics.

PubMed

Jungert, Tomas; Hesser, Hugo; Träff, Ulf

2014-10-01

In social cognitive theory, self-efficacy is domain-specific. An alternative model, the cross-domain influence model, would predict that self-efficacy beliefs in one domain might influence performance in other domains. Research has also found that children who receive special instruction are not good at estimating their performance. The aim was to test two models of how self-efficacy beliefs influence achievement, and to contrast children receiving special instruction in mathematics with normally-achieving children. The participants were 73 fifth-grade children who receive special instruction and 70 children who do not receive any special instruction. In year four and five, the children's skills in mathematics and reading were assessed by national curriculum tests, and in their fifth year, self-efficacy in mathematics and reading were measured. Structural equation modeling showed that in domains where children do not receive special instruction in mathematics, self-efficacy is a mediating variable between earlier and later achievement in the same domain. Achievement in mathematics was not mediated by self-efficacy in mathematics for children who receive special instruction. For normal achieving children, earlier achievement in the language domain had an influence on later self-efficacy in the mathematics domain, and self-efficacy beliefs in different domains were correlated. Self-efficacy is mostly domain specific, but may play a different role in academic performance depending on whether children receive special instruction. The results of the present study provided some support of the Cross-Domain Influence Model for normal achieving children. © 2014 Scandinavian Psychological Associations and John Wiley & Sons Ltd.

Patterns of interactions at grade 5 classroom in learning the topic of statistics viewed from cognitive load theory

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Setianingsih, R.

2018-01-01

The nature of interactions that occurs among teacher, students, learning sources, and learning environment creates different settings to enhance learning. Any setting created by a teacher is affected by 3 (three) types of cognitive load: intrinsic cognitive load, extraneous cognitive load, and germane cognitive load. This study is qualitative in nature, aims to analyse the patterns of interaction that are constituted in mathematics instructions by taking into account the cognitive load theory. The subjects of this study are 21 fifth-grade students who learn mathematics in small groups and whole-class interactive lessons. The data were collected through classroom observations which were videotaped, while field notes were also taken. The data analysis revealed that students engaged in productive interaction and inquiry while they were learning mathematics in small groups or in whole class setting, in which there was a different type of cognitive load that dominantly affecting the learning processes at each setting. During learning mathematics in whole class setting, the most frequently found interaction patterns were to discuss and compare solution based on self-developed models, followed by expressing opinions. This is consistent with the principles of mathematics learning, which gives students wide opportunities to construct mathematical knowledge through individual learning, learning in small groups as well as learning in whole class settings. It means that by participating in interactive learning, the students are habitually engaged in productive interactions and high level of mathematical thinking.

The Efficacy of Instructional Strategy on Mathematics Achievement, Attitudes, and Anxiety Levels of Developmental Math Students

ERIC Educational Resources Information Center

Thomas-Browne, Carmen G.

2009-01-01

This dissertation investigated three instructional strategies in developmental math classes to determine if instructional strategy had a positive effect on student achievement, attitude towards mathematics, and anxiety level towards mathematics at a college in western Pennsylvania for students majoring in applied arts. The significance of this…

Elementary-School Mathematics Instruction and Achievement of Fourth-Grade Students in Japan: Findings from the TIMSS 2007 Assessment

ERIC Educational Resources Information Center

House, J. Daniel

2009-01-01

Research findings indicate that specific instructional strategies, such as the use of real-world examples and independent learning activities, are positively related to mathematics achievement. This study was designed to investigate relationships between classroom instructional strategies and mathematics achievement of elementary-school students…

Development of an Instructional Model for Higher Order Thinking in Science among Secondary School Students: A Fuzzy Delphi Approach

ERIC Educational Resources Information Center

Saido, G. A. M.; Siraj, S.; DeWitt, D.; Al-Amedy, O. S.

2018-01-01

It is important for science students to develop higher order thinking (HOT) so that they can reason like scientists in the field. In this study, a HOT instructional model for secondary school science was developed with experts. The model would focus on reflective thinking (RT) and science process skills (SPS) among Grade 7 students. The Fuzzy…

The Impact of Problem-Based Learning Approach to Senior High School Students' Mathematics Critical Thinking Ability

ERIC Educational Resources Information Center

Widyatiningtyas, Reviandari; Kusumah, Yaya S.; Sumarmo, Utari; Sabandar, Jozua

2015-01-01

The study reported the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students' prior mathematical ability to student's mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from…

Mathematical Critical Thinking and Curiosity Attitude in Problem Based Learning and Cognitive Conflict Strategy: A Study in Number Theory Course

ERIC Educational Resources Information Center

Zetriuslita; Wahyudin; Jarnawi

2017-01-01

This research aims to describe and analyze result of applying Problem-Based Learning and Cognitive Conflict Strategy (PBLCCS) in increasing students' Mathematical Critical Thinking (MCT) ability and Mathematical Curiosity Attitude (MCA). Adopting a quasi-experimental method with pretest-posttest control group design and using mixed method with…

Entering into Dialogue about the Mathematical Value of Contextual Mathematising Tasks

ERIC Educational Resources Information Center

Yoon, Caroline; Chin, Sze Looi; Moala, John Griffith; Choy, Ban Heng

2018-01-01

Our project seeks to draw attention to the rich mathematical thinking that is generated when students work on contextual mathematising tasks. We use a design-based research approach to create ways of reporting that raise the visibility of this rich mathematical thinking while retaining and respecting its complexity. These reports will be aimed for…

Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability

ERIC Educational Resources Information Center

Saragih, Sahat; Napitupulu, Elvis

2015-01-01

The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…

The Effectiveness of Instructional Mathematics Coaching: A Study on How the Implementation of Instructional Mathematics Coaches in Elementary Schools Impacts Student Achievement and Promotes Teacher Self-Efficacy

ERIC Educational Resources Information Center

Taylor, Janice E.

2017-01-01

The State of Illinois adopted the Illinois Learning Standards for Mathematics on June 24, 2010 as a means for students to succeed in college, in a career and in life. The new standards had instructional shifts in content and practice that differed from the 1999 Illinois Learning Standards. The new mathematics standards contained fewer topics for…

Achieving meaningful mathematics literacy for students with learning disabilities. Cognition and Technology Group at Vanderbilt.

PubMed

Goldman, S R; Hasselbring, T S

1997-01-01

In this article we consider issues relevant to the future of mathematics instruction and achievement for students with learning disabilities. The starting point for envisioning the future is the changing standards for mathematics learning and basic mathematical literacy. We argue that the shift from behaviorist learning theories to constructivist and social constructivist theories (see Rivera, this series) provides an opportunity to develop and implement a hybrid model of mathematics instruction. The hybrid model we propose embeds, or situates, important skill learning in meaningful contexts. We discuss some examples of instructional approaches to complex mathematical problem solving that make use of meaningful contexts. Evaluation data on these approaches have yielded positive and encouraging results for students with learning disabilities as well as general education students. Finally, we discuss various ways in which technology is important for realizing hybrid instructional models in mathematics.

Creative Cognition in Secondary Science: An exploration of divergent thinking in science among adolescents

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Antink-Meyer, Allison; Lederman, Norman G.

2015-07-01

The divergent thinking skills in science of 282 US high school students were investigated across 16 weeks of instruction in order to determine whether typical academic time periods can significantly influence changes in thinking skills. Students' from 6 high school science classrooms completed the Scientific Structures Creativity Measure (SSCM) before and after a semester of instruction. Even the short time frame of a typical academic term was found to be sufficient to promote both improvements in divergent thinking skills as well as declining divergent thinking. Declining divergent thinking skills were more common in this time frame than were improvements. The nature of student performance on the SSCM and implications are discussed.

The Influence of Mathematics Vocabulary Instruction Embedded within Addition Tutoring for First-Grade Students with Mathematics Difficulty

ERIC Educational Resources Information Center

Powell, Sarah R.; Driver, Melissa K.

2015-01-01

Researchers and practitioners indicate students require explicit instruction on mathematics vocabulary terms, yet no study has examined the effects of an embedded vocabulary component within mathematics tutoring for early elementary students. First-grade students with mathematics difficulty (MD; n = 98) were randomly assigned to addition tutoring…

Middle School Mathematics Teachers Panel Perspectives of Instructional Practicess

ERIC Educational Resources Information Center

Ziegler, Cindy

2017-01-01

In a local middle school, students were not meeting standards on the state mathematics tests. The purpose of this qualitative study was to explore mathematics teachers' perspectives on effective mathematics instruction vis-a-vis the principles of the National Council of Teachers of Mathematics (NCTM). Within this framework, the 6 principles in the…

Student teachers’ mathematical questioning and courage in metaphorical thinking learning

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Hendriana, H.; Hidayat, W.; Ristiana, M. G.

2018-01-01

This study was designed in the form of experiments with control group design and post-test only which aimed to examine the role of metaphorical thinking learning in the mathematical questioning ability of student teachers based on the level of mathematical courage. The population of this study was student teachers of mathematics education study program in West Java Province, while the sample of this study was 152 student teachers which were set purposively and then randomly to be included in the experimental class and control class. Based on the results and discussion, it was concluded that: (a) the mathematical questioning ability of student teachers who received Metaphorical Thinking learning was better than those who received conventional learning seen from mathematical courage level; (b) learning and mathematical courage level factors affected the achievement of student teachers’ mathematical questioning ability. In addition, there was no interaction effect between learning and mathematical courage level (high, medium, and low) simultaneously in developing student teachers’ mathematical questioning ability; (c) achievement of mastering mathematical questioning ability of student teacher was still not well achieved on indicator of problem posing in the form of non-routine question and open question.

Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

PubMed

Morgan, Paul L; Farkas, George; Maczuga, Steve

2015-06-01

We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by 1 st grade teachers in the U.S. and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement-three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in 1 st grade classrooms was associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted ES s = .05-.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and student-centered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ES s = .03-.04). First-grade teachers in the U.S. may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD.

The Process of Thinking among Junior High School Students in Solving HOTS Question

ERIC Educational Resources Information Center

Bakry, Md Nor Bin Bakar

2015-01-01

Higher order thinking skills (HOTS) is one of the important aspect of teaching and learning mathematics. By using HOTS, student will be able to acquire a deep understand of mathematical concepts and can be applied in real life. Students ability to develop the capacity of the HOTS is closely related with thinking processes while solving mathematics…

Critical Thinking Skills of an Eighth Grade Male Student with High Mathematical Ability in Solving Problem

NASA Astrophysics Data System (ADS)

Ismail

2018-01-01

This study aims to describe student’s critical thinking skill of grade VIII in solving mathematical problem. A qualitative research was conducted to a male student with high mathematical ability. Student’s critical thinking skill was obtained from a depth task-based interview. The result show that male student’s critical thinking skill of the student as follows. In understanding the problem, the student did categorization, significance decoding, and meaning clarification. In devising a plan he examined his ideas, detected his argument, analyzed his argument and evaluated his argument. During the implementation phase, the skill that appeared were analyzing of the argument and inference skill such as drawing conclusion, deliver alternative thinking, and problem solving skills. At last, in rechecking all the measures, they did self-correcting and self-examination.

The Effect of Thinking Maps on Fifth Grade Science Achievement

NASA Astrophysics Data System (ADS)

Hudson, Darlene

Informational texts, such as those found in science education, have historically been reserved for secondary students. With the increased emphasis on elementary students' academic accountability, these high impact instructional strategies must also be utilized to support subject matter comprehension for younger students. This causal-comparative study, grounded in cognitive learning theory, sought to discover if 2 years of implementation and use of Thinking Maps, a visual tool program, had an effect on student achievement in elementary science as measured by Georgia's statewide assessment known as the Criterion-Referenced Competency Test (CRCT). Achievement data of 2 groups that received Thinking Maps instruction for 2 years was compared to 1 group that did not. An analysis of covariance was used to analyze the assessment data. The findings suggest that the students who did not use Thinking Maps performed significantly better than those who did use Thinking Maps, even though both groups showed positive mean score gains from 2010 to 2012 on the science portion of the CRCT. Limitations of the study, such as the lack of randomization and manipulation of the independent variable, suggest that further research is needed to fairly evaluate the program and its effectiveness. Also, the instructional setting and amount of time used for science instruction in the elementary classroom warrants additional investigation. Findings related to the implementation and use of graphic tools such as Thinking Maps will help school systems choose professional learning opportunities and effective instructional strategies to develop content literacy.

Effective Instruction: A Mathematics Coach's Perspective

ERIC Educational Resources Information Center

Nebesniak, Amy L.

2012-01-01

Effective instruction is multifaceted, dependent largely on the context and, consequently, on numerous variables. Although "effective instruction" is difficult to define, in the author's experience--and as the work of mathematics education specialists and researchers indicates--three key features of quality instruction stand out: (1) Teaching…

Mathematics Instruction for Students with Emotional and Behavioral Disorders: A Best-Evidence Synthesis

ERIC Educational Resources Information Center

Ralston, Nicole C.; Benner, Gregory J.; Tsai, Shu-Fei; Riccomini, Paul J.; Nelson, J. Ron

2014-01-01

The authors report findings of a best-evidence synthesis of the effects of mathematics instruction on the mathematics skills of students with emotional and behavioral disorders. The goal of the synthesis was to extend previous research by (a) detailing independent variables, instructional components, and outcome measures for each study; (b)…

Information Communication Technology Pedagogical Integration in Mathematics Instruction among Teachers in Secondary Schools in Kenya

ERIC Educational Resources Information Center

Wanjala, Martin

2016-01-01

This paper reports finding of the study that sought to ascertain the extent of ICT-pedagogical integration in mathematics instruction among secondary school teachers in Kenya. Information was sought on professional development experiences and needs in computer technology use in mathematics instruction, the type of computer software used in…

Secondary School Students' Attitudes towards Mathematics Computer--Assisted Instruction Environment in Kenya

ERIC Educational Resources Information Center

Mwei, Philip K.; Wando, Dave; Too, Jackson K.

2012-01-01

This paper reports the results of research conducted in six classes (Form IV) with 205 students with a sample of 94 respondents. Data represent students' statements that describe (a) the role of Mathematics teachers in a computer-assisted instruction (CAI) environment and (b) effectiveness of CAI in Mathematics instruction. The results indicated…

Quality Mathematics Instructional Practices Contributing to Student Achievements in Five High-Achieving Asian Education Systems: An Analysis Using TIMSS 2011 Data

ERIC Educational Resources Information Center

Cheng, Qiang

2014-01-01

Although teaching quality is seen as crucial in affecting students' performance, what types of instructional practices constitute quality teaching remains a question. With the theoretical assumptions of conceptual and procedural mathematics teaching as a guide, this study examined the types of quality mathematics instructional practices that…

A Methodology for Instructional Design in Mathematics--With the Generic and Epistemic Student at the Centre

ERIC Educational Resources Information Center

Strømskag, Heidi

2017-01-01

This theoretical paper presents a methodology for instructional design in mathematics. It is a theoretical analysis of a proposed model for instructional design, where tasks are embedded in situations that preserve meaning with respect to particular pieces of mathematical knowledge. The model is applicable when there is an intention of teaching…

Improving Mathematics Instruction Using Technology: A Vygotskian Perspective.

ERIC Educational Resources Information Center

Harvey, Francis A.; Charnitski, Christina Wotell

Strategies and programs for improving mathematics instruction should be derived from sound educational theory. The sociocultural learning theories of Vygotsky may offer guidance in developing technology-based mathematics curriculum materials consonant with the NCTM (National Council of Teachers of Mathematics) goals and objectives. Vygotsky's…

Hypnosis, suggestions, and altered states of consciousness: experimental evaluation of the new cognitive-behavioral theory and the traditional trance-state theory of "hypnosis".

PubMed

Barber, T X; Wilson, S C

1977-10-07

Sixty-six subjects were tested on a new scale for evaluating "hypnotic-like" experiences (The Creative Imagination Scale), which includes ten standardized test-suggestions (e.g. suggestions for arm heaviness, finger anesthesia, time distortion, and age regression). The subjects were randomly assigned to one of three treatment groups (Think-With Instructions, trance induction, and Control), with 22 subjects to each group. The new Cognitive-Behavioral Theory predicted that subjects exposed to preliminary instructions designed to demonstrate how to think and imagine along with the suggested themes (Think-With Instructions) would be more responsive to test-suggestions for anesthesia, time distortion, age regression, and so on, than subjects exposed to a trance-induction procedure. On the other hand, the traditional Trance State Theory predicted that a trance induction would be more effective than Think-With Instructions in enhancing responses to such suggestions. Subjects exposed to the Think-With Instructions obtained significantly higher scores on the test-suggestions than those exposed either to the traditional trance-induction procedure or to the control treatment. Scores of subjects who received the trance-induction procedure were not significantly different from those of the subjects who received the control treatment. The results thus supported the new Cognitive-Behavioral Theory and contradicted the traditional Trance State Theory of hypnosis. Two recent experiments, by De Stefano and by Katz, confirmed the above experimental results and offered further support for the Cognitive-Behavioral Theory. In both recent experiments, subjects randomly assigned to a "Think-With Instructions" treatment were more responsive to test-suggestions than those randomly assigned to a traditional trance-induction treatment.

Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

NASA Astrophysics Data System (ADS)

Misu, La; Ketut Budayasa, I.; Lukito, Agung

2018-03-01

This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

The Effects of a Computer-Assisted Teaching Material, Designed According to the ASSURE Instructional Design and the ARCS Model of Motivation, on Students' Achievement Levels in a Mathematics Lesson and Their Resulting Attitudes

ERIC Educational Resources Information Center

Karakis, Hilal; Karamete, Aysen; Okçu, Aydin

2016-01-01

This study examined the effects that computer-assisted instruction had on students' attitudes toward a mathematics lesson and toward learning mathematics with computer-assisted instruction. The computer software we used was based on the ASSURE Instructional Systems Design and the ARCS Model of Motivation, and the software was designed to teach…

Differentiated Instruction: Understanding the Personal Factors and Organizational Conditions that Facilitate Differentiated Instruction in Elementary Mathematics Classrooms

ERIC Educational Resources Information Center

Abbati, Diana Guglielmo

2012-01-01

Differentiated instruction is a widely held practice used by teachers to provide diverse learners with complex learning opportunities in the area of mathematics. Research on differentiated instruction shows a multitude of factors that support high quality instruction in mixed-ability elementary classrooms. These factors include small-class size,…

Setting Instructional Expectations: Patterns of Principal Leadership for Middle School Mathematics

ERIC Educational Resources Information Center

Katterfeld, Karin

2013-01-01

Principal instructional leadership has been found to support improved instruction. However, the methods through which principal leadership influences classroom instruction are less clear. This study investigates how principals' leadership may predict the expectations that mathematics teachers perceive for classroom practice. Results from a…

The Implementation of Open-Inquiry Approach to Improve Students' Learning Activities, Responses, and Mathematical Creative Thinking Skills

ERIC Educational Resources Information Center

Kadir; Lucyana; Satriawati, Gusni

2017-01-01

This study aims to reveal the improvement of the students' learning activities, responses, and mathematical creative thinking skills (MCTS) through open-inquiry approach (OIA). Other relevant studies in mathematics learning tend to focus on guided inquiry, and especially in Indonesia, OIA is still less applied. This study is conducted at State…

Thinking Out Loud while Studying Text: Rehearsing Key Ideas.

ERIC Educational Resources Information Center

Muth, K. Denise; And Others

1988-01-01

A study involving 32 undergraduate students was conducted to identify mechanisms by which instructional objectives affect learning. Protocols for thinking out loud were examined for evidence of rehearsal activity. Results suggest that instructional objectives enhanced real-time rehearsal activity, recall, and reading time. (TJH)

Teachers' Beliefs and Teaching Mathematics with Manipulatives

ERIC Educational Resources Information Center

Golafshani, Nahid

2013-01-01

To promote the implementation of manipulatives into mathematics instruction, this research project examined how the instructional practices of four Grade 9 applied mathematics teachers related to their beliefs about the use of manipulatives in teaching mathematics, its effects on students' learning, and enabling and disabling factors. Teacher…

Preservice Teachers' Perceptions of the Integration of Mathematics, Reading, and Writing.

ERIC Educational Resources Information Center

Reinke, Kathryn; Mokhtari, Kouider; Willner, Elizabeth

1997-01-01

Examined the perceptions of preservice elementary teachers enrolled in reading, mathematics, and integrating reading and mathematics methods courses about integrating mathematics, reading, and writing instruction at the elementary/middle school level. Surveys indicated that all students were generally positive about instructional integration. They…

The Role of Real-Life Mathematics Instruction on Mathematics Outcomes in Kindergarten

ERIC Educational Resources Information Center

Gottfried, Michael

2016-01-01

In an era of a declining quality and quantity of students entering and persisting in mathematics in the USA, researchers and policy makers are looking for new strategies to engage students in these fields and improve mathematics outcomes. One push has been to make mathematics instruction more relevant with real-world applications throughout the…

Effects of Animated Agents in Web-Based Instruction on Mathematics: Achievement and Attitudes toward Mathematics

ERIC Educational Resources Information Center

Lodree, Anika W.; Moore, Joi L.; Gilbert, Juan E.

2008-01-01

This article summarizes a quantitative study of the effects of animated agents in web-based instruction (WBI) on mathematics achievement and attitudes toward mathematics in postsecondary education. Eighty-one college students who were enrolled in a core mathematic course at a doctoral/research-extensive university in central Alabama participated…

An Analysis of Mathematics Interventions: Increased Time-on-Task Compared with Computer-Assisted Mathematics Instruction

ERIC Educational Resources Information Center

Calhoun, James M., Jr.

2011-01-01

Student achievement is not progressing on mathematics as measured by state, national, and international assessments. Much of the research points to mathematics curriculum and instruction as the root cause of student failure to achieve at levels comparable to other nations. Since mathematics is regarded as a gate keeper to many educational…

The Effectiveness of Local Culture-Based Mathematical Heuristic-KR Learning towards Enhancing Student's Creative Thinking Skill

ERIC Educational Resources Information Center

Tandiseru, Selvi Rajuaty

2015-01-01

The problem in this research is the lack of creative thinking skills of students. One of the learning models that is expected to enhance student's creative thinking skill is the local culture-based mathematical heuristic-KR learning model (LC-BMHLM). Heuristic-KR is a learning model which was introduced by Krulik and Rudnick (1995) that is the…

Integrating Mathematics, Science, and Language Arts Instruction Using the World Wide Web.

ERIC Educational Resources Information Center

Clark, Kenneth; Hosticka, Alice; Kent, Judi; Browne, Ron

1998-01-01

Addresses issues of access to World Wide Web sites, mathematics and science content-resources available on the Web, and methods for integrating mathematics, science, and language arts instruction. (Author/ASK)

Equity-Directed Instructional Practices: Beyond the Dominant Perspective

ERIC Educational Resources Information Center

Rubel, Laurie H.

2017-01-01

In this article, the author synthesizes four equity-directed instructional practices: standards-based mathematics instruction, complex instruction, culturally relevant pedagogy (CRP), and teaching mathematics for social justice (TMfSJ). The author organizes these practices according to the dominant and critical axes in Gutiérrez's (2007a) equity…

The Effect of an Instructional Model Utilizing Hands-on Learning and Manipulatives on Math Achievement of Middle School Students in Georgia

ERIC Educational Resources Information Center

White, Kara Morgan

2012-01-01

The concepts and ideas of mathematics is a major element of educational curriculum. Many different instructional strategies are implemented in mathematics classrooms. The purpose of this study was to evaluate the effect of an instructional model utilizing hands-on learning and use of manipulatives on mathematics achievement of middle school…

The materiality of mathematics: presenting mathematics at the blackboard.

PubMed

Greiffenhagen, Christian

2014-09-01

Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.

Single-Sex Mathematics Instruction in an Urban Independent School.

ERIC Educational Resources Information Center

Seitsinger, Anne M.; Barboza, Helen C.; Hird, Anne

An urban independent middle school grouped its 63 sixth and seventh graders into single-sex mathematics classes (SSMC) to improve girls' achievement in mathematics (AIM) and attitudes toward mathematics (ATM) with no negative impact on boys. Researchers analyzed AIM, ATM, and interactions/instruction. AIM measures included Metropolitan Achievement…

Preservice and Inservice Mathematics Teachers' Perspectives of High-Quality Mathematics Instruction

ERIC Educational Resources Information Center

Clooney, Sarah; Cunningham, Robert F.

2017-01-01

This study examined the perspectives of what high-quality mathematics instruction looks like. Written responses from preservice (n = 20) and inservice (n = 16) mathematics teachers were collected and categorized according to the Ten Principles developed by Anthony & Walshaw (2009). The responses of preservice teachers more often than inservice…

Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development.

ERIC Educational Resources Information Center

Stein, Mary Kay; Smith, Margaret Schwan; Henningsen, Marjorie A.; Silver, Edward A.

Teachers and teacher educators interested in synthesizing their current practice with new mathematics standards will welcome this highly useful volume. The QUASAR Project at the University of Pittsburgh presents prevalent cases of mathematics instruction drawn from their research of nearly 500 classroom lessons. The Mathematical Tasks…

Mathematics for Language, Language for Mathematics

ERIC Educational Resources Information Center

Prochazkova, Lenka Tejkalova

2013-01-01

The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

ERIC Educational Resources Information Center

Weber, Keith; Inglis, Matthew; Mejia-Ramos, Juan Pablo

2014-01-01

The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion…

Gender: Its relation to Mathematical Creative Thinking Skill

NASA Astrophysics Data System (ADS)

Permatasari, H. R.; Wahyudin, W.

2017-09-01

Mathematical creative thinking skill is one of the most important capabilities in the present century, both for men and women. One of the current issues is about gender and how gender mainstreaming can be realized optimally. The purpose of this study is to determine the comparison of the mathematical creative thinking skill increasing between male and female students after the application of Team Games Tournament (TGT) learning. This research was conducted at 28 students in the 4th grade of an elementary school in Bandung City. The research method used is quasi experiment because it is aimed to test wether there are differences in mathematical creative thinking skill improving between male and female students after being treatment in the form of learnig with TGT. The result of this research is that there is no difference in mathematical creative thinking skill improving between male and female students after the application of TGT learning. It is influenced by some factors such as how the teacher treats male and female with the same treatment in learning process. Recommendation of this research that can be done further research about this topic more deeply. Beside that, the teacher especially in elementary school can use the TGT learning application to reduce the gap between male and female students during the learning process.

Developing geospatial thinking and the science practices of investigation and evalutation with geographic information systems

NASA Astrophysics Data System (ADS)

Hamilton, Kelli

Geospatial thinking is a subset of spatial thinking, which has been identified by the National Geography Standards as an essential skill for students to gain through geography instruction (Heffron & Downs, 2013). One tool which has been shown to help students develop their geospatial thinking skills is Geographic Information Systems (GIS) (Kim & Bednraz, 2013; Lee & Bednarz, 2009; Patterson, 2007). Much of the research conducted with GIS has been in the context of social studies classrooms. This study examined the use of GIS with seventh grade students in a science classroom. Results of this study indicate that students who use GIS as part of their science instruction are able to practice geospatial thinking skills. In addition, this study examined how GIS could be used to enhance the instruction of the science practices of investigation and evaluation. The Next Generation Science Standards identify certain science practices which students should experience as part of science instruction (NGSS Lead States, 2013). Among those practices are investigation and evaluation. Students in this study used GIS to investigate and evaluate scientific data. Both the teacher and the students were able to identify ways that GIS enhanced both the investigation and evaluation of data.

Monitoring Reading Comprehension by Thinking Aloud. Instructional Resource No. 1.

ERIC Educational Resources Information Center

Baumann, James F.; And Others

A think-aloud instructional program was developed to help students acquire the ability to monitor their reading comprehension and to employ various strategies to deal with comprehension breakdowns. Several research studies indicate that comprehension monitoring abilities discriminate successful readers from less successful ones and that…

Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

PubMed Central

Morgan, Paul L.; Farkas, George; Maczuga, Steve

2015-01-01

We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by 1st grade teachers in the U.S. and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement—three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in 1st grade classrooms was associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted ESs = .05–.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and student-centered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ESs = .03–.04). First-grade teachers in the U.S. may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD. PMID:26180268

A Randomized Controlled Trial of the Impact of Schema-Based Instruction on Mathematical Outcomes for Third-Grade Students with Mathematics Difficulties

ERIC Educational Resources Information Center

Jitendra, Asha K.; Dupuis, Danielle N.; Rodriguez, Michael C.; Zaslofsky, Anne F.; Slater, Susan; Cozine-Corroy, Kelly; Church, Chris

2013-01-01

This study compared the effects of delivering a supplemental, small-group tutoring intervention on the mathematics outcomes of third-grade students at risk for mathematics difficulties (MD) who were randomly assigned to either a schema-based instruction (SBI) or control group. SBI emphasized the underlying mathematical structure of additive…

Improving Middle School Students’ Critical Thinking Skills Through Reading Infusion-Loaded Discovery Learning Model in the Science Instruction

NASA Astrophysics Data System (ADS)

Nuryakin; Riandi

2017-02-01

A study has been conducted to obtain a depiction of middle school students’ critical thinking skills improvement through the implementation of reading infusion-loaded discovery learning model in science instruction. A quasi-experimental study with the pretest-posttest control group design was used to engage 55 eighth-year middle school students in Tasikmalaya, which was divided into the experimental and control group respectively were 28 and 27 students. Critical thinking skills were measured using a critical thinking skills test in multiple-choice with reason format questions that administered before and after a given instruction. The test was 28 items encompassing three essential concepts, vibration, waves and auditory senses. The critical thinking skills improvement was determined by using the normalized gain score and statistically analyzed by using Mann-Whitney U test.. The findings showed that the average of students’ critical thinking skills normalized gain score of both groups were 59 and 43, respectively for experimental and control group in the medium category. There were significant differences between both group’s improvement. Thus, the implementation of reading infusion-loaded discovery learning model could further improve middle school students’ critical thinking skills than conventional learning.

Developing Mathematical Thinking in the Primary Classroom: Liberating Students and Teachers as Learners of Mathematics

ERIC Educational Resources Information Center

Hudson, Brian; Henderson, Sheila; Hudson, Alison

2015-01-01

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011-2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of…

La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

ERIC Educational Resources Information Center

Cable, John

2014-01-01

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…

Neurally and mathematically motivated architecture for language and thought.

PubMed

Perlovsky, L I; Ilin, R

2010-01-01

Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt's "firmness" of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined.

Neurally and Mathematically Motivated Architecture for Language and Thought

PubMed Central

Perlovsky, L.I; Ilin, R

2010-01-01

Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt’s “firmness” of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined. PMID:21673788

Supporting Productive Struggle with Communication Moves

ERIC Educational Resources Information Center

Freeburn, Ben; Arbaugh, Fran

2017-01-01

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014, p. 10) contains eight research-informed teaching practices that have been shown to support students' mathematical thinking and learning. Two teaching practices highlighted herein are "to elicit and use evidence of students' thinking" and "support…

Adding structure to the transition process to advanced mathematical activity

NASA Astrophysics Data System (ADS)

Engelbrecht, Johann

2010-03-01

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical deductive reasoning, required in advanced mathematics. It is necessary to assist students in this transition process, in moving from general to mathematical thinking. In this article some structure is suggested for this transition period. This essay is an argumentative exposition supported by personal experience and international literature. This makes this study theoretical rather than empirical.

The co-development and interrelation of proof and authority: The case of Yana and Ronit

NASA Astrophysics Data System (ADS)

Fried, Michael N.; Amit, Miriam

2008-12-01

Students' mathematical lives are characterized not only by a set of mathematical ideas and the engagement in mathematical thinking, but also by social relations, specifically, relations of authority. Watching student actions and speaking to students, one becomes cognizant of a `web of authority' ever present in mathematics classrooms. In past work, it has been shown how those relations of authority may sometimes interfere with students' reflecting on mathematical ideas. However, "…by shifting the emphasis from domination and obedience to negotiation and consent…" (Amit & Fried, 2005, p.164) it has also been stressed that these relations are fluid and are, in fact, a sine qua non in the process of students' defining their place in a mathematical community. But can these fluid relations be operative also in the formation of specific mathematical ideas? It is my contention that they may at least coincide with students' thinking about one significant mathematical idea, namely, the idea of proof. In this talk, I shall discuss both the general question of authority in the mathematics classroom and its specific connection with students' thinking about proof in the context of work done in two 8th grade classrooms.

Strengthening Mathematics And Science Education (SMASE) For Improving The Quality Of Teachers in Nigeria

NASA Astrophysics Data System (ADS)

Shuaibu, Zainab Muhammad

2016-04-01

The education system in Nigeria, especially at the basic education level, teachers who teach mathematics and science need to be confident with what they are teaching, they need to have appropriate techniques and strategies of motivating the pupils. If these subjects are not taught well at the basic education level its extraordinarily hard to get them (pupils/students) back to track, no matter what will be done in the secondary and tertiary level. Teachers as the driving force behind improvements in the education system are in the best position to understand and propose solutions to problems faced by students. Teachers must have access to sustainable, high quality professional development in order to improve teaching and student learning. Teachers' professional development in Nigeria, however, has long been criticized for its lack of sustainability and ability to produce effective change in teaching and students achievement. Education theorists today believe that a critical component of educational reform lies in providing teachers with various opportunities and supports structures that encourage ongoing improvement in teachers' pedagogy and discipline-specific content knowledge. However, the ongoing reforms in education sector and the need to refocus the Nigeria education system towards the goal of the National Economical Empowerment and Development Strategies (NEEDS) demand that the existing In-service and Education Training (INSET) in Nigeria be refocused. It is against this premise that an INSET programme aimed at Strengthening Mathematics And Science Education (SMASE) for primary and secondary school teachers was conceived. The relevance of the SMASE INSET according to the Project Design Matrix (PDM) was derived from an In-service aimed at enhancing the quality of teachers in terms of positive attitude, teaching methodology, mastery of content, resource mobilization and utilization of locally available teaching and learning materials. The intervention of Strengthening Mathematics And Science Education (SMASE) in training and re-training of teachers at enhancing quality classroom activities in Mathematics and Science subjects through Activity, Student-centre, Experiments, Improvisation (ASEI)-Plan, Do, See, Improve (PDSI) instructional strategy. This instructional strategy has cultivates learner's mathematical and scientific thinking ability and have provided one of the best regular INSET for primary and secondary Mathematics and Science teachers as observed during the SMASE impact survey in the three piloted states in Nigeria. To build a common ground for teaching method irrespective of teacher and teaching style School-Based Training (SBT) is now advocated in SMASE, SBT is aimed at improving teaching and learning activities in the classroom through Lesson Study model. Lesson Study is a teaching improvement and knowledge building process that has its origin in the Japanese elementary education it involves a comprehensive process of planning, observation, analysis and identifying the best approaches in a classroom. This an inquiry approach to professional development that requires teachers to identify an area of instructional interest, collect data to analyses and make instructional changes based on the data. This kind of professional development make teachers acquires current and up to date knowledge in the field of mathematics and science.

Using Performance Task Data to Improve Instruction

ERIC Educational Resources Information Center

Abbott, Amy L.; Wren, Douglas G.

2016-01-01

Two well-accepted ideas among educators are (a) performance assessment is an effective means of assessing higher-order thinking skills and (b) data-driven instruction planning is a valuable tool for optimizing student learning. This article describes a locally developed performance task (LDPT) designed to measure critical thinking, problem…

Developing Reflective Thinking Instructional Model for Enhancing Students' Desirable Learning Outcomes

ERIC Educational Resources Information Center

Porntaweekul, Satjatam; Raksasataya, Sarintip; Nethanomsak, Teerachai

2016-01-01

This work aims to investigate the reflective thinking instructional model for enhancing empowerment of pre-service and in-service educational students in Roi-Et Rajabhat University, Thailand. In this research, qualitative methods, observation, interview, short note, and group discussion were used to indicate students' desirable learning outcomes,…

Meaningful Gamification for Journalism Students to Enhance Their Critical Thinking Skills

ERIC Educational Resources Information Center

Huang, Ling-Yi; Yeh, Yu-Chu

2017-01-01

Training in critical thinking is essential for the professional development of journalism students. To achieve this goal, this study developed a gamified platform and a blended learning curriculum. During an 18-week experimental instruction period, a series of instructional activities, which included online discussions as well as classroom…

Critical Thinking: Comparing Instructional Methodologies in a Senior-Year Learning Community

ERIC Educational Resources Information Center

Zelizer, Deborah A.

2013-01-01

This quasi-experimental, nonequivalent control group study compared the impact of Ennis's (1989) mixed instructional methodology to the immersion methodology on the development of critical thinking in a multicultural, undergraduate senior-year learning community. A convenience sample of students (n =171) were selected from four sections of a…

Thinking and Content Learning of Mathematics and Science as Cognitional Development in Content and Language Integrated Learning (CLIL): Teaching Through a Foreign Language in Finland

ERIC Educational Resources Information Center

Jappinen, Aini-Kristiina

2005-01-01

This paper presents a study on thinking and learning processes of mathematics and science in teaching through a foreign language, in Finland. The entity of thinking and content learning processes is, in this study, considered as cognitional development. Teaching through a foreign language is here called Content and Language Integrated Learning or…

The QUASAR Project: The "Revolution of the Possible" in Mathematics Instructional Reform in Urban Middle Schools.

ERIC Educational Resources Information Center

Silver, Edward A.; Stein, Mary Kay

1996-01-01

Examines critical features of the QUASAR Project, a mathematics instruction program oriented toward helping students develop a meaningful understanding of mathematical ideas through challenging mathematical tasks, and discusses findings regarding the positive impact it has had on students. Challenges and obstacles in implementing the project are…

Using Five-Frames in Preschool Mathematics Instruction

ERIC Educational Resources Information Center

Rizer, Jennifer

2017-01-01

Mathematics education is a critical part of instruction for students around the globe. The foundation for understanding basic mathematical concepts begins early in life. Preschool classrooms can provide the early skills in mathematical reasoning that will be needed later in life. In this study, the author sought to determine if the use of…

A Framework for Describing Mathematics Discourse in Instruction and Interpreting Differences in Teaching

ERIC Educational Resources Information Center

Adler, Jill; Ronda, Erlina

2015-01-01

We describe and use an analytical framework to document mathematics discourse in instruction (MDI), and interpret differences in mathematics teaching. MDI is characterised by four interacting components in the teaching of a mathematics lesson: exemplification (occurring through a sequence of examples and related tasks), explanatory talk (talk that…

Support of mathematical thinking through embodied cognition: Nondigital and digital approaches.

PubMed

Tran, Cathy; Smith, Brandon; Buschkuehl, Martin

2017-01-01

Research on mathematics education has shown that learners' actions can influence how they think and vice versa. Much of this work has been rooted in the use of manipulatives, gestures, and body movements. Our article dissects the mechanisms that underscore the impact of embodied activities and applies this lens to explore how to harness the affordances of new technology to enhance mathematical thinking. This is especially crucial given the increasing accessibility of technology-such as digital touch devices, 3D printers, and location sensors-for constructing embodied experiences. Providing guidance for incorporating those tools, we focus on the role that embodied cognition can play in communicating mathematical concepts as well as in allowing learners to experiment and evolve their ideas. To inspire future integration of theory in the development of technologically enhanced embodied mathematics experiences, we provide examples of how this can be done. Finally, we outline future directions in the areas of design, implementation, and assessment of embodied learning of mathematics.

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

NASA Astrophysics Data System (ADS)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

Discrete mathematics in deaf education: a survey of teachers' knowledge and use.

PubMed

Pagliaro, Claudia M; Kritzer, Karen L

The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United States. Findings indicate that deaf education teachers are familiar with many discrete mathematics topics but do not include them in instruction because they consider the concepts too complicated for their students. Also, regardless of familiarity level, deaf education teachers are not familiar with discrete mathematics terminology; nor is their mathematics teaching structured to provide opportunities to apply the real-world-oriented activities used in discrete mathematics instruction. Findings emphasize the need for higher expectations of students with hearing loss, and for reform in mathematics curriculum and instruction within deaf education.

Technology to Develop Algebraic Reasoning

ERIC Educational Resources Information Center

Polly, Drew

2011-01-01

Students' use of technology allows them to generate and manipulate multiple representations of a concept, compute numbers with relative ease, and focus more on mathematical concepts and higher-order thinking skills. In elementary school mathematics classrooms, students develop higher-order thinking skills by completing complex tasks that require…

Promoting middle school students’ mathematical creative thinking ability using scientific approach

NASA Astrophysics Data System (ADS)

Istiqomah, A.; Perbowo, K. S.; Purwanto, S. E.

2018-01-01

This research aims to identify the strength of scientific approach in order to develop mathematical creative thinking in junior high school. Descriptive qualitative method is used in this research. 34 students in 7th grade are chosen using purposive sampling. For collecting data, this research uses test, observation, and interview. The test consists of 6 items which have been tested for their validity and reliability and used in pre-test and post-test. The pre-test shows that students average score in mathematical creative thinking is 43 (low), while in post-test it is 69 (middle). The N-gain in mathematical creative thinking point is 0.461, which is classified in the middle grade. Furthermore, the N-gain for each indicator, they score 0.438 for fluency; 0.568 for flexibility; and 0.382 for novelty. The N-gain for those indicators falls under middle grade. The research shows that scientific approach develops more flexibility, and, on the other hand, it develops less novelty.

Precalculus teachers' perspectives on using graphing calculators: an example from one curriculum

NASA Astrophysics Data System (ADS)

Karadeniz, Ilyas; Thompson, Denisse R.

2018-01-01

Graphing calculators are hand-held technological tools currently used in mathematics classrooms. Teachers' perspectives on using graphing calculators are important in terms of exploring what teachers think about using such technology in advanced mathematics courses, particularly precalculus courses. A descriptive intrinsic case study was conducted to analyse the perspectives of 11 teachers using graphing calculators with potential Computer Algebra System (CAS) capability while teaching Functions, Statistics, and Trigonometry, a precalculus course for 11th-grade students developed by the University of Chicago School Mathematics Project. Data were collected from multiple sources as part of a curriculum evaluation study conducted during the 2007-2008 school year. Although all teachers were using the same curriculum that integrated CAS into the instructional materials, teachers had mixed views about the technology. Graphing calculator features were used much more than CAS features, with many teachers concerned about the use of CAS because of pressures from external assessments. In addition, several teachers found it overwhelming to learn a new technology at the same time they were learning a new curriculum. The results have implications for curriculum developers and others working with teachers to update curriculum and the use of advanced technologies simultaneously.

The development of a valid discovery-based learning module to improve students' mathematical connection

NASA Astrophysics Data System (ADS)

Kuneni, Erna; Mardiyana, Pramudya, Ikrar

2017-08-01

Geometry is the most important branch in mathematics. The purpose of teaching this material is to develop students' level of thinking for a better understanding. Otherwise, geometry in particular, has contributed students' failure in mathematics examinations. This problem occurs due to special feature in geometry which has complexity of correlation among its concept. This relates to mathematical connection. It is still difficult for students to improve this ability. This is because teachers' lack in facilitating students towards it. Eventhough, facilitating students can be in the form of teaching material. A learning module can be a solution because it consists of series activities that should be taken by students to achieve a certain goal. A series activities in this case is adopted by the phases of discovery-based learning model. Through this module, students are facilitated to discover concept by deep instruction and guidance. It can build the mathematical habits of mind and also strengthen the mathematical connection. Method used in this research was ten stages of research and development proposed by Bord and Gall. The research purpose is to create a valid learning module to improve students' mathematical connection in teaching quadrilateral. The retrieved valid module based on media expert judgment is 2,43 for eligibility chart aspect, 2,60 for eligibility presentation aspect, and 3,00 for eligibility contents aspect. Then the retrieved valid module based on material expert judgment is 3,10 for eligibility content aspect, 2,87 for eligibility presentation aspect, and 2,80 for eligibility language and legibility aspect.

Exploring the Possibilities of Using Tic-Tac-Toe to Think and Communicate about Mathematics

ERIC Educational Resources Information Center

Clarkson, Philip C.

2008-01-01

Doing mathematics, and thinking about how you are doing it at the same time, are not the easiest things to do. It is even more difficult if students are not aware that they should be attempting both processes at the same time. They are likely to concentrate on the immediate task of "doing" the mathematics, rather than trying to access the deeper…

Growing of the mathematical thinking imaginative to students in designing of the teaching aids for CWD towards to joyful learning

NASA Astrophysics Data System (ADS)

Sugiman; Sugiharti, E.; Kurniawati, N. F.

2018-03-01

Government and the private parties had also organized of Special School (SS) and Inclusive School. SS requires of math teachers who were professional in the material, but also master the needs of Children with Disabilities (CwD) in teaching-learning process. The problem: How to design the Teaching Aids for CwD through Extra-Curriculum Training (ECT) activities to Joyful Learning? The purposes of this research: (1) To find new ways how to grow the imaginative in mathematical thinking for students of Mathematics Education. (2) To find a Teaching Aids Design that suitable for CwD who studying in SS. (3) In order to create a Teaching Aids for CwD through activities based on ECT to Joyful Learning. The research method was done by qualitative approach. The research subjects were 6 students of Mathematics Education Study Program of FMIPA UNNES who were interested in attending of the training activities based on ECT. The results: (1) ECT can be a place to grow an Imaginative in Mathematical Thinking of students, (2) created the design of the teaching aids for CwD through activities based on ECT to Joyful Learning as a mirror of the imaginative growth in mathematical thinking for students.

Examination of the Computational Thinking Skills of Students

ERIC Educational Resources Information Center

Korucu, Agah Tugrul; Gencturk, Abdullah Tarik; Gundogdu, Mustafa Mucahit

2017-01-01

Computational thinking is generally considered as a kind of analytical way of thinking. According to Wings (2008) it shares with mathematical thinking, engineering thinking and scientific thinking in the general ways in which we may use for solving a problem, designing and evaluating complex systems or understanding computability and intelligence…

Indicators of Multiplicative Reasoning among Fourth Grade Students

ERIC Educational Resources Information Center

Carrier, James A.

2010-01-01

Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

2012 National Survey of Science and Mathematics Education: Status of Middle School Mathematics

ERIC Educational Resources Information Center

Fulkerson, William O.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

2012 National Survey of Science and Mathematics Education: Status of Elementary School Mathematics

ERIC Educational Resources Information Center

Malzahn, Kristen A.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

Teachers' Beliefs and Technology: Calculator Use in Mathematics Instruction in Junior Secondary Schools in Botswana

ERIC Educational Resources Information Center

Salani, End

2013-01-01

Lesson starts are transitional events which may cause management problems for teachers. This study sought junior secondary school mathematics teachers' beliefs about calculator use in mathematics instruction in Botswana and was descriptive in nature adopting a survey design. The sample of seventeen (17) mathematics teachers from four (4) junior…

2012 National Survey of Science and Mathematics Education: Status of High School Mathematics

ERIC Educational Resources Information Center

Smith, Adrienne A.

2013-01-01

The 2012 National Survey of Science and Mathematics Education was designed to provide up-to-date information and to identify trends in the areas of teacher background and experience, curriculum and instruction, and the availability and use of instructional resources. A total of 7,752 science and mathematics teachers in schools across the United…

Mathematics Instruction for Middle School Students with and At-Risk for Behavioral Disorders: A Survey Study

ERIC Educational Resources Information Center

Jones, Stacey Eagan Lefort

2012-01-01

This survey study was designed to investigate mathematics instruction for middle school students with and at-risk for emotional and behavioral disorders (EBD). It sought to identify who is teaching mathematics to students with and at-risk for EBD, investigate if mathematics and special education teachers are implementing recommended curricula and…

Efficacy of the Technological/Engineering Design Approach: Imposed Cognitive Demands within Design-Based Biotechnology Instruction

ERIC Educational Resources Information Center

Wells, John G.

2016-01-01

Though not empirically established as an efficacious pedagogy for promoting higher order thinking skills, technological/engineering design-based learning in K-12 STEM education is increasingly embraced as a core instructional method for integrative STEM learning that promotes the development of student critical thinking skills (Honey, Pearson,…

Developing the Strategic Thinking of Instructional Leaders. Occasional Paper No. 13.

ERIC Educational Resources Information Center

Hallinger, Philip; McCary, C. E.

Emerging research on instructional leadership is examined in this paper, with a focus on the new perspective on strategic thinking. The main theme is that research must address the reasoning that underlies the exercise of leadership rather than describe discrete behaviors of effective leaders. A computer simulation designed to facilitate the…

Helping Librarians To Encourage Critical Thinking through Active Learning Techniques in Library Instruction.

ERIC Educational Resources Information Center

Swaine, Cynthia Wright

Encouraging librarians to incorporate critical thinking skills and active learning techniques in their course instruction requires more than talking about it in a department meeting or distributing articles on the topic. At Old Dominion University (Virginia), librarians have tried conducting workshops, had readily-accessible binders of articles…

Systematic Design of a Learning Environment for Domain-Specific and Domain-General Critical Thinking Skills

ERIC Educational Resources Information Center

Tiruneh, Dawit Tibebu; Weldeslassie, Ataklti G.; Kassa, Abrham; Tefera, Zinaye; De Cock, Mieke; Elen, Jan

2016-01-01

Identifying effective instructional approaches that stimulate students' critical thinking (CT) has been the focus of a large body of empirical research. However, there is little agreement on the instructional principles and procedures that are theoretically sound and empirically valid to developing both domain-specific and domain-general CT…

Cognitive Science and Instructional Technology: Improvements in Higher Order Thinking Strategies.

ERIC Educational Resources Information Center

Tennyson, Robert D.

This paper examines the cognitive processes associated with higher-order thinking strategies--i.e., cognitive processes directly associated with the employment of knowledge in the service of problem solving and creativity--in order to more clearly define a prescribed instructional method to improve problem-solving skills. The first section of the…

Development of Mathematics Learning Strategy Module, Based on Higher Order Thinking Skill (Hots) To Improve Mathematic Communication And Self Efficacy On Students Mathematics Department

NASA Astrophysics Data System (ADS)

Andriani, Ade; Dewi, Izwita; Halomoan, Budi

2018-03-01

In general, this research is conducted to improve the quality of lectures on mathematics learning strategy in Mathematics Department. The specific objective of this research is to develop learning instrument of mathematics learning strategy based on Higher Order Thinking Skill (HOTS) that can be used to improve mathematical communication and self efficacy of mathematics education students. The type of research is development research (Research & Development), where this research aims to develop a new product or improve the product that has been made. This development research refers to the four-D Model, which consists of four stages: defining, designing, developing, and disseminating. The instrument of this research is the validation sheet and the student response sheet of the instrument.

Teachers' Self-Efficacy in Mathematics and Teaching Mathematics, Instructional Practices, and the Mississippi Curriculum Test, Second Edition for Mathematics in Grades 3-5

ERIC Educational Resources Information Center

Yates, Tracy Hardwell

2014-01-01

The purpose of this correlational study was to examine the relationship among the mathematical self-efficacies, mathematical teaching self-efficacies, and instructional practices of elementary teachers. This study was also designed to determine how these variables influence an individual teacher's QDI in relation to MCT2 math scores in grades 3-5.…

The analysis of student’s critical thinking ability on discovery learning by using hand on activity based on the curiosity

NASA Astrophysics Data System (ADS)

Sulistiani, E.; Waluya, S. B.; Masrukan

2018-03-01

This study aims to determine (1) the effectiveness of Discovery Learning model by using Hand on Activity toward critical thinking abilities, and (2) to describe students’ critical thinking abilities in Discovery Learning by Hand on Activity based on curiosity. This study is mixed method research with concurrent embedded design. Sample of this study are students of VII A and VII B of SMP Daarul Qur’an Ungaran. While the subject in this study is based on the curiosity of the students groups are classified Epistemic Curiosity (EC) and Perceptual Curiosity (PC). The results showed that the learning of Discovery Learning by using Hand on Activity is effective toward mathematics critical thinking abilities. Students of the EC type are able to complete six indicators of mathematics critical thinking abilities, although there are still two indicators that the result is less than the maximum. While students of PC type have not fully been able to complete the indicator of mathematics critical thinking abilities. They are only strong on indicators formulating questions, while on the other five indicators they are still weak. The critical thinking abilities of EC’s students is better than the critical thinking abilities of the PC’s students.

Making instruction and assessment responsive to diverse students' progress: group-administered dynamic assessment in teaching mathematics.

PubMed

Jeltova, Ida; Birney, Damian; Fredine, Nancy; Jarvin, Linda; Sternberg, Robert J; Grigorenko, Elena L

2011-01-01

This study entailed a 3 (instructional intervention) × 2 (assessment-type) between-subjects experimental design employing a pretest-intervention-posttest methodology. The instructional interventions were administered between subjects in three conditions: (a) dynamic instruction, (b) triarchic or theory of successful intelligence-control instruction, and (c) standard-control instruction. The assessment-type consisted between subjects of either (a) a group-administered dynamic posttest or (b) the same group-administered posttest interspersed with a control filler activity. Performance in different mathematics content areas taught in fourth grade was investigated. In total, 1,332 students and 63 classroom teachers in 24 schools across six school districts participated in the study. The results indicate the advantages of using dynamic instruction and assessment in regular classrooms while teaching mathematics, especially when the student body is highly ethnically diverse.

Subject-Specific Characteristics of Instructional Quality in Mathematics Education

ERIC Educational Resources Information Center

Schlesinger, Lena; Jentsch, Armin; Kaiser, Gabriele; König, Johannes; Blömeke, Sigrid

2018-01-01

Instructional research in German-speaking countries has conceptualized teaching quality recently according to three generic dimensions, namely, classroom management, student support and cognitive activation. However, as these dimensions are mainly regarded as generic, subject-specific aspects of mathematics instruction, e.g., the mathematical…

Successful Mathematics Teaching for Middle-School Grades.

ERIC Educational Resources Information Center

Clayton, Gypsy Abbott; And Others

Several competencies and instructional strategies necessary to accommodate the changing role of teachers of mathematics at middle-school level are described. Also provided are teacher-generated and teacher-tested instructional activities that can be used to facilitate student success in learning mathematical concepts. After describing the…

Cognitive Technologies for Mathematics Education. Technical Report No. 37.

ERIC Educational Resources Information Center

Pea, Roy D.

This paper provides an historical perspective on the possible roles of cognitive technologies in thinking as "reorganizers" of the mind. It suggests that by understanding the transformational roles of advanced technologies for mathematical thinking, positive contributions can be made to research and practice on the use of computers in…

Thinking Process of Pseudo Construction in Mathematics Concepts

ERIC Educational Resources Information Center

Subanji; Nusantara, Toto

2016-01-01

This article aims at studying pseudo construction of student thinking in mathematical concepts, integer number operation, algebraic forms, area concepts, and triangle concepts. 391 junior high school students from four districts of East Java Province Indonesia were taken as the subjects. Data were collected by means of distributing the main…

Hoop Hoop Hooray!

ERIC Educational Resources Information Center

Tomsett, Ruth

2008-01-01

The author believes that Venn diagrams are a useful, yet hugely underused resource, to encourage purposeful talk, reasoning and logical thinking both within mathematics and across the curriculum. Here, she describes ways in which Venn diagrams can be used to add challenge and develop reasoning, discussion and mathematical thinking at Key Stage 2.…

Teachers' Considerations of Students' Thinking during Mathematics Lesson Design

ERIC Educational Resources Information Center

Amador, Julie M.

2016-01-01

Teachers' abilities to design mathematics lessons are related to their capability to mobilize resources to meeting intended learning goals based on their noticing. In this process, knowing how teachers consider Students' thinking is important for understanding how they are making decisions to promote student learning. While teaching, what teachers…

The Value of Why for Student and Teacher Learning

ERIC Educational Resources Information Center

Guarino, Jody; Sykes, Marie; Santagata, Rossella

2013-01-01

The authors believe teaching for understanding begins with the development of a few essential orientations. Teachers must have an appreciation for student centered mathematics teaching, valuing an approach that builds on student thinking. In addition, teachers must appreciate the complexity of students' mathematical thinking and ideas. Once these…

An Inside Track: Fostering Mathematical Practices

ERIC Educational Resources Information Center

Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia

2015-01-01

Classroom teachers may not initially consider games as opportunities for students to engage in deep mathematical thinking. However, this article reveals how a second grade veteran teacher used Attribute Trains, a game adapted from NCTM Illuminations, to foster his students' thinking related to key ideas within the Standards for Mathematical…

Of Nasa and Neanderthals, Elephants and Machines: Metaphors and the Conceptualization of Homeland Security

DTIC Science & Technology

2013-12-01

study of nature, just as they have in mathematics . Hence, even in our day of hyper abstract thinking , mathematics continues to be the language of...way of thinking . 2. Those successfully completing education and apprenticeship have professed a self-sacrificing commitment to serving society...overreaches. Pinker points out that the contextual school ignores the predictive reality of science and mathematics .73 This does not mean that metaphors

A Comparison of Traditional and Holistic Instructional Methods in Developing Positive Attitudes Toward Mathematics Instruction in Students at Malcolm X College.

ERIC Educational Resources Information Center

Williams, Richard W.

The purpose of this study was to explore whether "holistic" instruction is an effective way to improve student attitudes toward instruction. Study participants were students in two Mathematics 111 classes at Malcolm X College (Illinois), 27 in the experimental and 27 in the control group. The experimental group received holistic…

The effect of mathematical model development on the instruction of acceleration to introductory physics students

NASA Astrophysics Data System (ADS)

Sauer, Tim Allen

The purpose of this study was to evaluate the effectiveness of utilizing student constructed theoretical math models when teaching acceleration to high school introductory physics students. The goal of the study was for the students to be able to utilize mathematical modeling strategies to improve their problem solving skills, as well as their standardized scientific and conceptual understanding. This study was based on mathematical modeling research, conceptual change research and constructivist theory of learning, all of which suggest that mathematical modeling is an effective way to influence students' conceptual connectiveness and sense making of formulaic equations and problem solving. A total of 48 students in two sections of high school introductory physics classes received constructivist, inquiry-based, cooperative learning, and conceptual change-oriented instruction. The difference in the instruction for the 24 students in the mathematical modeling treatment group was that they constructed every formula they needed to solve problems from data they collected. In contrast, the instructional design for the control group of 24 students allowed the same instruction with assigned problems solved with formulas given to them without explanation. The results indicated that the mathematical modeling students were able to solve less familiar and more complicated problems with greater confidence and mental flexibility than the control group students. The mathematical modeling group maintained fewer alternative conceptions consistently in the interviews than did the control group. The implications for acceleration instruction from these results were discussed.

Millennial generation student nurses' perceptions of the impact of multiple technologies on learning.

PubMed

Montenery, Susan M; Walker, Marjorie; Sorensen, Elizabeth; Thompson, Rhonda; Kirklin, Dena; White, Robin; Ross, Carl

2013-01-01

To determine how millennial nursing students perceive the effects of instructional technology on their attentiveness, knowledge, critical thinking, and satisfaction. BACKGROUND Millennial learners develop critical thinking through experimentation, active participation, and multitasking with rapid shifts between technological devices. They desire immediate feedback. METHOD; A descriptive, longitudinal, anonymous survey design was used with a convenience sample of 108 sophomore, junior, and senior baccalaureate nursing students (participation rates 95 percent, winter, 85 percent, spring). Audience response, virtual learning, simulation, and computerized testing technologies were used. An investigator-designed instrument measured attentiveness, knowledge, critical thinking, and satisfaction (Cronbach's alphas 0.73, winter; 0.84, spring). Participants positively rated the audience response, virtual learning, and simulation instructional technologies on their class participation, learning, attention, and satisfaction. They strongly preferred computerized testing. Consistent with other studies, these students engaged positively with new teaching strategies using contemporary instructional technology. Faculty should consider using instructional technologies.

The integrated learning management using the STEM education for improve learning achievement and creativity in the topic of force and motion at the 9th grade level

NASA Astrophysics Data System (ADS)

Kakarndee, Nampetch; Kudthalang, Nukool; Jansawang, Natchanok

2018-01-01

The aims of this research study were to investigate and analyze the processing performances and the performance results (E1/E2) efficiency at the determining criteria for planning students' improvements to their learning processes toward their scientific knowledge were investigated, carry out the investigations, gathering evidence, and proposing explanations were developed and predicted. Students' engagements to their needs in unambiguous and clearly content of science teaching onto the instructional processes were attempted for establishing a national approach with the STEM education instructional method were strategized. Research administrations were designed to a sample size consisted of 40 secondary students in science class at the 9th grade level in Borabu School with the purposive sampling technique was selected. Using the STEM Education instructional innovation's lesson plans were managed learning activities. Students' learning achievements were assessed with the Pre-Test and Post-Test designs of 30 items. Students' creative thinking abilities were determined of their perceptions that obtained of the 3-item Creative Thinking Ability Test. The results for the effectiveness of the innovative instructional lesson plans based on the STEM Education Method, the lessoning effectiveness (E1/E2) evidences of 78.95/76.58 over the threshold setting is 75/75. Pretest-posttest designs for assessing students' learning achievements that impact a student's ability to achieve and explains with the STEM education instructional method were differences, significantly (ρ<.001) and the posttest of the 3-item Creative Thinking Ability Test designs for assessing Students' creative thinking abilities that impact a student's ability to have a good skill level in originality, fluency and flexibility thinking with the STEM education instructional method were differences, significantly (ρ<.001).

Effects of Mathematical Vocabulary Instruction on Students' Achievement in Mathematics in Secondary Schools of Murang'a County, Kenya

ERIC Educational Resources Information Center

Wanjiru, Benson; O-Connor, Miheso

2015-01-01

This article is based on a study whose main objective was to determine the effects of mathematical vocabulary instruction on students' achievement in Mathematics in Secondary schools in Murang'a County, Kenya. The study was a non-equivalent control group pretest-posttest quasi-experimental design and was conducted in the two purposively selected…

Weaving Mathematical Instructional Strategies into Inclusive Settings.

ERIC Educational Resources Information Center

Karp, Karen S.; Voltz, Deborah L.

2000-01-01

This article describes a framework that allows teachers in inclusive elementary settings to interweave instructional strategies from a variety of paradigms to meet individual learning needs in inclusive mathematics classes. Factors to be considered are highlighted and an instructional continuum from more teacher-centered strategies to more…

Mathematics and Science Instruction in Southern California.

ERIC Educational Resources Information Center

Myers, Edwin C.; Mineo, R. James

To provide information to support school district considerations of changes in mathematics and science instruction, three issues were considered: (1) the adequacy of the California Basic Education Data System (CBEDS) for supporting an analysis of subject matter instruction; (2) the distribution of teaching effort and student enrollments among…

Should Science Be Used to Teach Mathematical Skills?

ERIC Educational Resources Information Center

Kren, Sandra R.; Huntsberger, John P.

1977-01-01

Studies elementary school childrens' abilities in (1) measuring and constructing angles, and (2) interpreting and constructing linear graphs as a result of instructional formats. Partitioned into instructional treatments of (1) science, (2) science-mathematics, (3) mathematics, and (4) control were 161 fourth- and fifth-grade children. Mathematics…

Conceptualizing "Homework" in Flipped Mathematics Classes

ERIC Educational Resources Information Center

de Araujo, Zandra; Otten, Samuel; Birisci, Salih

2017-01-01

Flipped instruction is becoming more common in the United States, particularly in mathematics classes. One of the defining characteristics of this increasingly popular instructional format is the homework teachers assign. In contrast to traditional mathematics classes in which homework consists of problem sets, homework in flipped classes often…

Mathematics Teacher Professional Development as a Virtual Boundary Encounter

ERIC Educational Resources Information Center

Matranga, Anthony Vincent

2017-01-01

Mathematics instruction in US schools is largely inconsistent with visions of research and policy, which suggest instruction should be student-centered, maintain high levels of cognitive demand, and support rich mathematical discussion and argumentation. Professional development (PD) figures prominently in addressing this issue, and studies have…

Commentary: Teaching creativity and innovative thinking in medicine and the health sciences.

PubMed

Ness, Roberta B

2011-10-01

The National Academies of Science recently criticized the state of scientific innovation and competitiveness in the United States. Evaluations of already-established creativity training programs--examining a broad array of students, from school age to adult and with a wide range of abilities--have shown that such courses improve thinking skills, attitudes, and performance. Although academic medicine provides informal training in creativity and innovation, it has yet to incorporate formal instruction on these topics into medical education. A number of existing, thoughtfully constructed and evaluated creativity programs in other fields provide a pedagogical basis for developing creativity training programs for the health sciences. The content of creativity training programs typically includes instruction and application in (1) divergent thinking, (2) problem solving, and (3) creative production. Instructional formats that have been shown to elicit the best outcomes are an admixture of lectures, discussion, and guided practice. A pilot program to teach innovative thinking to health science students at the University of Texas includes instruction in recognizing and finding alternatives to frames or habitual cognitive patterns, in addition to the constructs already mentioned. As innovation is the engine of scientific progress, the author, founder of Innovative Thinking, the creativity training pilot program at the University of Texas, argues in this commentary that academic health centers should implement and evaluate new methods for enhancing science students' innovative thinking to keep the United States as a worldwide leader in scientific discovery.

Fostering 21st-Century Evolutionary Reasoning: Teaching Tree Thinking to Introductory Biology Students.

PubMed

Novick, Laura R; Catley, Kefyn M

2016-01-01

The ability to interpret and reason from Tree of Life (ToL) diagrams has become a vital component of science literacy in the 21st century. This article reports on the effectiveness of a research-based curriculum, including an instructional booklet, laboratory, and lectures, to teach the fundamentals of such tree thinking in an introductory biology class for science majors. We present the results of a study involving 117 undergraduates who received either our new research-based tree-thinking curriculum or business-as-usual instruction. We found greater gains in tree-thinking abilities for the experimental instruction group than for the business-as-usual group, as measured by performance on our novel assessment instrument. This was a medium size effect. These gains were observed on an unannounced test that was administered ∼5-6 weeks after the primary instruction in tree thinking. The nature of students' postinstruction difficulties with tree thinking suggests that the critical underlying concept for acquiring expert-level competence in this area is understanding that any specific phylogenetic tree is a subset of the complete, unimaginably large ToL. © 2016 L. R. Novick and K. M. Catley. CBE—Life Sciences Education © 2016 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

The use of scientific direct instruction model with video learning of ethnoscience to improve students’ critical thinking skills

NASA Astrophysics Data System (ADS)

Sudarmin, S.; Mursiti, S.; Asih, A. G.

2018-04-01

In this disruption era, students are encouraged to develop critical thinking skills and important cultural conservation characters. Student's thinking skill in chemistry learning has not been developed because learning chemistry in schools still uses teacher-centered, lecture method, is less interesting and does not utilize local culture as a learning resource. The purpose of this research is to know the influence of the application of direct Instruction (DI) model with video learning of ethnoscience on the improvement of students’ critical thinking skills. This study was experimental research. The population was the students from class XI MIPA MA Negeri Gombong with the sample chosen by purposive random sampling. The material of local wisdom as the study of ethnosciences which was the focus of the research was the production of genting, dawet, lanting, and sempor reservoirs which is integrated with colloidal chemical contents. The learning video of ethnoscience before being applied was validated by experts. Students’ critical thinking skills were revealed through the concept of conceptualizing test instruments. The data analysis technique used was the test of proportion and Kolmogorov-Smirnov test. The results of this study suggested that the experimental class that was treated by scientific direct instruction model with the learning video of ethnoscience shows cognitive learning and critical thinking which were better than the control class. Besides, the students indicated their interest in the application of scientific direct instruction model with ethnoscience learning video.

Development and Validation of Instruments to Measure Learning of Expert-Like Thinking

ERIC Educational Resources Information Center

Adams, Wendy K.; Wieman, Carl E.

2011-01-01

This paper describes the process for creating and validating an assessment test that measures the effectiveness of instruction by probing how well that instruction causes students in a class to think like experts about specific areas of science. The design principles and process are laid out and it is shown how these align with professional…

Effectiveness of Critical Thinking Instruction in Higher Education: A Systematic Review of Intervention Studies

ERIC Educational Resources Information Center

Tiruneh, Dawit T.; Verburgh, An; Elen, Jan

2014-01-01

Promoting students' critical thinking (CT) has been an essential goal of higher education. However, despite the various attempts to make CT a primary focus of higher education, there is little agreement regarding the conditions under which instruction could result in greater CT outcomes. In this review, we systematically examined current empirical…

Teaching Students Who Struggle with Learning to Think before, while, and after Reading: Effects of Self-Regulated Strategy Development Instruction

ERIC Educational Resources Information Center

Mason, Linda H.

2013-01-01

Explicit strategy instruction combined with student-directed self-regulation in conjunction with cognitive strategies has proven effective in supporting low-achieving students' reading comprehension. Experts have extended 1 such approach, self-regulated strategy development (SRSD) for the expository reading comprehension Think before reading,…

Effect of Instructional Strategy on Critical Thinking and Content Knowledge: Using Problem-Based Learning in the Secondary Classroom

ERIC Educational Resources Information Center

Burris, Scott; Garton, Bryan L.

2007-01-01

The purpose of the study was to determine the effect of problem-based learning (PBL) on critical thinking ability and content knowledge among selected secondary agriculture students in Missouri. The study employed a quasi-experimental, non-equivalent comparison group design. The treatment consisted of two instructional strategies: problem-based…

Cognitive Coaching: An Examination of the Reflective Journaling of Teacher Candidates

ERIC Educational Resources Information Center

Henry, Aiyana Genae

2012-01-01

Cognitive Coaching is a method of instruction that recognizes the strength in thinking about thinking and fosters independent learning. Cognitive Coaching is one method of instruction that can help to better prepare teachers for the classroom. The purpose of this study was to determine the impact that Cognitive Coaching had on teacher candidates…

The Relationship of Teacher-Facilitated, Inquiry-Based Instruction to Student Higher-Order Thinking

ERIC Educational Resources Information Center

Marshall, Jeff C.; Horton, Robert M.

2011-01-01

Commissions, studies, and reports continue to call for inquiry-based learning approaches in science and math that challenge students to think critically and deeply. While working with a group of middle school science and math teachers, we conducted more than 100 classroom observations, assessing several attributes of inquiry-based instruction. We…

Physics Teachers' Professional Development in the Project "physics in Context"

NASA Astrophysics Data System (ADS)

Mikelskis-Seifert, Silke; Duit, Reinders

2013-06-01

Developing teachers' ways of thinking about "good" instruction as well as their views of the teaching and learning process is generally seen as essential for improving teaching behaviour and implementation of more efficient teaching and learning settings. Major deficiencies of German physics instruction as revealed by a nationwide video-study on the practice of physics instruction are addressed. Teachers participating in the project are made familiar with recent views of efficient instruction on the one hand and develop context-based instructional settings on the other. The evaluation resulted in partly encouraging findings. However, it also turned out that a number of teachers' ways of thinking about good instruction did only develop to a somewhat limited degree. The most impressive changes occurred for teachers who enjoyed the most intensive coaching.

Physics Teachers' Professional Development in the Project "physics in Context"

NASA Astrophysics Data System (ADS)

Mikelskis-Seifert, Silke; Duit, Reinders

2012-12-01

Developing teachers' ways of thinking about "good" instruction as well as their views of the teaching and learning process is generally seen as essential for improving teaching behaviour and implementation of more efficient teaching and learning settings. Major deficiencies of German physics instruction as revealed by a nationwide video-study on the practice of physics instruction are addressed. Teachers participating in the project are made familiar with recent views of efficient instruction on the one hand and develop context-based instructional settings on the other. The evaluation resulted in partly encouraging findings. However, it also turned out that a number of teachers' ways of thinking about good instruction did only develop to a somewhat limited degree. The most impressive changes occurred for teachers who enjoyed the most intensive coaching.

Gender differences in algebraic thinking ability to solve mathematics problems

NASA Astrophysics Data System (ADS)

Kusumaningsih, W.; Darhim; Herman, T.; Turmudi

2018-05-01

This study aimed to conduct a gender study on students' algebraic thinking ability in solving a mathematics problem, polyhedron concept, for grade VIII. This research used a qualitative method. The data was collected using: test and interview methods. The subjects in this study were eight male and female students with different level of abilities. It was found that the algebraic thinking skills of male students reached high group of five categories. They were superior in terms of reasoning and quick understanding in solving problems. Algebraic thinking ability of high-achieving group of female students also met five categories of algebraic thinking indicators. They were more diligent, tenacious and thorough in solving problems. Algebraic thinking ability of male students in medium category only satisfied three categories of algebraic thinking indicators. They were sufficient in terms of reasoning and understanding in solving problems. Algebraic thinking ability group of female students in medium group also satisfied three categories of algebraic thinking indicators. They were fairly diligent, tenacious and meticulous on working on the problems.

The Promise of Differentiated Instruction for Enhancing the Mathematical Understandings of College Students

ERIC Educational Resources Information Center

Chamberlin, Michelle; Powers, Robert

2010-01-01

Mathematics instructors must respond to diverse needs of individual students, including different abilities, interests, learning styles and cultural backgrounds. To do so, grade kindergarten-12 teachers have been using differentiated instruction, a process of proactively modifying instruction based on students' needs. It is supported by literature…

Development of an Intelligent Instruction System for Mathematical Computation

ERIC Educational Resources Information Center

Kim, Du Gyu; Lee, Jaemu

2013-01-01

In this paper, we propose the development of a web-based, intelligent instruction system to help elementary school students for mathematical computation. We concentrate on the intelligence facilities which support diagnosis and advice. The existing web-based instruction systems merely give information on whether the learners' replies are…

Task Analysis in Instructional Design: Some Cases from Mathematics.

ERIC Educational Resources Information Center

Resnick, Lauren B.

Task analysis as a tool in the design of instruction is the subject of this paper. Some of the major historical approaches (associationist/behaviorist, gestalt, and Piagetian) are described using examples from mathematics. The usefulness of these approaches to instructional design is evaluated on the basis of four criteria: instructional…

On Using Various Mathematics Instructions versus Traditional Instruction: An Action Research

ERIC Educational Resources Information Center

Alzabut, Jehad

2017-01-01

In this research, I provide an overview of potentially selected interactive mathematical instructions that help learners-educators identifying the most effective practices for teaching a course on differential equations. Based on my practical experience, positive and negative aspects of the used techniques are discussed. Immediate reactions on the…

Professional Development in Elementary School Mathematics

ERIC Educational Resources Information Center

Scoggins, C.

2010-01-01

This study was an investigation of mathematics instruction and professional development at a rural elementary school. The Department of Education in a southern U.S. state implemented a new curriculum in 2007 that required major changes in mathematics instruction. The problems were that teachers engaged in different levels of training and many…

Improving Intuition Skills with Realistic Mathematics Education

ERIC Educational Resources Information Center

Hirza, Bonita; Kusumah, Yaya S.; Darhim; Zulkardi

2014-01-01

The intention of the present study was to see the improvement of students' intuitive skills. This improvement was seen by comparing the Realistic Mathematics Education (RME)-based instruction with the conventional mathematics instruction. The subject of this study was 164 fifth graders of elementary school in Palembang. The design of this study…

A Mathematics Educator's Introduction to Rural Policy Issues

ERIC Educational Resources Information Center

Waters, Michael S., Ed.

2005-01-01

Most of the scholarship and commentary on mathematics education deals with issues of curriculum and instruction; this is understandable in a field logically belonging to the domain of curriculum and instruction. Moreover, issues of teaching and learning are compelling to people who love to learn and teach mathematics. Policy receives shorter…

Effects of Mastery Learning Strategies on Community College Mathematics Students' Achievement and Success Rate.

ERIC Educational Resources Information Center

Abadir, Laila; And Others

The effects of mastery learning strategies, interactive video mathematics (IVM), individualized instruction (IND), and the lecture method on mathematics achievement of community college students was studied. Interactions among instructional methods, gender, and age were examined; and the grade success rate was determined for each instructional…

A Reflection Framework for Teaching Mathematics

ERIC Educational Resources Information Center

Merritt, Eileen G.; Rimm-Kaufman, Sara E.; Berry, Robert Q., III; Walkowiak, Temple A.; McCracken, Erin R.

2010-01-01

Mathematics teachers confront dozens of daily decisions about how to instruct students. It is well established that high-quality instruction provides benefits for students with diverse learning and family backgrounds. However, it is often difficult for teachers to identify the critical aspects of a successful mathematics lesson as they strive to…

A Phenomenological Study of Parents' Involvement in Mathematics Instruction

ERIC Educational Resources Information Center

Delbridge, Natalie H.

2013-01-01

Many areas of support are needed when educating children and youth in mathematics education. One of the untapped areas is that of parental support and involvement. The purpose of this phenomenological study is to describe the "lived" experiences of parental involvement in their children's mathematics home instruction through individual…

The Concrete-Representational-Abstract Sequence of Instruction in Mathematics Classrooms

ERIC Educational Resources Information Center

Mudaly, Vimolan; Naidoo, Jayaluxmi

2015-01-01

The purpose of this paper is to explore how master mathematics teachers use the concrete-representational-abstract (CRA) sequence of instruction in mathematics classrooms. Data was collected from a convenience sample of six master teachers by observations, video recordings of their teaching, and semi-structured interviews. Data collection also…

Crossing Boundaries in Undergraduate Biology Education

ERIC Educational Resources Information Center

Vanderklein, Dirk; Munakata, Mika; McManus, Jason

2016-01-01

In an effort to make mathematics relevant to biology students, the authors developed two modules that sought to integrate mathematics and ecology instruction to differing degrees. The modules were developed by a team of biology and mathematics educators and were implemented in an ecology course using three different instructional methods for three…

Analyzing Tasks to Promote Equity in Secondary Mathematics Teacher Education

ERIC Educational Resources Information Center

Mintos, Alexia

2017-01-01

The purpose of this study is to understand characteristics and outcomes of instructional tasks used to support preservice secondary mathematics teachers (PSMTs) in learning about equity in secondary mathematics methods courses. This study focuses on five instructional tasks from four purposefully chosen teacher education programs. These activities…

Mathematical Tasks as a Framework for Reflection: From Research To Practice.

ERIC Educational Resources Information Center

Stein, Mary Kay; Smith, Margaret Schwan

1998-01-01

Describes the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) national reform project aimed at studying and fostering the development and implementation of enhanced mathematics instructional programs. It is a framework for reflection based on mathematical tasks used during classroom instruction and the ways in…

Effects of Virtual Manipulatives with Different Approaches on Students' Knowledge of Slope

ERIC Educational Resources Information Center

Demir, Mustafa

2018-01-01

Virtual Manipulatives (VMs) are computer-based, dynamic, and visual representations of mathematical concepts, provide interactive learning environments to advance mathematics instruction (Moyer et al., 2002). Despite their broad use, few research explored the integration of VMs into mathematics instruction (Moyer-Packenham & Westenskow, 2013).…

Persuasive Pedagogy: A New Paradigm for Mathematics Education

ERIC Educational Resources Information Center

Hennessey, Maeghan N.; Higley, Kelli; Chesnut, Steven R.

2012-01-01

Mathematics teachers face a myriad of instructional obstacles. Since the early 1990s, mathematics education researchers have proposed the use of constructivist practices to counteract these ever-prevalent obstacles. While we do give credit to the choices of instructional activities the constructivist paradigm promotes, there are problems with its…

Special Educators and Mathematics Phobia: An Initial Qualitative Investigation

ERIC Educational Resources Information Center

Humphrey, Michael; Hourcade, Jack J.

2010-01-01

Special educators are uniquely challenged to be content experts in all curricular areas, including mathematics, because students in their caseloads may require academic instruction in any area. However, special educators with math phobia may be limited in their ability to provide effective instruction to their students with mathematical deficits…

Mathematical literacy skills of students' in term of gender differences

NASA Astrophysics Data System (ADS)

Lailiyah, Siti

2017-08-01

Good mathematical literacy skills will hopefully help maximize the tasks and role of the prospective teacher in activities. Mathematical literacy focus on students' ability to analyze, justify, and communicate ideas effectively, formulate, solve and interpret mathematical problems in a variety of forms and situations. The purpose of this study is to describe the mathematical literacy skills of the prospective teacher in term of gender differences. This research used a qualitative approach with a case study. Subjects of this study were taken from two male students and two female students of the mathematics education prospective teacher who have followed Community Service Program (CSP) in literacy. Data were collected through methods think a loud and interviews. Four prospective teachers were asked to fill mathematical literacy test and video taken during solving this test. Students are required to convey loud what he was thinking when solving problems. After students get the solution, researchers grouped the students' answers and results think aloud. Furthermore, the data are grouped and analyzed according to indicators of mathematical literacy skills. Male students have good of each indicator in mathematical literacy skills (the first indicator to the sixth indicator). Female students have good of mathematical literacy skills (the first indicator, the second indicator, the third indicator, the fourth indicator and the sixth indicator), except for the fifth indicators that are enough.

Seeking mathematics success for college students: a randomized field trial of an adapted approach

NASA Astrophysics Data System (ADS)

Gula, Taras; Hoessler, Carolyn; Maciejewski, Wes

2015-11-01

Many students enter the Canadian college system with insufficient mathematical ability and leave the system with little improvement. Those students who enter with poor mathematics ability typically take a developmental mathematics course as their first and possibly only mathematics course. The educational experiences that comprise a developmental mathematics course vary widely and are, too often, ineffective at improving students' ability. This trend is concerning, since low mathematics ability is known to be related to lower rates of success in subsequent courses. To date, little attention has been paid to the selection of an instructional approach to consistently apply across developmental mathematics courses. Prior research suggests that an appropriate instructional method would involve explicit instruction and practising mathematical procedures linked to a mathematical concept. This study reports on a randomized field trial of a developmental mathematics approach at a college in Ontario, Canada. The new approach is an adaptation of the JUMP Math program, an explicit instruction method designed for primary and secondary school curriculae, to the college learning environment. In this study, a subset of courses was assigned to JUMP Math and the remainder was taught in the same style as in the previous years. We found consistent, modest improvement in the JUMP Math sections compared to the non-JUMP sections, after accounting for potential covariates. The findings from this randomized field trial, along with prior research on effective education for developmental mathematics students, suggest that JUMP Math is a promising way to improve college student outcomes.

Characterizing a Highly Accomplished Teacher's Noticing of Third-Grade Students' Mathematical Thinking

ERIC Educational Resources Information Center

Taylan, Rukiye Didem

2017-01-01

This study investigated a highly accomplished third-grade teacher's noticing of students' mathematical thinking as she taught multiplication and division. Through an innovative method, which allowed for documenting in-the-moment teacher noticing, the author was able to explore teacher noticing and reflective practices in the context of classroom…

Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

ERIC Educational Resources Information Center

Mairing, Jackson Pasini

2017-01-01

Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

Creative Construction of Mathematics and Science Concepts in Early Childhood.

ERIC Educational Resources Information Center

Gallenstein, Nancy L.

Noting that effective teaching models that emphasize critical thinking in mathematics and science are used less often in early childhood classrooms than in those for older students, this book provides early childhood educators with an explanation of teaching models that promote 3- to 8-year-olds critical thinking, problem solving, decision making,…

Artificial Intelligence, Computational Thinking, and Mathematics Education

ERIC Educational Resources Information Center

Gadanidis, George

2017-01-01

Purpose: The purpose of this paper is to examine the intersection of artificial intelligence (AI), computational thinking (CT), and mathematics education (ME) for young students (K-8). Specifically, it focuses on three key elements that are common to AI, CT and ME: agency, modeling of phenomena and abstracting concepts beyond specific instances.…

Symbols and the Bifurcation between Procedural and Conceptual Thinking.

ERIC Educational Resources Information Center

Tall, David; Gray, Eddie; Bin Ali, Maselan; Crowley, Lillie; DeMarois, Phil; McGowen, Mercedes; Pitta, Demetra; Pinto, Marcia; Thomas, Michael; Yusof, Yudariah

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this presentation, the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and…

VStops: A Thinking Strategy and Visual Representation Approach in Mathematical Word Problem Solving toward Enhancing STEM Literacy

ERIC Educational Resources Information Center

Abdullah, Nasarudin; Halim, Lilia; Zakaria, Effandi

2014-01-01

This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…

Accommodation in the Formal World of Mathematical Thinking

ERIC Educational Resources Information Center

Stewart, Sepideh; Schmidt, Ralf

2017-01-01

In this study, we examined a mathematician and one of his students' teaching journals and thought processes concurrently as the class was moving towards the proof of the Fundamental Theorem of Galois Theory. We employed Tall's framework of three worlds of mathematical thinking as well as Piaget's notion of accommodation to theoretically study the…

Mathematics for Young Learners: 60 Games & Activities for Ages 3 through 7.

ERIC Educational Resources Information Center

Ellerby, Richard S.

By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without…

Introductory science and mathematics education for 21st-Century biologists.

PubMed

Bialek, William; Botstein, David

2004-02-06

Galileo wrote that "the book of nature is written in the language of mathematics"; his quantitative approach to understanding the natural world arguably marks the beginning of modern science. Nearly 400 years later, the fragmented teaching of science in our universities still leaves biology outside the quantitative and mathematical culture that has come to define the physical sciences and engineering. This strikes us as particularly inopportune at a time when opportunities for quantitative thinking about biological systems are exploding. We propose that a way out of this dilemma is a unified introductory science curriculum that fully incorporates mathematics and quantitative thinking.

Technology Use in Higher Education Instruction

ERIC Educational Resources Information Center

Elzarka, Sammy

2012-01-01

The significance of integrating technology use in higher education instruction is undeniable. The benefits include those related to access to instruction by underserved populations, adequately preparing students for future careers, capitalizing on best instructional practices, developing higher order thinking activities, and engaging students…

Improving students’ creative mathematical reasoning ability students through adversity quotient and argument driven inquiry learning

NASA Astrophysics Data System (ADS)

Hidayat, W.; Wahyudin; Prabawanto, S.

2018-01-01

This study aimed to investigate the role factors of Adversity Quotient (AQ) and Argument-Driven Inquiry (ADI) instruction in improving mathematical creative reasoning ability from students’ who is a candidate for a math teacher. The study was designed in the form of experiments with a pretest-posttest control group design that aims to examine the role of Adversity Quotient (AQ) and Argument-Driven Inquiry (ADI) learning on improving students’ mathematical creative reasoning abilities. The population in this research was the student of mathematics teacher candidate in Cimahi City, while the sample of this research was 90 students of the candidate of the teacher of mathematics specified purposively then determined randomly which belong to experiment class and control class. Based on the results and discussion, it was concluded that: (1) Improvement the ability of mathematical creative reasoning of students’ who was a candidate for a math teacher who received Argument-Driven Inquiry (ADI) instruction is better than those who received direct instruction is reviewed based on the whole; (2) There was no different improvement the ability of mathematical creative reasoning of students’ who is a candidate for a math teacher who received Argument-Driven Inquiry (ADI) instruction and direct instruction was reviewed based on the type of Adversity Quotient (Quitter / AQ Low, Champer / AQ Medium, and the Climber / AQ High); (3) Learning factors and type of Adversity Quotient (AQ) affected the improvement of students’ mathematical creative reasoning ability. In addition, there was no interaction effect between learning and AQ together in developing of students’ mathematical creative reasoning ability; (4) mathematical creative reasoning ability of students’ who is a candidate for math teacher had not been achieved optimally on the indicators novelty.

Critical Thinking and the Use of Nontraditional Instructional Methodologies.

PubMed

Orique, Sabrina B; McCarthy, Mary Ann

2015-08-01

The purpose of this study was to examine the relationship between critical thinking and the use of concept mapping (CM) and problem-based learning (PBL) during care plan development. A quasi-experimental study with a pretest-posttest design was conducted using a convenience sample (n = 49) of first-semester undergraduate baccalaureate nursing students. Critical thinking was measured using the Holistic Critical Thinking Scoring Rubric. Data analysis consisted of a repeated measures analysis of variance with post hoc mean comparison tests using the Bonferroni method. Findings indicated that mean critical thinking at phase 4 (CM and PBL) was significantly higher, compared with phase 1 (baseline), phase 2 (PBL), and phase 3 (CM [p < 0.001]). The results support the utilization of nontraditional instructional (CM and PBL) methodologies in undergraduate nursing curricula. Copyright 2015, SLACK Incorporated.

Development and evaluation of form three mathematics i-Think module (Mi-T3) on algebraic formulae topic

NASA Astrophysics Data System (ADS)

Sam, Sazilah; Abdullah, Mohd Faizal Nizam Lee

2017-05-01

This article introduces the Form Three Mathematics i-Think Module (Mi-T3). The main objective of this Mi-T3 is to assist form three students develop their higher order thinking skills (HOTS). The Sidek Module Development Model (SMDM) and eight innovative thinking maps (i-Think) were applied as a guideline in developing Mi-T3. A validation stage was carried out by eight experts, and content validation achievement more than 90% obtained. A group of form three students and teachers was piloted to check the module's reliability through one to one and small group evaluation and Cronbach Alpha more than 0.90 was obtained. Implications of the study are discussed in this article.

Investigating Students' Reflective Thinking in the Introductory Physics Course

NASA Astrophysics Data System (ADS)

Boudreaux, Andrew

2010-10-01

Over the past 30 years, physics education research has guided the development of instructional strategies that can significantly enhance students' functional understanding of concepts in introductory physics. Recently, attention has shifted to instructional goals that, while widely shared by teachers of physics, are often more implicit than explicit in our courses. These goals involve the expectations and attitudes that students have about what it means to learn and understand physics, together with the behaviors and actions students think they should engage in to accomplish this learning. Research has shown that these ``hidden'' elements of the curriculum are remarkably resistant to instruction. In fact, traditional physics courses tend to produce movement away from expert-like behaviors. At Western Washington University, we are exploring ways of promoting metacognition, an aspect of the hidden curriculum that involves the conscious monitoring of one's own thinking and learning. We have found that making this reflective thinking an explicit part of the course may not be enough: adequate framing and scaffolding may be necessary for students to meaningfully engage in metacognition. We have thus taken the basic approach of developing metacognition, like conceptual understanding, through guided inquiry. During our teaching experiments, we have collected written and video data, with twin goals of guiding iterative modifications to the instruction as well as contributing to the knowledge base about student metacognition in introductory physics. This talk will provide examples of metacognition activities from course assignments and labs, and will present written data to assess the effectiveness of instruction and to illustrate specific modes of students' reflective thinking.

The Effect of Instructional Analogies in Interaction with Logical Thinking Ability on Achievement and Attitude toward Chemistry

ERIC Educational Resources Information Center

Eskandar, Fathi-Azar; Bayrami, Mansor; Vahedi, Shahram; Ansar, Vahideh Abdollahi Adli

2013-01-01

We investigated the effect of instructional analogies in interaction with logical thinking ability on achievement and attitude towards chemistry. The participants were 147 female students from 6 8th grade classes in three public junior high schools selected by using a random multistage sampling method from five education districts in Tabriz, a…

Assessment of the Impact of Integrated Simulation on Critical Thinking and Clinical Judgment in Nursing Instruction

ERIC Educational Resources Information Center

Meyer, Rita Allen

2012-01-01

The purpose of this study was to explore the effects of using simulation and didactic instruction on critical thinking and clinical judgment with student nurses enrolled in a fall semester medical-surgical class. Specifically, it was of interest to compare the performance of these fall semester nursing students with the performance of nursing…

Cultivating Critical Thinkers: Exploring Transfer of Learning from Pre-Service Teacher Training to Classroom Practice

ERIC Educational Resources Information Center

Yang, Ya-Ting Carolyn

2012-01-01

This study explores the transfer of critical thinking skills and dispositions from pre-service teacher training to classroom practice and student achievement in the cases of two graduates from a course on critical thinking-integrated instruction. Two 7th and two 8th grade classes were randomly assigned as experimental (CT-integrated instruction),…

The Designer-by-Assignment in Practice: Instructional Design Thinking of Subject Matter Experts

ERIC Educational Resources Information Center

Pesce, Sandra V.

2012-01-01

Designers-by-assignment, or subject matter experts (SMEs) who are pressed into training service, have become common in the workplace. A review of more than 24 studies on expert and novice instructional designers, however, revealed that little is known about how designers-by-assignment think about design and make design decisions in the field. A…

Student Perceptions of Effective Instruction and the Development of Critical Thinking: A Replication and Extension

ERIC Educational Resources Information Center

Loes, Chad N.; Salisbury, Mark H.; Pascarella, Ernest T.

2015-01-01

This study utilized data from the Wabash National Study of Liberal Arts Education to test the robustness of research conducted by Pascarella et al. ("J Coll Stud Dev" 37:7-19, 1996) that explored the relationship between student perceptions of exposure to organized and clear instruction and growth in critical thinking skills among…

Older Adults Can Suppress Unwanted Memories When Given an Appropriate Strategy

PubMed Central

2015-01-01

Memory suppression refers to the ability to exclude distracting memories from conscious awareness, and this ability can be assessed with the think/no-think paradigm. Recent research with older adults has provided evidence suggesting both intact and deficient memory suppression. The present studies seek to understand the conditions contributing to older adults’ ability to suppress memories voluntarily. We report 2 experiments indicating that the specificity of the think/no-think task instructions contributes to older adults’ suppression success: When older adults receive open-ended instructions that require them to develop a retrieval suppression strategy on their own, they show diminished memory suppression compared with younger adults. Conversely, when older adults receive focused instructions directing them to a strategy thought to better isolate inhibitory control, they show suppression-induced forgetting similar to that exhibited by younger adults. Younger adults demonstrate memory suppression regardless of the specificity of the instructions given, suggesting that the ability to select a successful suppression strategy spontaneously may be compromised in older adults. If so, this deficit may be associated with diminished control over unwanted memories in naturalistic settings if impeded strategy development reduces the successful deployment of inhibitory control. PMID:25602491

Visual Representation in Mathematics: Special Education Teachers' Knowledge and Emphasis for Instruction

ERIC Educational Resources Information Center

van Garderen, Delinda; Scheuermann, Amy; Poch, Apryl; Murray, Mary M.

2018-01-01

The use of visual representations (VRs) in mathematics is a strongly recommended practice in special education. Although recommended, little is known about special educators' knowledge of and instructional emphasis about VRs. Therefore, in this study, the authors examined special educators' own knowledge of and their instructional emphasis with…

A Practical Approach to Using Learning Styles in Math Instruction.

ERIC Educational Resources Information Center

Midkiff, Ruby Bostick; Thomasson, Rebecca Davis

Instruction based on learning styles has received little attention in the recent reform efforts in mathematics education. The purpose of this book is to address the improvement of mathematics instruction through sensitivity to learning styles. The introduction discusses the scope and rationale of the book. Chapter 2 documents the need for…

Mathematical Learning Models that Depend on Prior Knowledge and Instructional Strategies

ERIC Educational Resources Information Center

Pritchard, David E.; Lee, Young-Jin; Bao, Lei

2008-01-01

We present mathematical learning models--predictions of student's knowledge vs amount of instruction--that are based on assumptions motivated by various theories of learning: tabula rasa, constructivist, and tutoring. These models predict the improvement (on the post-test) as a function of the pretest score due to intervening instruction and also…

Infrastructure Redesign and Instructional Reform in Mathematics: Formal Structure and Teacher Leadership

ERIC Educational Resources Information Center

Hopkins, Megan; Spillane, James P.; Jakopovic, Paula; Heaton, Ruth M.

2013-01-01

Designing infrastructures to support instruction remains a challenge in educational reform. This article reports on a study of one school system's efforts to redesign its infrastructure for mathematics instruction by promoting teacher leadership. Using social network and interview data from 12 elementary schools, we explore how the district's…

Improving Seventh Grade Students' Learning of Ratio and Proportion: The Role of Schema-Based Instruction

ERIC Educational Resources Information Center

Jitendra, Asha K.; Star, Jon R.; Starosta, Kristin; Leh, Jayne M.; Sood, Sheetal; Caskie, Grace; Hughes, Cheyenne L.; Mack, Toshi R.

2009-01-01

The present study evaluated the effectiveness of an instructional intervention (schema-based instruction, SBI) that was designed to meet the diverse needs of middle school students by addressing the research literatures from both special education and mathematics education. Specifically, SBI emphasizes the role of the mathematical structure of…

Models of Influence on Mathematics Instructional Coaches

ERIC Educational Resources Information Center

Brown, Sue; Harrell, Scott; Browning, Sandra

2017-01-01

In our study, we examine the factors influencing the implementation of a mathematics coaching initiative at four high schools including the assets an instructional coach brings to the position and the challenges unique to each school. In our case study we include data collected in individual interviews with instructional coaches, focus groups with…

Designing a Bridging Discourse: Re-Mediation of a Mathematical Learning Disability

ERIC Educational Resources Information Center

Lewis, Katherine E.

2017-01-01

Students with disabilities present a unique instructional design challenge. These students often have qualitatively different ways of processing information, meaning that standard instructional approaches may not be effective. In this study I present a case study of a student with a mathematical learning disability for whom standard instruction on…

Assessment of Higher Order Thinking Skills. Current Perspectives on Cognition, Learning and Instruction

ERIC Educational Resources Information Center

Schraw, Gregory, Ed.; Robinson, Daniel H., Ed.

2011-01-01

This volume examines the assessment of higher order thinking skills from the perspectives of applied cognitive psychology and measurement theory. The volume considers a variety of higher order thinking skills, including problem solving, critical thinking, argumentation, decision making, creativity, metacognition, and self-regulation. Fourteen…

Using Higher Order Thinking Questions to Foster Critical Thinking: A Classroom Study

ERIC Educational Resources Information Center

Barnett, Jerrold E.; Francis, Alisha L.

2012-01-01

To determine if quizzes containing higher order thinking questions are related to critical thinking and test performance when utilised in conjunction with an immersion approach to instruction and effort-based grading, sections of an "Educational Psychology" course were assigned to one of three quizzing conditions. Quizzes contained…

Hybrid Tasks: Promoting Statistical Thinking and Critical Thinking through the Same Mathematical Activities

ERIC Educational Resources Information Center

Aizikovitsh-Udi, Einav; Clarke, David; Kuntze, Sebastian

2014-01-01

Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should…

A Preliminary Discourse Analysis of Constructivist-Oriented Mathematics Instruction for a Student with Learning Disabilities

ERIC Educational Resources Information Center

Xin, Yan Ping; Liu, Jia; Jones, Sarah R.; Tzur, Ron; Si, Luo

2016-01-01

Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of…

Development of Ideas in a GeoGebra-Aided Mathematics Instruction

ERIC Educational Resources Information Center

Ljajko, Eugen; Ibro, Vait

2013-01-01

With GeoGebra introduced into mathematics instruction the teaching/learning process is not improved in terms of speed and quality only. Mathematical concepts, rules and procedures must be adjusted to the new environment. On the other hand, characteristics of the computer and the educational software in use must be thoroughly examined and a…

REASON: A Self-Instruction Strategy for Twice-Exceptional Learners Struggling With Common Core Mathematics

ERIC Educational Resources Information Center

Van Boxtel, Joanne M.

2016-01-01

Educators across the nation are now well under way in implementing the Common Core State Standards (CCSS; National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA & CCSSO], 2010) for mathematics. The emerging literature regarding CCSS mathematics instruction for students with disabilities urges…

Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics.

ERIC Educational Resources Information Center

Artzt, Alice F.; Armour-Thomas, Eleanor

1998-01-01

Uses a "teaching as problem solving" perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning secondary-school mathematics teachers. Data analysis of observations, lesson plans, videotapes, and audiotapes of structured interviews suggests that the metacognition of…

Applying Piaget's Theory of Cognitive Development to Mathematics Instruction

ERIC Educational Resources Information Center

Ojose, Bobby

2008-01-01

This paper is based on a presentation given at National Council of Teachers of Mathematics (NCTM) in 2005 in Anaheim, California. It explicates the developmental stages of the child as posited by Piaget. The author then ties each of the stages to developmentally appropriate mathematics instruction. The implications in terms of not imposing…

Ability Grouping, Classroom Instruction, and Students' Mathematics Gains in Charter and Traditional Public Schools

ERIC Educational Resources Information Center

Berends, Mark; Donaldson, Kristi

2011-01-01

In this paper, the authors examine differences between school types in the uses of ability grouping, instructional differences, and relationship of ability grouping to student mathematics achievement. Specifically, they address the following questions with teacher reports of students' mathematics placement in middle school: (1) Does the use of…

More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction

ERIC Educational Resources Information Center

Small, Marian; Lin, Amy

2010-01-01

Teachers know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math…

A Framework for Re-Envisioning Mathematics Instruction for English Language Learners

ERIC Educational Resources Information Center

Council of the Great City Schools, 2016

2016-01-01

The overarching purpose of this document is to define a new vision for mathematics instruction that explicitly attends to the needs of English Language Learners (ELLs), addressing the interdependence of language and mathematics. The sections in this report are devoted to (1) making clear that the grade-level college- and career-readiness…

Instructional Characteristics in Mathematics Classrooms: Relationships to Achievement Goal Orientation and Student Engagement

ERIC Educational Resources Information Center

Lazarides, Rebecca; Rubach, Charlott

2017-01-01

This longitudinal study examined relationships between student-perceived teaching for meaning, support for autonomy, and competence in mathematic classrooms (Time 1), and students' achievement goal orientations and engagement in mathematics 6 months later (Time 2). We tested whether student-perceived instructional characteristics at Time 1…

Middle Grades Mathematics Engagement: How Action Research Informs What Counts

ERIC Educational Resources Information Center

Ivory, Pateakia Lachelle

2017-01-01

The purpose of the study was to examine how action research informs instructional changes that need to take place in the middle grades mathematics classroom. There is a need for an increase in engagement in middle grades mathematics by educators being critically reflective of their instructional practices. The research question addressed in this…

Improving Primary Students' Mathematical Literacy through Problem Based Learning and Direct Instruction

ERIC Educational Resources Information Center

Firdaus, Fery Muhamad; Wahyudin; Herman, Tatang

2017-01-01

This research was done on primary school students who are able to understand mathematical concepts, but unable to apply them in solving real life problems. Therefore, this study aims to improve primary school students' mathematical literacy through problem-based learning and direct instruction. In addition, the research was conducted to determine…

Mathematics Teachers' Use of Information and Communication Technologies: An International Comparison

ERIC Educational Resources Information Center

Kiru, Elisheba W.

2018-01-01

There is an urgent need to understand how often teachers use information and communication technologies (ICT) in mathematics instruction. This information can provide vital links that can help stakeholders make connections about ICT use in mathematics instruction and student learning experiences with ICT. Scholars in the field have reported on the…

Creating Printed Materials for Mathematics with a Macintosh Computer.

ERIC Educational Resources Information Center

Mahler, Philip

This document gives instructions on how to use a Macintosh computer to create printed materials for mathematics. A Macintosh computer, Microsoft Word, and objected-oriented (Draw-type) art program, and a function-graphing program are capable of producing high quality printed instructional materials for mathematics. Word 5.1 has an equation editor…

Perceptual Preferences of Mathematically Deficient Elementary Students: Implications for Instruction.

ERIC Educational Resources Information Center

McCoy, Leah P.

Two groups of elementary school students were tested and compared on learning style perceptual preference. One group was comprised of 11 students identified as being in need of remedial instruction in mathematics. The other group consisted of eight average/above average students experiencing slight or no difficulties in mathematics. Grade levels…

Good Questions: Great Ways to Differentiate Mathematics Instruction. Second Edition

ERIC Educational Resources Information Center

Small, Marian

2012-01-01

Expanded to include connections to Common Core State Standards, as well as National Council of Teachers of Mathematics (NCTM) standards, this critically acclaimed book will help every teacher and coach to meet the challenges of differentiating mathematics instruction in the K-8 classroom. In this bestseller, math education expert Marian Small…

Instructional Technologies and Pre-Service Mathematics Teachers' Selection of Technology

ERIC Educational Resources Information Center

Akcay, Ahmet Oguz

2017-01-01

There are many available technologies that can assist future teachers to deliver instruction. The purpose of this paper is to provide a brief review of literature identifying available technology tools in mathematics education and which technologies are selected by PSTs to design mathematics lesson activities. The most commonly used and available…

Mathematics Instruction in Tokyo's and Hawaii's Junior High Schools. Final Report.

ERIC Educational Resources Information Center

Hawaii Univ., Honolulu. Coll. of Education.

Mathematics instruction in junior high schools in Tokyo and Hawaii was compared in order to gain knowledge of how mathematics teachers' effectiveness in the classroom may be improved. Because they were likely to influence teachers' behavior, these factors were considered: teachers' background and teaching load, allocation of time, views on…

Mathematics Beliefs, Instructional Strategies, and Algebra Achievement of Adolescent Students in Japan: Results from the TIMSS 1999 Assessment

ERIC Educational Resources Information Center

House, J. Daniel

2006-01-01

An important area for the application of instructional design is the development of effective teaching strategies for mathematics. Activities that include the use of computers, cooperative learning, and active learning materials are associated with mathematics achievement. Student self-beliefs are also significantly related to mathematics…

The Devalued Student: Misalignment of Current Mathematics Knowledge and Level of Instruction

ERIC Educational Resources Information Center

LeMire, Steven D.; Melby, Marcella L.; Haskins, Anne M.; Williams, Tony

2012-01-01

Within this study, we investigated the association between 10th-grade students' mathematics performance and their feelings of instructional misalignment between their current mathematics knowledge and educator support. Data from the 2002 Education Longitudinal Study, which included a national sample of 750 public and private high schools in the…

A Qualitative Study of One District's Efforts to Improve Mathematics Instruction to Scale

ERIC Educational Resources Information Center

Osborne, Brian George

2011-01-01

Mathematics learning is critical for student success, and frequently acts as a gatekeeper, preventing students from graduating from high school and pursuing higher education. While many districts have attempted to improve mathematics instruction by implementing some sort of reform, few districts have attempted to execute a multifaceted systems…

The Influences of Middle School Mathematics Teachers' Practical Rationality on Instructional Decision Making Regarding the Common Core State Standards for Mathematical Practices

ERIC Educational Resources Information Center

Sobolewski-McMahon, Lauren M.

2017-01-01

The purpose of this study was to examine the influences of various facets of middle school mathematics teachers' practical rationality on their instructional decision making as they plan to enact the Common Core State Standards for Mathematical Practice, CCSS-MP1 (perseverance in problem solving) and CCSS-MP3 (communicating and critiquing). The…

Efforts to Improve Mathematics Teacher Competency Through Training Program on Design Olympiad Mathematics Problems Based on Higher Order Thinking Skills in The Junior High School

NASA Astrophysics Data System (ADS)

Arnellis, A.; Jamaan, E. Z.; Amalita, N.

2018-04-01

The goal to analyse a improvement of teacher competence after being trained in preparing high-order math olympicad based on high order thinking skills in junior high school teachers in Pesisir Selatan Regency. The sample of these activities are teachers at the MGMP junior high school in Pesisir Selatan District. Evaluation of the implementation is done by giving a pre test and post test, which will measure the success rate of the implementation of this activities. The existence of the devotion activities is expected to understand the enrichment of mathematics olympiad material and training in the preparation of math olympiad questions for the teachers of South Pesisir district junior high school, motivating and raising the interest of the participants in order to follow the mathematics olympiad with the enrichment of mathematics materials and the training of problem solving about mathematics olympiad for junior high school teachers, the participants gain experience and gain insight, as well as the ins and outs of junior mathematics olympiad and implement to teachers and students in olympic competitions. The result of that the post-test is better than the result of pretest in the training of mathematics teacher competence improvement in composing the mathematics olympiad problem based on high order thinking skills of junior high school (SMP) in Pesisir Selatan District, West Sumatra, Indonesia.

A Different Perspective of the Teaching Philosophy of RL Moore

ERIC Educational Resources Information Center

Jones, Stephen L.

2017-01-01

Dr RL Moore was undoubtedly one of the finest mathematics teachers ever. He developed a unique teaching method designed to teach his students to think like mathematicians. His method was not designed to convey any particular mathematical knowledge. Instead, it was designed to teach his students to think. Today, his method has been modified to…

The Role of Visualisation in Developing Critical Thinking in Mathematics

ERIC Educational Resources Information Center

Makina, A.

2010-01-01

Research has been conducted on the role and importance of visualisation in many fields, including psychology, but very little has been done to extend its role to mathematics education in particular. Furthermore, much research has been done on the importance of critical thinking. However, to date not much has been done to clarify the fact that…

Mathematical Thinking Process of Autistic Students in Terms of Representational Gesture

ERIC Educational Resources Information Center

Mustafa, Sriyanti; Nusantara, Toto; Subanji; Irawati, Santi

2016-01-01

The aim of this study is to describe the mathematical thinking process of autistic students in terms of gesture, using a qualitative approach. Data collecting is conducted by using 3 (three) audio-visual cameras. During the learning process, both teacher and students' activity are recorded using handy cam and digital camera (full HD capacity).…

Student Strategies Suggesting Emergence of Mental Structures Supporting Logical and Abstract Thinking: Multiplicative Reasoning

ERIC Educational Resources Information Center

Carrier, Jim

2014-01-01

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

The Stakes of Movement: A Dynamic Approach to Mathematical Thinking

ERIC Educational Resources Information Center

Roth, Wolff-Michael; Maheux, Jean-François

2015-01-01

Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what…

Five Affordances of Computational Thinking to Support Elementary Mathematics Education

ERIC Educational Resources Information Center

Gadanidis, George

2017-01-01

With the increased focus on computational thinking (CT) in education, it is important to investigate the affordances that CT may offer to support teaching and learning. This paper outlines five affordances of CT that may support elementary mathematics education, whose conceptualization was refined in a year-long study involving eight Grades 3-4…

Relationship between Professional Values and Critical Thinking Disposition of Science-Technology and Mathematics Teachers

ERIC Educational Resources Information Center

Sahin, Senar Alkin; Tunca, Nihal; Altinkurt, Yahya; Yilmaz, Kürsad

2016-01-01

The purpose of this study is to determine the relationship between the professional values and critical thinking disposition of science-technology and mathematics teachers working in middle schools. The survey research method was employed in the study. The sample of the study is comprised of 193 teachers (90 science-technology and 103 mathematics…