Making Algebra Work: Instructional Strategies that Deepen Student Understanding, within and between Algebraic Representations

ERIC Educational Resources Information Center

Star, Jon R.; Rittle-Johnson, Bethany

2009-01-01

Competence in algebra is increasingly recognized as a critical milestone in students' middle and high school years. The transition from arithmetic to algebra is a notoriously difficult one, and improvements in algebra instruction are greatly needed (National Research Council, 2001). Algebra historically has represented students' first sustained…

Learning Activity Package, Algebra.

ERIC Educational Resources Information Center

Evans, Diane

A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…

Oleanna Math Program Materials.

ERIC Educational Resources Information Center

Coole, Walter A.

This document is a collection of course outlines, syllabi, and test materials designed for several high school level and lower division mathematics courses taught in an auto-tutorial learning laboratory at Skagit Valley College (Washington). The courses included are: Pre-Algebra, Basic Algebra, Plan Geometry, Intermediate Algebra, Probability and…

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics

PubMed Central

Simzar, Rahila M.; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics. PMID:26942210

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics.

PubMed

Simzar, Rahila M; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics.

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.

Attributions for Success and Failure in Algebra of Samoan Community College Students: A Profile Analysis.

ERIC Educational Resources Information Center

Powers, Stephen; And Others

Sex differences in attributions for success and failure in algebra of Samoan community college students were examined and compared with attributions of a large group of mainland U.S. students. study included the Mathematics Attribution Scale: Algebra Version (MAS), which assessed students' attributions of achievement in algebra to their effort,…

Teaching Strategies to Improve Algebra Learning

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Larson, Matthew R.

2015-01-01

Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

Algebra: A Challenge at the Crossroads of Policy and Practice

ERIC Educational Resources Information Center

Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.

2011-01-01

The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…

A Characterization of a Unified Notion of Mathematical Function: The Case of High School Function and Linear Transformation

ERIC Educational Resources Information Center

Zandieh, Michelle; Ellis, Jessica; Rasmussen, Chris

2017-01-01

As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear…

UCSMP Algebra. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2007

2007-01-01

"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

Characterizing the Nature of Students' Feature Noticing-and-Using with Respect to Mathematical Symbols across Different Levels of Algebra Exposure

ERIC Educational Resources Information Center

Sullivan, Patrick

2013-01-01

The purpose of this study is to examine the nature of what students notice about symbols and use as they solve unfamiliar algebra problems based on familiar algebra concepts and involving symbolic inscriptions. The researcher conducted a study of students at three levels of algebra exposure: (a) students enrolled in a high school pre-calculus…

The Effect of Scheduling Models for Introductory Algebra on 9th-Grade Students, Test Scores and Grades

ERIC Educational Resources Information Center

O'Hanlon, Angela L.

2011-01-01

The purpose of the study was to determine the effect of pacing and scheduling of algebra coursework on assigned 9th-grade students who traditionally would qualify for pre-algebra instruction and same course 9th-grade students who traditionally would qualify for standard algebra instruction. Students were selected based on completion of first-year…

Meanings Given to Algebraic Symbolism in Problem-Posing

ERIC Educational Resources Information Center

Cañadas, María C.; Molina, Marta; del Río, Aurora

2018-01-01

Some errors in the learning of algebra suggest that students might have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing to analyze the students' capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process, depending on the characteristics of the algebraic…

A Meta-Analysis of Algebra Interventions for Learners with Disabilities and Struggling Learners

ERIC Educational Resources Information Center

Hughes, Elizabeth M.; Witzel, Bradley S.; Riccomini, Paul J.; Fries, Karen M.; Kanyongo, Gibbs Y.

2014-01-01

The need for global competence in mathematics is apparent. Algebra is considered a gateway course to prepare students for the demands of a competitive global market. Many students demonstrate low performance in algebra; this is especially true for students with disabilities. Effective algebra instruction is essential to increase algebra…

The role of difficulty and gender in numbers, algebra, geometry and mathematics achievement

NASA Astrophysics Data System (ADS)

Rabab'h, Belal Sadiq Hamed; Veloo, Arsaythamby; Perumal, Selvan

2015-05-01

This study aims to identify the role of difficulty and gender in numbers, algebra, geometry and mathematics achievement among secondary schools students in Jordan. The respondent of the study were 337 students from eight public secondary school in Alkoura district by using stratified random sampling. The study comprised of 179 (53%) males and 158 (47%) females students. The mathematics test comprises of 30 items which has eight items for numbers, 14 items for algebra and eight items for geometry. Based on difficulties among male and female students, the findings showed that item 4 (fractions - 0.34) was most difficult for male students and item 6 (square roots - 0.39) for females in numbers. For the algebra, item 11 (inequality - 0.23) was most difficult for male students and item 6 (algebraic expressions - 0.35) for female students. In geometry, item 3 (reflection - 0.34) was most difficult for male students and item 8 (volume - 0.33) for female students. Based on gender differences, female students showed higher achievement in numbers and algebra compare to male students. On the other hand, there was no differences between male and female students achievement in geometry test. This study suggest that teachers need to give more attention on numbers and algebra when teaching mathematics.

Using Student Work to Develop Teachers' Knowledge of Algebra

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth A.; Phillips, Elizabeth Difanis

2005-01-01

This article describes a set of learning activities that use algebraic problems and written student work to help preservice and in-service teachers understand students' algebraic thinking. (Contains 4 figures.)

Using CRA to Teach Algebra to Students with Math Difficulties in Inclusive Settings

ERIC Educational Resources Information Center

Witzel, Bradley S.

2005-01-01

The importance of algebra instruction has increased in the United States in the past few years. Thus, in most states, middle school students are required to take Algebra 1. Middle school students with math difficulties in inclusion algebra settings may require a different instructional approach. The purpose of this research was to compare student…

Reinventing Fractions and Division as They Are Used in Algebra: The Power of Preformal Productions

ERIC Educational Resources Information Center

Peck, Frederick; Matassa, Michael

2016-01-01

In this paper, we explore algebra students' mathematical realities around fractions and division, and the ways in which students reinvented mathematical productions involving fractions and division. We find that algebra students' initial realities do not include the fraction-as-quotient sub-construct. This can be problematic because in algebra,…

Exploring Teacher Noticing of Student Algebraic Thinking in a Video Club

ERIC Educational Resources Information Center

Walkoe, Janet

2015-01-01

Learning algebra is critical for students in the USA today, yet many students in the USA struggle in algebra classes. Researchers claim that one reason for these difficulties is that algebra classes often focus on symbol manipulation and procedures above, and many times at the expense of, a more conceptual understanding of the content. Teaching…

Utilization of variation theory in the classroom: Effect on students' algebraic achievement and motivation

NASA Astrophysics Data System (ADS)

Jing, Ting Jing; Tarmizi, Rohani Ahmad; Bakar, Kamariah Abu; Aralas, Dalia

2017-01-01

This study investigates the effect of utilizing Variation Theory Based Strategy on students' algebraic achievement and motivation in learning algebra. The study used quasi-experimental non-equivalent control group research design and involved 56 Form Two (Secondary Two) students in two classes (28 in experimental group, 28 in control group) in Malaysia The first class of students went through algebra class taught with Variation Theory Based Strategy (VTBS) while the second class of students experienced conventional teaching strategy. The instruments used for the study were a 24-item Algebra Test and 36-item Instructional Materials Motivation Survey. Result from analysis of Covariance indicated that experimental group students achieved significantly better test scores than control group. Result of Multivariate Analysis of Variance also shows evidences of significant effect of VTBS on experimental students' overall motivation in all the five subscales; attention, relevance, confidence, and satisfaction. These results suggested the utilization of VTBS would improve students' learning in algebra.

Conceptualizing Routines of Practice That Support Algebraic Reasoning in Elementary Schools: A Constructivist Grounded Theory

ERIC Educational Resources Information Center

Store, Jessie Chitsanzo

2012-01-01

There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research…

A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2016-12-01

Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.

Assessment of polytechnic students' understanding of basic algebra

NASA Astrophysics Data System (ADS)

Mokmin, Nur Azlina Mohamed; Masood, Mona

2015-12-01

It is important for engineering students to excel in algebra. Previous studies show that the algebraic fraction is a subtopic of algebra that was found to be the most challenging for engineering students. This study is done with 191 first semester engineering students who have enrolled in engineering programs in Malaysian polytechnic. The respondents are divided into Group 1 (Distinction) and Group 2 (Credit) based on their Mathematics SPM result. A computer application is developed for this study to assess student information and understanding of the algebraic fraction topic. The result is analyzed using SPSS and Microsoft Excel. The test results show that there are significant differences between Group 1 and Group 2 and that most of the students scored below the minimum requirement.

The Impact of New State Accountability Standards on Algebra I Students

ERIC Educational Resources Information Center

Heath, Kyle G.

2013-01-01

The purpose of this quasi-experimental quantitative study was to determine if a new Algebra I curriculum resulted in improved student performance on the state Algebra I exam. The treatment group consisted of 383 9th grade Algebra I students who received the college-ready standards-based (CRSB) curricula. The control group consisted of 338 9th…

Card Games and Algebra Tic Tacmatics on Achievement of Junior Secondary II Students in Algebraic Expressions

ERIC Educational Resources Information Center

Okpube, Nnaemeka Michael; Anugwo, M. N.

2016-01-01

This study investigated the Card Games and Algebra tic-Tacmatics on Junior Secondary II Students' Achievement in Algebraic Expressions. Three research questions and three null hypotheses guided the study. The study adopted the pre-test, post-test control group design. A total of two hundred and forty (240) Junior Secondary School II students were…

Difficulties in initial algebra learning in Indonesia

NASA Astrophysics Data System (ADS)

Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

2014-12-01

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 1). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School, First Course in Algebra, Part 1. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the student text for part one of a three-part SMSG algebra course for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables; operations;…

Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

NASA Astrophysics Data System (ADS)

Aryani, F.; Amin, S. M.; Sulaiman, R.

2018-01-01

Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.

Those Do What? Connecting Eigenvectors and Eigenvalues to the Rest of Linear Algebra: Using Visual Enhancements to Help Students Connect Eigenvectors to the Rest of Linear Algebra

ERIC Educational Resources Information Center

Nyman, Melvin A.; Lapp, Douglas A.; St. John, Dennis; Berry, John S.

2010-01-01

This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…

Symbolic Notations and Students' Achievements in Algebra

ERIC Educational Resources Information Center

Peter, Ebiendele E.; Olaoye, Adetunji A.

2013-01-01

This study focuses on symbolic notations and its impact on students' achievement in Algebra. The main reason for this study rests on the observation from personal and professional experiences on students' increasing hatred for Algebra. One hundred and fifty (150) Senior Secondary School Students (SSS) from Ojo Local Education District, Ojo, Lagos,…

What Students Choose to Do and Have to Say about Use of Multiple Representations in College Algebra

ERIC Educational Resources Information Center

Herman, Marlena

2007-01-01

This report summarizes findings on strategies chosen by students (n=38) when solving algebra problems related to various functions with the freedom to use a TI-83 graphing calculator, influences on student problem-solving strategy choices, student ability to approach algebra problems with use of multiple representations, and student beliefs on how…

Algebra for All: The Effect of Algebra Coursework and Classroom Peer Academic Composition on Low-Achieving Students

ERIC Educational Resources Information Center

Nomi, Takako; Raudenbush, Stephen W.

2014-01-01

Algebra is often considered as a gateway for later achievement. A recent report by the Mathematics Advisory Panel (2008) underscores the importance of improving algebra learning in secondary school. Today, a growing number of states and districts require algebra for all students in ninth grade or earlier. Chicago is at the forefront of this…

Contextualizing symbol, symbolizing context

NASA Astrophysics Data System (ADS)

Maudy, Septiani Yugni; Suryadi, Didi; Mulyana, Endang

2017-08-01

When students learn algebra for the first time, inevitably they are experiencing transition from arithmetic to algebraic thinking. Once students could apprehend this essential mathematical knowledge, they are cultivating their ability in solving daily life problems by applying algebra. However, as we dig into this transitional stage, we identified possible students' learning obstacles to be dealt with seriously in order to forestall subsequent hindrance in studying more advance algebra. We come to realize this recurring problem as we undertook the processes of re-personalization and re-contextualization in which we scrutinize the very basic questions: 1) what is variable, linear equation with one variable and their relationship with the arithmetic-algebraic thinking? 2) Why student should learn such concepts? 3) How to teach those concepts to students? By positioning ourselves as a seventh grade student, we address the possibility of children to think arithmetically when confronted with the problems of linear equation with one variable. To help them thinking algebraically, Bruner's modes of representation developed contextually from concrete to abstract were delivered to enhance their interpretation toward the idea of variables. Hence, from the outset we designed the context for student to think symbolically initiated by exploring various symbols that could be contextualized in order to bridge student traversing the arithmetic-algebraic fruitfully.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Henan, E-mail: wuhenanby@163.com; Chen, Qiufan; Yue, Xiaoqing

The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.

Math Placement Validation Study: A Summary of the Criterion-Related Validity Evidence and Multiple Measures Data for the San Diego Community College District.

ERIC Educational Resources Information Center

Armstrong, William B.

In Fall 1994, the San Diego Community College District (SDCCD), in California, conducted a study to determine the validity of the Mathematics Diagnostic Testing Project (MDTP) placement test. The MDTP provides tests at four levels (i.e., algebra readiness, elementary algebra, intermediate algebra, and pre-calculus) and is used in the District for…

Using Students' Interests as Algebraic Models

ERIC Educational Resources Information Center

Whaley, Kenneth A.

2012-01-01

Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

Students' Perceptions about the Symbols, Letters and Signs in Algebra and How Do These Affect Their Learning of Algebra: A Case Study in a Government Girls Secondary School Karachi

ERIC Educational Resources Information Center

Samo, Mashooque Ali

2009-01-01

Algebra uses symbols for generalizing arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by on the students' difficulties in understanding letters in Algebra, the overall image that emerges from the…

College Algebra Students' Attitudes toward Mathematics in Their Careers

ERIC Educational Resources Information Center

Champion, Joe; Parker, Frieda; Mendoza-Spencer, Bernadette; Wheeler, Ann

2011-01-01

The purpose of this study was to identify the degree to which college algebra students' value mathematical skills in their prospective careers. A survey was administered to N = 144 students in 6 college algebra classes at a mid-sized doctoral granting university. Students in half the classes completed a data analysis project, and half of the…

Linear Algebra Revisited: An Attempt to Understand Students' Conceptual Difficulties

ERIC Educational Resources Information Center

Britton, Sandra; Henderson, Jenny

2009-01-01

This article looks at some of the conceptual difficulties that students have in a linear algebra course. An overview of previous research in this area is given, and the various theories that have been espoused regarding the reasons that students find linear algebra so difficult are discussed. Student responses to two questions testing the ability…

A Proposed Algebra Assessment for Use in a Problem-Analysis Framework

ERIC Educational Resources Information Center

Walick, Christopher M.; Burns, Matthew K.

2017-01-01

Algebra is critical to high school graduation and college success, but student achievement in algebra frequently falls significantly below expected proficiency levels. While existing research emphasizes the importance of quality algebra instruction, there is little research about how to conduct problem analysis for struggling secondary students.…

Students’ Algebraic Thinking Process in Context of Point and Line Properties

NASA Astrophysics Data System (ADS)

Nurrahmi, H.; Suryadi, D.; Fatimah, S.

2017-09-01

Learning of schools algebra is limited to symbols and operating procedures, so students are able to work on problems that only require the ability to operate symbols but unable to generalize a pattern as one of part of algebraic thinking. The purpose of this study is to create a didactic design that facilitates students to do algebraic thinking process through the generalization of patterns, especially in the context of the property of point and line. This study used qualitative method and includes Didactical Design Research (DDR). The result is students are able to make factual, contextual, and symbolic generalization. This happen because the generalization arises based on facts on local terms, then the generalization produced an algebraic formula that was described in the context and perspective of each student. After that, the formula uses the algebraic letter symbol from the symbol t hat uses the students’ language. It can be concluded that the design has facilitated students to do algebraic thinking process through the generalization of patterns, especially in the context of property of the point and line. The impact of this study is this design can use as one of material teaching alternative in learning of school algebra.

Implementation of Algebra I in Eighth Grade: An "Ex-Post Facto" Study on Student Achievement

ERIC Educational Resources Information Center

Realdine, Dorothy S.

2010-01-01

Only recently have school districts across the nation begun to offer Algebra I to all eighth grade students. Currently, most eighth grade Algebra I curriculum does not have a national consistent focus of topics or level of rigor. A key issue of implementing Algebra I in eighth grade is defining national Algebra I concepts and skills that students…

Does Early Algebraic Reasoning Differ as a Function of Students’ Difficulty with Calculations versus Word Problems?

PubMed Central

Powell, Sarah R.; Fuchs, Lynn S.

2014-01-01

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2nd- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. PMID:25309044

Funny Face Contest: A Formative Assessment

ERIC Educational Resources Information Center

Colen, Yong S.

2010-01-01

Many American students begin their high school mathematics study with the algebra 1-geometry-algebra 2 sequence. After algebra 2, then, students with average or below-average mathematical ability face a dilemma in choosing their next mathematics course. For students to succeed in higher mathematics, understanding the concept of functions is…

Learning Algebra from Worked Examples

ERIC Educational Resources Information Center

Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.

2014-01-01

For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

Improving Algebra Preparation: Implications from Research on Student Misconceptions and Difficulties

ERIC Educational Resources Information Center

Welder, Rachael M.

2012-01-01

Through historical and contemporary research, educators have identified widespread misconceptions and difficulties faced by students in learning algebra. Many of these universal issues stem from content addressed long before students take their first algebra course. Yet elementary and middle school teachers may not understand how the subtleties of…

Ten-Year-Old Students Solving Linear Equations

ERIC Educational Resources Information Center

Brizuela, Barbara; Schliemann, Analucia

2004-01-01

In this article, the authors seek to re-conceptualize the perspective regarding students' difficulties with algebra. While acknowledging that students "do" have difficulties when learning algebra, they also argue that the generally espoused criteria for algebra as the ability to work with the syntactical rules for solving equations is…

The Effect of an Intelligent Tutoring System (ITS) on Student Achievement in Algebraic Expression

ERIC Educational Resources Information Center

Chien, Tsai Chen; Md. Yunus, Aida Suraya; Ali, Wan Zah Wan; Bakar, Ab. Rahim

2008-01-01

In this experimental study, use of Computer Assisted Instruction (CAI) followed by use of an Intelligent Tutoring System (CAI+ITS) was compared to the use of CAI (CAI only) in tutoring students on the topic of Algebraic Expression. Two groups of students participated in the study. One group of 32 students studied algebraic expression in a CAI…

Build an Early Foundation for Algebra Success

ERIC Educational Resources Information Center

Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela

2016-01-01

Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…

A Balancing Act: Making Sense of Algebra

ERIC Educational Resources Information Center

Gavin, M. Katherine; Sheffield, Linda Jensen

2015-01-01

For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

Unifying the Algebra for All Movement

ERIC Educational Resources Information Center

Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.

2015-01-01

There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…

Using Linguistics in the Teaching of Developmental and Remedial Algebra.

ERIC Educational Resources Information Center

Lesnak, Richard J.

Basic algebra at Robert Morris College (RMC) in Pittsburgh, Pennsylvania, is a remedial course for students with virtually no algebra background, and for students whose previous experiences with algebra have created math blocks and math anxiety. A study was conducted in an effort to measure quantitatively the benefits of using linguistic methods…

Dienes AEM as an alternative mathematics teaching aid to enhance Indonesian students’ understanding of algebra concept

NASA Astrophysics Data System (ADS)

Soro, S.; Maarif, S.; Kurniawan, Y.; Raditya, A.

2018-01-01

The aim of this study is to find out the effect of Dienes AEM (Algebra Experience Materials) on the ability of understanding concept of algebra on the senior high school student in Indonesia. This research is an experimental research with subject of all high school students in Indonesia. The samples taken were high school students in three provinces namely DKI Jakarta Province, West Java Province and Banten Province. From each province was taken senior high school namely SMA N 9 Bekasi West Java, SMA N 94 Jakarta and SMA N 5 Tangerang, Banten. The number of samples in this study was 114 high school students of tenth grade as experimental class and 115 high school students of tenth grade as control class. Learning algebra concept is needed in learning mathematics, besides it is needed especially to educate students to be able to think logically, systematically, critically, analytically, creatively, and cooperation. Therefore in this research will be developed an effective algebra learning by using Dienes AEM. The result of this research is that there is a significant influence on the students’ concept comprehension ability taught by using Dienes AEM learning as an alternative to instill the concept of algebra compared to the students taught by conventional learning. Besides, the students’ learning motivation increases because students can construct the concept of algebra with props.

Building Students' Reasoning Skills by Promoting Student-Led Discussions in an Algebra II Class

ERIC Educational Resources Information Center

DeJarnette, Anna F.; González, Gloriana

2013-01-01

Current research and professional organizations call for greater emphasis on reasoning and sense making in algebra (Chazan, 2000; Cuoco, Goldenberg, & Mark, 1996; Harel & Sowder, 2005; National Council of Teachers of Mathematics [NCTM], 2009, 2010). This paper illustrates how students in an Algebra II class had opportunities to develop…

The Effects of Representations, Constructivist Approaches, and Engagement on Middle School Students' Algebraic Procedure and Conceptual Understanding

ERIC Educational Resources Information Center

Ross, Amanda; Willson, Victor

2012-01-01

This study examined the effects of types of representations, constructivist teaching approaches, and student engagement on middle school algebra students' procedural knowledge and conceptual understanding. Data gathered from 16 video lessons and algebra pretest/posttests were used to run three multilevel structural equation models. Symbolic…

Curriculum Guide for Baccalaureate Oriented Courses in Mathematics.

ERIC Educational Resources Information Center

Darnes, G. Robert, Ed.

A mathematics curriculum guide is presented for the purpose of offering statewide guidelines to colleges for determining the content of those courses which might be considered standard courses in the first two years of the college curriculum. Courses covered include: intermediate algebra, college algebra, trigonometry, analytic geometry,…

The Unintended Consequences of an Algebra-for-All Policy on High-Skill Students: Effects on Instructional Organization and Students' Academic Outcomes

ERIC Educational Resources Information Center

Nomi, Takako

2012-01-01

In 1997, Chicago implemented a policy that required algebra for all ninth-grade students, eliminating all remedial coursework. This policy increased opportunities to take algebra for low-skill students who had previously enrolled in remedial math. However, little is known about how schools respond to the policy in terms of organizing math…

Learning to Apply Algebra in the Community for Adults with Intellectual Developmental Disabilities

ERIC Educational Resources Information Center

Rodriguez, Anthony M.

2016-01-01

Students with intellectual and developmental disabilities (IDD) are routinely excluded from algebra and other high-level mathematics courses. High school students with IDD take courses in arithmetic and life skills rather than having an opportunity to learn algebra. Yet algebra skills can support the learning of money and budgeting skills. This…

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…

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…

Solving the Unknown with Algebra: Poster/Teaching Guide for Pre-Algebra Students. Expect the Unexpected with Math[R

ERIC Educational Resources Information Center

Actuarial Foundation, 2013

2013-01-01

"Solving the Unknown with Algebra" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards and designed to help students practice pre-algebra skills including using formulas, solving for unknowns, and manipulating equations. Developed by The Actuarial Foundation with Scholastic, this program provides…

Developing "Algebraic Thinking": Two Key Ways to Establish Some Early Algebraic Ideas in Primary Classrooms

ERIC Educational Resources Information Center

Ormond, Christine

2012-01-01

Primary teachers play a key role in their students' future mathematical success in the early secondary years. While the word "algebra" may make some primary teachers feel uncomfortable or worried, the basic arithmetic ideas underlying algebra are vitally important for older primary students as they are increasingly required to use "algebraic…

Investigating Students' Modes of Thinking in Linear Algebra: The Case of Linear Independence

ERIC Educational Resources Information Center

Çelik, Derya

2015-01-01

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

Algebra and Algebraic Thinking in School Math: 70th YB

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2008

2008-01-01

Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

Teaching Structure in Algebra

ERIC Educational Resources Information Center

Merlin, Ethan M.

2013-01-01

This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

Fostering Middle School Students' Relational Thinking of the Equal Sign Using GeoGebra

ERIC Educational Resources Information Center

Ko, Yi-Yin; Karadag, Zekeriya

2013-01-01

Current reforms in mathematics education have called for a stronger emphasis on the teaching and learning of algebra for all students at all grade levels. Succeeding in algebra can prepare students to learn and understand more advanced mathematics in the future. One topic in algebra--the equal sign--has received considerable attention in middle…

Constructing and Modeling Algebraic Statements in the Multiplicative Domain: Investigating Fourth-Grade Student and Teacher Learning

ERIC Educational Resources Information Center

Grandau, Laura

2013-01-01

This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…

An Uncommon Approach to a Common Algebraic Error

ERIC Educational Resources Information Center

Rossi, Paul S.

2008-01-01

The basic rules of elementary algebra can often appear beyond the grasp of many students. Even though most subjects, including calculus, prove to be more difficult, it is the simple rules of algebra that continue to be the "thorn in the side" of many mathematics students. In this paper we present a result intended to help students achieve a…

Using Example Problems to Improve Student Learning in Algebra: Differentiating between Correct and Incorrect Examples

ERIC Educational Resources Information Center

Booth, Julie L.; Lange, Karin E.; Koedinger, Kenneth R.; Newton, Kristie J.

2013-01-01

In a series of two "in vivo" experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly…

Using Example Problems to Improve Student Learning in Algebra: Differentiating between Correct and Incorrect Examples

ERIC Educational Resources Information Center

Booth, Julie L.; Lange, Karin E.; Koedinger, Kenneth R.; Newton, Kristie J.

2013-01-01

In a series of two in vivo experiments, we examine whether correct and incorrect examples with prompts for self-explanation can be effective for improving students' conceptual understanding and procedural skill in Algebra when combined with guided practice. In Experiment 1, students working with the Algebra I Cognitive Tutor were randomly assigned…

Student and Instructor Perceptions of a Flipped College Algebra Classroom

ERIC Educational Resources Information Center

Jaster, Robert W.

2017-01-01

Each year about half a million students fail to make planned academic progress due to college algebra, hence the need for researchers to find ways of improving the quality of instruction in the course. Recent research suggests that flipping college algebra to allow time for active learning in the classroom may improve student performance. Also,…

Developing Meaning for Algebraic Procedures: An Exploration of the Connections Undergraduate Students Make between Algebraic Rational Expressions and Basic Number Properties

ERIC Educational Resources Information Center

Yantz, Jennifer

2013-01-01

The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting the postsecondary success of students majoring in STEM fields. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. The present study…

From No to Yes: The Impact of an Intervention on The Persistence of Algebraic Misconceptions among Secondary School Algebra Students

ERIC Educational Resources Information Center

Zielinski, Susan F.

2017-01-01

Many students enter high school with persistent algebraic misconceptions that limit their success in mathematics and, by extension, limit potential educational attainment and future earnings. The purpose of this study was to assess the effectiveness of a warm conceptual change based intervention on remediating algebraic misconceptions held by…

A Study of Improving Eighth Graders' Learning Deficiency in Algebra by Applying a Realistic Context Instructional Design

ERIC Educational Resources Information Center

Chang, Yu-Liang; Huang, Yu-I

2014-01-01

The intention of this study was to improve the learning deficiency in algebraic learning and to enhance Taiwanese middle students' learning achievement and interest in algebra. By using a grade skipping experimental design, the research team intended to find out an effective way to benefit these students' leaning in abstract algebraic concepts.…

Linking Computer Algebra Systems and Paper-and-Pencil Techniques To Support the Teaching of Mathematics.

ERIC Educational Resources Information Center

van Herwaarden, Onno A.; Gielen, Joseph L. W.

2002-01-01

Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…

Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students. Educator's Practice Guide. What Works Clearinghouse.™ NCEE 2015-4010

ERIC Educational Resources Information Center

Star, Jon R.; Foegen, Anne; Larson, Matthew R.; McCallum, William G.; Porath, Jane; Zbiek, Rose Mary; Caronongan, Pia; Furgeson, Joshua,; Keating, Betsy; Lyskawa, Julia

2015-01-01

Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students". The methods and examples included in…

Analysis of Secondary School Students’ Algebraic Thinking and Math-Talk Learning Community to Help Students Learn

NASA Astrophysics Data System (ADS)

Nurhayati, D. M.; Herman, T.; Suhendra, S.

2017-09-01

This study aims to determine the difficulties of algebraic thinking ability of students in one of secondary school on quadrilateral subject and to describe Math-Talk Learning Community as the alternative way that can be done to overcome the difficulties of the students’ algebraic thinking ability. Research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and twenty three students as the sample that was chosen by purposive sampling technique. Data of algebraic thinking were collected through essay test. The results showed the percentage of achievement of students’ algebraic thinking’s indicators on three aspects: a) algebra as generalized arithmetic with the indicators (conceptually based computational strategies and estimation); b) algebra as the language of mathematics (meaning of variables, variable expressions and meaning of solution); c) algebra as a tool for functions and mathematical modelling (representing mathematical ideas using equations, tables, or words and generalizing patterns and rules in real-world contexts) is still low. It is predicted that because the secondary school students was not familiar with the abstract problem and they are still at a semi-concrete stage where the stage of cognitive development is between concrete and abstract. Based on the percentage achievement of each indicators, it can be concluded that the level of achievement of student’s mathematical communication using conventional learning is still low, so students’ algebraic thinking ability need to be improved.

Solving Our Algebra Problem: Getting All Students through Algebra I to Improve Graduation Rates

ERIC Educational Resources Information Center

Schachter, Ron

2013-01-01

graduation as well as admission to most colleges. But taking algebra also can turn into a pathway for failure, from which some students never recover. In 2010, a national U.S. Department of Education study…

STUDY OF VARIABLES ASSOCIATED WITH FINAL GRADES IN MATHEMATICS COURSES.

ERIC Educational Resources Information Center

DAVIS, ELTON C.; RISSER, JOHN J.

THIS STUDY WAS CONDUCTED IN ORDER TO DETERMINE THE RELATIVE VALUE OF PREVIOUS GRADES IN MATHEMATICS COURSES, THE OVERALL HIGH SCHOOL GRADE POINT AVERAGE, AND THE PLACEMENT TEST IN MATHEMATICS DEVELOPED AT THE COLLEGE AS PREDICTORS OF ACHIEVEMENT IN INTRODUCTORY AND INTERMEDIATE ALGEBRA, IN COLLEGE ALGEBRA, IN TRIGONOMETRY, AND IN ANALYTIC GEOMETRY…

Preliminary Success and Retention Rates in Selected Math Courses. Research Report.

ERIC Educational Resources Information Center

Cuesta Coll., San Luis Obispo, CA. Matriculation and Research Services.

This report presents findings of exploratory research on success, retention, and persistence in math courses at Cuesta College. The following research questions were addressed: (1) How do success rates in Math 23 (elementary algebra) and Math 27 (intermediate algebra) compare with traditional and computer-assisted formats? (2) What are the…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 1), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for High School, First Course in Algebra, Part 1, Teacher's Commentary. Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the teacher's commentary for part one of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables;…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 2). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School, First Course in Algebra, Part 2. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real numbers, subtraction and division…

The effects of an integrated Algebra 1/physical science curriculum on student achievement in Algebra 1, proportional reasoning and graphing abilities

NASA Astrophysics Data System (ADS)

Lawrence, Lettie Carol

1997-08-01

The purpose of this investigation was to determine if an integrated curriculum in algebra 1/physical science facilitates acquisition of proportional reasoning and graphing abilities better than a non-integrated, traditional, algebra 1 curriculum. Also, this study was to ascertain if the integrated algebra 1/physical science curriculum resulted in greater student achievement in algebra 1. The curriculum used in the experimental class was SAM 9 (Science and Mathematics 9), an investigation-based curriculum that was written to integrate physical science and basic algebra content. The experiment was conducted over one school year. The subjects in the study were 61 ninth grade students. The experimental group consisted of one class taught concurrently by a mathematics teacher and a physical science teacher. The control group consisted of three classes of algebra 1 students taught by one mathematics teacher and taking physical science with other teachers in the school who were not participating in the SAM 9 program. This study utilized a quasi-experimental non-randomized control group pretest-posttest design. The investigator obtained end-of-algebra 1 scores from student records. The written open-ended graphing instruments and the proportional reasoning instrument were administered to both groups as pretests and posttests. The graphing instruments were also administered as a midtest. A two sample t-test for independent means was used to determine significant differences in achievement on the end-of-course algebra 1 test. Quantitative data from the proportional reasoning and graphing instruments were analyzed using a repeated measures analysis of variance to determine differences in scores over time for the experimental and control groups. The findings indicate no significant difference between the experimental and control groups on the end-of-course algebra 1 test. Results also indicate no significant differences in proportional reasoning and graphing abilities between the two groups over time. However, all subjects (experimental and control groups) made significant improvement in graphing abilities over one school year. In this study, students participating in an investigation-based curriculum integrating algebra 1 and physical science performed as well on the instruments as the students in the traditional curriculum. Therefore, an argument can be made that instruction using an integrated curriculum (algebra l/physical science) is a viable alternative to instruction using a more traditional algebra 1 curriculum. Finally, the integrated curriculum adheres to the constructivist theoretical perspective (Krupnik-Gotlieb, 1995) and is more consistent with recommendations in the NCTM Standards (1992) than the traditional curriculum.

Mathematics in the Real World.

ERIC Educational Resources Information Center

Borenstein, Matt

1997-01-01

The abstract nature of algebra causes difficulties for many students. Describes "Real-World Data," an algebra course designed for students with low grades in algebra and provides multidisciplinary experiments (linear functions and variations; quadratic, square-root, and inverse relations; and exponential and periodic variation)…

How Do Algebra I Course Repetition Rates Vary among English Learner Students by Length of Time to Reclassification as English Proficient? REL 2017-222

ERIC Educational Resources Information Center

Jaquet, Karina; Fong, Anthony B.

2017-01-01

Research has found high repetition rates for students in Algebra I, with one study finding a repetition rate of 44 percent for students in a large urban high school district. Less is known about how math performance and Algebra I course repetition rates vary among students with different levels of English proficiency. This report examines Algebra…

Comparing the Impact of Traditional and Modeling College Algebra Courses on Student Performance in Survey of Calculus

ERIC Educational Resources Information Center

West, Jerry G.

2013-01-01

Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…

The Struggle to Pass Algebra: Online vs. Face-to-Face Credit Recovery for At-Risk Urban Students

ERIC Educational Resources Information Center

Heppen, Jessica B.; Sorensen, Nicholas; Allensworth, Elaine; Walters, Kirk; Rickles, Jordan; Taylor, Suzanne Stachel; Michelman, Valerie

2017-01-01

Students who fail algebra are significantly less likely to graduate on time, and algebra failure rates are consistently high in urban districts. Identifying effective credit recovery strategies is critical for getting students back on track. Online courses are now widely used for credit recovery, yet there is no rigorous evidence about the…

Enhancing Engagement in Algebra: Didactical Strategies Implemented and Discussed by Teachers

ERIC Educational Resources Information Center

Nyman, Rimma; Kilhamn, Cecilia

2015-01-01

The aim of this study is to investigate student engagement from the point of view of the teacher, by focusing on teacher's didactical strategies used to engage students during algebra introduction. Eight teachers in grade 6 and 7 participated in a focus-group interview study. The findings are based on episodes of student engagement in algebra and…

An Investigation of Selected Variables Related to Student Algebra I Performance in Mississippi

ERIC Educational Resources Information Center

Scott, Undray

2016-01-01

This research study attempted to determine if specific variables were related to student performance on the Algebra I subject-area test. This study also sought to determine in which of grades 8, 9, or 10 students performed better on the Algebra I Subject Area Test. This study also investigated the different criteria that are used to schedule…

The Effects of Teacher Collective Responsibility on the Mathematics Achievement of Students Who Repeat Algebra

ERIC Educational Resources Information Center

Morales-Chicas, Jessica; Agger, Charlotte

2017-01-01

In this article, the authors use the national High School Longitudinal Study of 2009 (HSLS:09) dataset to explore (a) if repeating algebra in the eighth grade was associated with overall mathematics grades and course-taking patterns by twelfth grade, (b) if repeating algebra in the eighth grade was associated with students' final grade in algebra,…

Learning to Apply Algebra in the Community for Adults With Intellectual Developmental Disabilities.

PubMed

Rodriguez, Anthony M

2016-02-01

Students with intellectual and developmental disabilities (IDD) are routinely excluded from algebra and other high-level mathematics courses. High school students with IDD take courses in arithmetic and life skills rather than having an opportunity to learn algebra. Yet algebra skills can support the learning of money and budgeting skills. This study explores the feasibility of algebra instruction for adults with IDD through an experimental curriculum. Ten individuals with IDD participated in a 6-week course framing mathematics concepts within the context of everyday challenges in handling money. The article explores classroom techniques, discusses student strategies, and proposes possible avenues for future research analyzing mathematics instructional design strategies for individuals with IDD.

A Worked Example for Creating Worked Examples

ERIC Educational Resources Information Center

McGinn, Kelly M.; Lange, Karin E.; Booth, Julie L.

2015-01-01

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

Relational Algebra and SQL: Better Together

ERIC Educational Resources Information Center

McMaster, Kirby; Sambasivam, Samuel; Hadfield, Steven; Wolthuis, Stuart

2013-01-01

In this paper, we describe how database instructors can teach Relational Algebra and Structured Query Language together through programming. Students write query programs consisting of sequences of Relational Algebra operations vs. Structured Query Language SELECT statements. The query programs can then be run interactively, allowing students to…

Primary School Students' Strategies in Early Algebra Problem Solving Supported by an Online Game

ERIC Educational Resources Information Center

van den Heuvel-Panhuizen, Marja; Kolovou, Angeliki; Robitzsch, Alexander

2013-01-01

In this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10-12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the…

Solving Absolute Value Equations Algebraically and Geometrically

ERIC Educational Resources Information Center

Shiyuan, Wei

2005-01-01

The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.

Flipping College Algebra: Effects on Student Engagement and Achievement

ERIC Educational Resources Information Center

Ichinose, Cherie; Clinkenbeard, Jennifer

2016-01-01

This study compared student engagement and achievement levels between students enrolled in a traditional college algebra lecture course and students enrolled in a "flipped" course. Results showed that students in the flipped class had consistently higher levels of achievement throughout the course than did students in the traditional…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 2), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for High School, First Course in Algebra, Part 2, Teacher's Commentary. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the teacher's commentary for part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real…

Algebridge. Concept Based Instructional Assessment.

ERIC Educational Resources Information Center

College Entrance Examination Board, Princeton, NJ.

Students who study algebra are more likely to attend college than those who don't. A major hurdle for students in studying algebra is the transition from arithmetic to algebra. In response to overcoming this hurdle, the College Board and Educational Testing Service has developed "Algebridge," a teaching supplement that integrates…

The Zero Product Principle Error.

ERIC Educational Resources Information Center

Padula, Janice

1996-01-01

Argues that the challenge for teachers of algebra in Australia is to find ways of making the structural aspects of algebra accessible to a greater percentage of students. Uses the zero product principle to provide an example of a common student error grounded in the difficulty of understanding the structure of algebra. (DDR)

Astro Algebra [CD-ROM].

ERIC Educational Resources Information Center

1997

Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…

Three Phase Ranking Framework for Assessing Conceptual Understanding in Algebra Using Multiple Representations

ERIC Educational Resources Information Center

Panasuk, Regina M.

2010-01-01

Algebra students may often demonstrate a certain degree of proficiency when manipulating algebraic expressions and verbalizing their behaviors. Do these abilities imply conceptual understanding? What is a reliable indicator that would provide educators with a relatively trustworthy and consistent measure to identify whether students learn…

Seeing through Symbols: The Case of Equivalent Expressions.

ERIC Educational Resources Information Center

Kieran, Carolyn; Sfard, Anna

1999-01-01

Presents a teaching experiment to turn students from external observers into active participants in a game of algebra learning where students use graphs to build meaning for equivalence of algebraic expressions. Concludes that the graphic-functional approach seems to make the introduction to algebra much more meaningful for the learner. (ASK)

The impact of fraction magnitude knowledge on algebra performance and learning.

PubMed

Booth, Julie L; Newton, Kristie J; Twiss-Garrity, Laura K

2014-02-01

Knowledge of fractions is thought to be crucial for success with algebra, but empirical evidence supporting this conjecture is just beginning to emerge. In the current study, Algebra 1 students completed magnitude estimation tasks on three scales (0-1 [fractions], 0-1,000,000, and 0-62,571) just before beginning their unit on equation solving. Results indicated that fraction magnitude knowledge, and not whole number knowledge, was especially related to students' pretest knowledge of equation solving and encoding of equation features. Pretest fraction knowledge was also predictive of students' improvement in equation solving and equation encoding skills. Students' placement of unit fractions (e.g., those with a numerator of 1) was not especially useful for predicting algebra performance and learning in this population. Placement of non-unit fractions was more predictive, suggesting that proportional reasoning skills might be an important link between fraction knowledge and learning algebra. Copyright © 2013 Elsevier Inc. All rights reserved.

Solving Geometric Problems by Using Algebraic Representation for Junior High School Level 3 in Van Hiele at Geometric Thinking Level

ERIC Educational Resources Information Center

Suwito, Abi; Yuwono, Ipung; Parta, I. Nengah; Irawati, Santi; Oktavianingtyas, Ervin

2016-01-01

This study aims to determine the ability of algebra students who have 3 levels van Hiele levels. Follow its framework Dindyal framework (2007). Students are required to do 10 algebra shaped multiple choice, then students work 15 about the geometry of the van Hiele level in the form of multiple choice questions. The question has been tested levels…

Trends in Algebra II Completion and Failure Rates for Students Entering Texas Public High Schools. REL 2018-289

ERIC Educational Resources Information Center

Stoker, Ginger; Mellor, Lynn; Sullivan, Kate

2018-01-01

This study examines Algebra II completion and failure rates for students entering Texas public high schools from 2007/08 through 2014/15. This period spans the time when Texas students, beginning with the 2007/08 grade 9 cohort, were required to take four courses each in English, math (including Algebra II), science, and social studies (called the…

Designing Virtual Worlds for Use in Mathematics Education.

ERIC Educational Resources Information Center

Winn, William; Bricken, William

Virtual Reality (VR) is a computer generated, multi-dimensional, inclusive environment that can build axioms of algebra into the behavior of the world. This paper discusses the use of VR to represent part of the algebra curriculum in order to improve students' classroom experiences in learning algebra. Students learn to construct their knowledge…

Activities for Students: Biology as a Source for Algebra Equations--The Heart

ERIC Educational Resources Information Center

Horak, Virginia M.

2005-01-01

The high school course that integrated first year algebra with an introductory environmental biology/anatomy and physiology course, in order to solve algebra problems is discussed. Lessons and activities for the course were taken by identifying the areas where mathematics and biology content intervenes may help students understand biology concepts…

Analyzing Algebraic Thinking Using "Guess My Number" Problems

ERIC Educational Resources Information Center

Patton, Barba; De Los Santos, Estella

2012-01-01

The purpose of this study was to assess student knowledge of numeric, visual and algebraic representations. A definite gap between arithmetic and algebra has been documented in the research. The researchers' goal was to identify a link between the two. Using four "Guess My Number" problems, seventh and tenth grade students were asked to write…

Digital Tools for Algebra Education: Criteria and Evaluation

ERIC Educational Resources Information Center

Bokhove, Christian; Drijvers, Paul

2010-01-01

In the Netherlands, as in many other countries, the algebraic expertise of students graduating from secondary education is an issue. The use of digital tools for algebra education is expected to change epistemologies, activity structures and student achievement. Therefore, a study was set up to investigate in what way the use of ICT in upper…

Ready, Set, Algebra?

ERIC Educational Resources Information Center

Levy, Alissa Beth

2012-01-01

The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…

Deriving the Regression Line with Algebra

ERIC Educational Resources Information Center

Quintanilla, John A.

2017-01-01

Exploration with spreadsheets and reliance on previous skills can lead students to determine the line of best fit. To perform linear regression on a set of data, students in Algebra 2 (or, in principle, Algebra 1) do not have to settle for using the mysterious "black box" of their graphing calculators (or other classroom technologies).…

Connected Representations of Knowledge: Do Undergraduate Students Relate Algebraic Rational Expressions to Rational Numbers?

ERIC Educational Resources Information Center

Yantz. Jennifer

2013-01-01

The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting students' postsecondary success as STEM majors. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. In the present study, the connections…

Just-in-Time Algebra: A Problem Solving Approach Including Multimedia and Animation.

ERIC Educational Resources Information Center

Hofmann, Roseanne S.; Hunter, Walter R.

2003-01-01

Describes a beginning algebra course that places stronger emphasis on learning to solve problems and introduces topics using real world applications. Students learn estimating, graphing, and algebraic algorithms for the purpose of solving problems. Indicates that applications motivate students by appearing to be a more relevant topic as well as…

Using the Internet To Investigate Algebra.

ERIC Educational Resources Information Center

Sherwood, Walter

The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…

Introduction to Matrix Algebra, Student's Text, Unit 23.

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

Unit 23 in the SMSG secondary school mathematics series is a student text covering the following topics in matrix algebra: matrix operations, the algebra of 2 X 2 matrices, matrices and linear systems, representation of column matrices as geometric vectors, and transformations of the plane. Listed in the appendix are four research exercises in…

Emphasizing Language and Visualization in Teaching Linear Algebra

ERIC Educational Resources Information Center

Hannah, John; Stewart, Sepideh; Thomas, Mike

2013-01-01

Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his…

Application of Algebra Curriculum-Based Measurements for Decision Making in Middle and High School

ERIC Educational Resources Information Center

Johnson, Evelyn S.; Galow, Patricia A.; Allenger, Robert

2013-01-01

This article reports the results of a study examining the utility of curriculum-based measurement (CBM) in algebra for predicting performance on a state math assessment and informing instructional placement decisions for students in seventh, eighth, and tenth grades. Students completed six Basic Skills algebra probes across different time…

Early Integration of Tutorial Support in Beginning Algebra

ERIC Educational Resources Information Center

Copus, Colleen; McKinney, Betsy

2016-01-01

Anecdotal observations reveal that most students with strong arithmetic skills will succeed in the Beginning Algebra course even if they have no previous experience with algebra. In trying to quantify this with an initial teacher-created survey of arithmetic skills, it was observed, for three consecutive semesters, that students who scored in the…

Balancing the Equation: Do Course Variations in Algebra 1 Provide Equal Student Outcomes?

ERIC Educational Resources Information Center

Kenfield, Danielle M.

2013-01-01

Historically, algebra has served as a gatekeeper that divides students into academic programs with varying opportunities to learn and controls access to higher education and career opportunities. Successful completion of Algebra 1 demonstrates mathematical proficiency and allows access to a sequential and progressive path of advanced study that…

The Effectiveness of Alternative Certification Teachers versus Traditionally Trained Teachers in Three School Districts in Texas on Hispanic Students' Scores in 9th Grade Algebra I: What Leaders Should Know

ERIC Educational Resources Information Center

Trevino, Anysia R.

2013-01-01

The purpose of this quantitative study is to measure the effectiveness of alternative certification teachers versus traditionally trained teachers of 9th grade Hispanic students enrolled in Algebra I. The dependent variable, teacher effectiveness, will be measured by the students' raw score on the Texas Algebra I End Of Course (EOC) Assessment.…

Factors That Have an Effect on Students' Scores on the Florida Algebra 1 End-of-Course Assessment in Algebra 1 Classrooms Using Interactive Whiteboard Tools

ERIC Educational Resources Information Center

Kelley, Ginno Paoli

2012-01-01

This study examined the factors that have an effect on student scores on the Florida End-of-Course (EOC) Assessment in four secondary Algebra 1 classrooms using interactive whiteboard tools (IWTs). Four teachers and 335 students were observed in one public suburban school in central Florida during the second half of the spring term. Hierarchical…

Emphasizing language and visualization in teaching linear algebra

NASA Astrophysics Data System (ADS)

Hannah, John; Stewart, Sepideh; Thomas, Mike

2013-06-01

Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his approach in both lectures and tutorials, and how he employed visualization and an emphasis on language to encourage conceptual thinking. We use Tall's framework of three worlds of mathematical thinking to reflect on the effect of these activities in students' learning. An analysis of students' attitudes to the course and their test and examination results help to answer questions about the value of such an approach, suggesting ways forward in teaching linear algebra.

Hearing Math: Algebra Supported eText for Students With Visual Impairments.

PubMed

Bouck, Emily C; Weng, Pei-Lin

2014-01-01

Supported eText for students with visual impairments in mathematics has a promising, emerging literature base, although little of the existing research focuses on implementation within a classroom setting. This qualitative study sought to understand the use of supported eText to deliver algebra to students with visual impairments enrolled in algebra mathematics courses. The study also sought to explore supported eText in contrast to students' traditional means of accessing an algebra text. The main results suggest supported eText holds potential in terms of delivering mathematics content; however, more research and more reflection on the field is needed regarding this approach as a sole means of presenting text. Implications for teacher professional development and implementation practices are discussed.

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.

Characterizing and Supporting Change in Algebra Students' Representational Fluency in a CAS/Paper-and-Pencil Environment

ERIC Educational Resources Information Center

Fonger, Nicole L.

2012-01-01

Representational fluency (RF) includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students' RF in learning environments that utilize both computer algebra systems…

Implications of Eighth Grade Algebra I on High School Mathematics Achievement

ERIC Educational Resources Information Center

Bayard, Robert

2012-01-01

As of 2008, approximately 40% of eighth grade students in the United States enroll in Algebra I (National Council of Teachers of Mathematics, 2008). Although research has shown that students have more opportunities to take advanced mathematics courses by taking eighth grade Algebra I, in the United States, approximately only one-third to one-half…

Interactions between Language and Mathematics with Deaf Students: Defining the "Language-Mathematics" Equation.

ERIC Educational Resources Information Center

Hillegeist, Eleanor; Epstein, Kenneth

The study examined the relationship between language and mathematics with 11 classes of deaf students taking Algebra 1 or Algebra 2 at the Gallaudet University School of Preparatory Studies. Specifically, the study attempted to predict the difficulty of a variety of relatively simple algebra problems based on the abstractness of the math and the…

Questions Arise about Algebra 2 for All Students

ERIC Educational Resources Information Center

Robelen, Erik W.

2013-01-01

Should all students take Algebra 2? Florida seemed to say "no" this spring with the passage of a law striking it from graduation requirements. Texas said much the same in legislation Republican Gov. Rick Perry signed this week that also backs away from Algebra 2 for all. Those steps come as the Common Core State Standards for math set…

A Modeling-Based College Algebra Course and Its Effect on Student Achievement

ERIC Educational Resources Information Center

Ellington, Aimee J.

2005-01-01

In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…

Supporting Students' Understanding of Linear Equations with One Variable Using Algebra Tiles

ERIC Educational Resources Information Center

Saraswati, Sari; Putri, Ratu Ilma Indra; Somakim

2016-01-01

This research aimed to describe how algebra tiles can support students' understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students…

Curriculum Reform in Irish Secondary Schools--A Focus on Algebra

ERIC Educational Resources Information Center

Prendergast, Mark; Treacy, Paraic

2018-01-01

Algebra has long been identified as an area of difficulty in the teaching and learning of mathematics. Evidence of this difficulty can be found in Irish secondary-level classrooms. Chief Examiner Reports have consistently identified algebra as an area of student weakness in State examinations. In light of poor student performance, and as part of a…

Introducing Algebra through the Graphical Representation of Functions: A Study among LD Students

ERIC Educational Resources Information Center

Sauriol, Jennifer

2013-01-01

This longitudinal study evaluates the impact of a new Algebra 1 course at a High School for language-based learning-disabled (LD) students. The new course prioritized the teaching of relationship graphs and functions as an introduction to algebra. Across three studies, the dissertation documents and evaluates the progress made by LD high school…

A Framework for Understanding and Cultivating the Transition from Arithmetic to Algebraic Reasoning

ERIC Educational Resources Information Center

Nathan, Mitchell J.; Koellner, Karen

2007-01-01

Algebraic reasoning stands as a formidable gatekeeper for students in their efforts to progress in mathematics and science, and to obtain economic opportunities (Ladson-Billings, 1998; RAND, 2003). Currently, mathematics education research has focused on algebra in order to provide access and opportunities for more students. There is now a growing…

Selecting Students for Pre-Algebra: Examination of the Relative Utility of the Anchorage Pre-Algebra Screening Tests and the State of Alaska Standards Based Benchmark 2 Mathematics Study. An Examination of Consequential Validity and Recommendation.

ERIC Educational Resources Information Center

Fenton, Ray

This study examined the relative efficacy of the Anchorage (Alaska) Pre-Algebra Test and the State of Alaska Benchmark in 2 Math examination as tools used in the process of recommending grade 6 students for grade 7 Pre-Algebra placement. The consequential validity of the tests is explored in the context of class placements and grades earned. The…

Exploring Algebraic Misconceptions with Technology

ERIC Educational Resources Information Center

Sakow, Matthew; Karaman, Ruveyda

2015-01-01

Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…

Using Technology to Facilitate Reasoning: Lifting the Fog from Linear Algebra

ERIC Educational Resources Information Center

Berry, John S.; Lapp, Douglas A.; Nyman, Melvin A.

2008-01-01

This article discusses student difficulties in grasping concepts from linear algebra. Using an example from an interview with a student, we propose changes that might positively impact student understanding of concepts within a problem-solving context. In particular, we illustrate barriers to student understanding and suggest technological…

Generalized intermediate long-wave hierarchy in zero-curvature representation with noncommutative spectral parameter

NASA Astrophysics Data System (ADS)

Degasperis, A.; Lebedev, D.; Olshanetsky, M.; Pakuliak, S.; Perelomov, A.; Santini, P. M.

1992-11-01

The simplest generalization of the intermediate long-wave hierarchy (ILW) is considered to show how to extend the Zakharov-Shabat dressing method to nonlocal, i.e., integro-partial differential, equations. The purpose is to give a procedure of constructing the zero-curvature representation of this class of equations. This result obtains by combining the Drinfeld-Sokolov formalism together with the introduction of an operator-valued spectral parameter, namely, a spectral parameter that does not commute with the space variable x. This extension provides a connection between the ILWk hierarchy and the Saveliev-Vershik continuum graded Lie algebras. In the case of ILW2 the Fairlie-Zachos sinh-algebra was found.

Diagnosing students' misconceptions in algebra: results from an experimental pilot study.

PubMed

Russell, Michael; O'Dwyer, Laura M; Miranda, Helena

2009-05-01

Computer-based diagnostic assessment systems hold potential to help teachers identify sources of poor performance and to connect teachers and students to learning activities designed to help advance students' conceptual understandings. The present article presents findings from a study that examined how students' performance in algebra and their overcoming of common algebraic misconceptions were affected by the use of a diagnostic assessment system that focused on important algebra concepts. This study used a four-group randomized cluster trial design in which teachers were assigned randomly to one of four groups: a "business as usual" control group, a partial intervention group that was provided with access to diagnostic tests results, a partial intervention group that was provided with access to the learning activities, and a full intervention group that was given access to the test results and learning activities. Data were collected from 905 students (6th-12th grade) nested within 44 teachers. We used hierarchical linear modeling techniques to compare the effects of full, partial, and no (control) intervention on students' algebraic ability and misconceptions. The analyses indicate that full intervention had a net positive effect on ability and misconception measures.

Examining the Conceptual Organization of Students in an Integrated Algebra and Physical Science Class.

ERIC Educational Resources Information Center

Westbrook, Susan L.

1998-01-01

Compares the conceptual organization of students in an integrated algebra and physical science class (SAM 9) with that of students in a discipline-specific physical science class (PSO). Analysis of students' concept maps indicates that the SAM9 students used a greater number of procedural linkages to connect mathematics and science concepts than…

Chinese Algebra: Using Historical Problems to Think about Current Curricula

ERIC Educational Resources Information Center

Tillema, Erik

2005-01-01

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

Prospective Teachers' Views on the Use of Calculators with Computer Algebra System in Algebra Instruction

ERIC Educational Resources Information Center

Ozgun-Koca, S. Ash

2010-01-01

Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…

Undergraduate Mathematics Students' Pronumeral Misconceptions

ERIC Educational Resources Information Center

Bardini, Caroline; Vincent, Jill; Pierce, Robyn; King, Deborah

2014-01-01

Despite an emphasis on manipulative algebraic techniques in secondary school algebra, many tertiary mathematics students have mastered these skills without conceptual understanding. A significant number of students with high tertiary entrance ranks enrolled in first semester university mathematics were found to have misconceptions relating to…

A Tale of Two Students

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2008-01-01

The article describes the performance of several individual students in a college algebra/precalculus course that focuses on the development of conceptual understanding and the use of mathematical modeling and discusses the likely differences in outcome if the students took a traditional algebra-skills focused course.

Degrees of Freedom: Varying Routes to Math Readiness and the Challenge of Intersegmental Alignment (Report 2 of a 3-Part Series)

ERIC Educational Resources Information Center

Burdman, Pamela

2015-01-01

The conventional algebra-intensive math curriculum commonly dictates students' options for entering and completing college, including their ability to transfer from two-year to four-year institutions. The assumption that higher-level algebra is necessary for college success has led some equity advocates to promote algebra for all students. Nearly…

The Algebra Teacher's Guide to Reteaching Essential Concepts and Skills: 150 Mini-Lessons for Correcting Common Mistakes

ERIC Educational Resources Information Center

Muschla, Judith A.; Muschla, Gary Robert; Muschla, Erin

2011-01-01

Many students have trouble grasping algebra. In this book, bestselling authors Judith, Gary, and Erin Muschla offer help for math teachers who must instruct their students (even those who are struggling) about the complexities of algebra. In simple terms, the authors outline 150 classroom-tested lessons, focused on those concepts often most…

The Impact of an Elementary Algebra Course on Success in a College-Level Liberal Arts Math Course and Persistence in College

ERIC Educational Resources Information Center

Austin, Lori Ann

2017-01-01

Many students enter community college underprepared for college-level math and are placed into developmental elementary algebra without consideration if the algebra will provide a foundation for their needed college-level math course. Large percentages of those students are unable to succeed in the developmental course and, therefore, are unable…

Pay-Offs from Expanding Summer Credit Recovery in Algebra

ERIC Educational Resources Information Center

Allensworth, Elaine; Nomi, Takako; Heppen, Jessica

2013-01-01

The consequences of failing core academic courses during the first year are dire. In Chicago, over a quarter of students fail at least one semester of algebra in their ninth grade year, and only 13% of students who fail both semesters of Algebra I in ninth grade graduate in 4 years. Offering credit recovery options is one strategy to deal with…

Exploring How Teacher-Related Factors Relate to Student Achievement in Learning Advanced Algebra in Technology-Enhanced Classrooms

ERIC Educational Resources Information Center

Hegedus, Stephen J.; Tapper, John; Dalton, Sara

2016-01-01

In this study, we examine the relationship between contextual variables related to teachers and student performance in Advanced Algebra classrooms in the USA. The data were gathered from a cluster-randomized study on the effects of SimCalc MathWorlds®, a curricular and technological intervention as a replacement for Algebra 2 curriculum, on…

The Effects of Dynamic Graphing Utilities on Student Attitudes and Conceptual Understanding in College Algebra

ERIC Educational Resources Information Center

Thomas, Ryan Vail

2016-01-01

The goal of this study is to explore and characterize the effects of using a dynamic graphing utility (DGU) on conceptual understanding and attitudes toward mathematics, measured by the responses of college algebra students to an attitude survey and concepts assessment. Two sections of college algebra taught by the primary researcher are included…

Underprepared Students' Performance on Algebra in a Double-Period High School Mathematics Program

ERIC Educational Resources Information Center

Martinez, Mara V.; Bragelman, John; Stoelinga, Timothy

2016-01-01

The primary goal of the Intensified Algebra I (IA) program is to enable mathematically underprepared students to successfully complete Algebra I in 9th grade and stay on track to meet increasingly rigorous high school mathematics graduation requirements. The program was designed to bring a range of both cognitive and non-cognitive supports to bear…

Algebra Matters: An Ethnographic Study of Successful African American Male Algebra 1 Students in a Suburban Middle School

ERIC Educational Resources Information Center

Kirkwood, Kirk

2012-01-01

Alarming statistics reveal that African American male students are encountering long-standing challenges in K-12 mathematics. However, few studies have explored the phenomena associated with African American males and K-12 mathematics education, particularly at the middle school level in the context of an Algebra 1 course of study. The purpose of…

District Decision-Makers' Considerations of Equity and Equality Related to Students' Opportunities to Learn Algebra

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth A.; Keazer, Lindsay; Traynor, Anne

2018-01-01

Background/Context: In this article we explore equity issues related to school district decision-making about students' opportunities to learn algebra. We chose algebra because of the important role it plays in the U.S. as a gatekeeper to future academic success. Current research has not yet explored issues of equity in district-level…

The Effect of Brain Based Instruction on Student Achievement in Algebra I

ERIC Educational Resources Information Center

Vass, Melissa G.

2010-01-01

This quantitative quasi-experimental study examined the effect of brain-based instruction compared to teacher-centered instruction on student achievement in algebra I. A pre-test and post-test were given to a control group of 30 and experimental group of 42 before and after a unit if study in algebra I, which was taught using the two instructional…

Factors Related to Problem Solving by College Students in Developmental Algebra.

ERIC Educational Resources Information Center

Schonberger, Ann K.

A study was conducted to contrast the characteristics of three groups of college students who completed a developmental algebra course at the University of Maine at Orono during 1980-81. On the basis of a two-part final examination, involving a multiple-choice test of algebraic concepts and skills and a free-response test of problem-solving…

Relationships between Student and Instructional Factors and Algebra Achievement of Students in the United States and Japan: An Analysis of TIMSS 2003 Data

ERIC Educational Resources Information Center

House, J. Daniel; Telese, James A.

2008-01-01

Algebra knowledge is a critical part of middle-school mathematics achievement, and success in algebra is necessary for taking higher level mathematics courses and leads to higher scores on standardized tests. The purpose of this study was to simultaneously examine relationships between mathematics beliefs, classroom instructional strategies, and…

Indicators of Student Engagement: What Teachers Notice during Introductory Algebra Lessons

ERIC Educational Resources Information Center

Nyman, Rimma

2015-01-01

This article presents results from an empirical study of how student engagement is visible during introductory algebra. Previously, the notion of engagement in mathematics has been studied from students' and researchers' perspectives. This study is instead focused on teachers' perspectives on student engagement. Eight teachers in grade 6-7 have…

Undergraduate Mathematics Students' Emotional Experiences in Linear Algebra Courses

ERIC Educational Resources Information Center

Martínez-Sierra, Gustavo; García-González, María del Socorro

2016-01-01

Little is known about students' emotions in the field of Mathematics Education that go beyond students' emotions in problem solving. To start filling this gap this qualitative research has the aim to identify emotional experiences of undergraduate mathematics students in Linear Algebra courses. In order to obtain data, retrospective focus group…

Associations of Students' Beliefs with Self-Regulated Problem Solving in College Algebra

ERIC Educational Resources Information Center

Cifarelli, Victor; Goodson-Espy, Tracy; Chae, Jeong-Lim

2010-01-01

This paper reports results from a study of self-regulated problem solving actions of students enrolled in College Algebra (N = 139). The study examined the associations between the expressed mathematical beliefs of students and the students' self-regulated actions in solving mathematics problems. The research questions are: (a) What are some…

Subspace in Linear Algebra: Investigating Students' Concept Images and Interactions with the Formal Definition

ERIC Educational Resources Information Center

Wawro, Megan; Sweeney, George F.; Rabin, Jeffrey M.

2011-01-01

This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from…

Strengthening Grade 3-5 Students' Foundational Knowledge of Rational Numbers

ERIC Educational Resources Information Center

Good, Thomas L.; Wood, Marcy B.; Sabers, Darrell; Olson, Amy M.; Lavigne, Alyson Leah; Sun, Huaping; Kalinec-Craig, Crystal

2013-01-01

Background: American students have done poorly in algebra and that has generated policy concerns about preparing students for STEM careers. There has been growing recognition that the algebra problem may begin in earlier grades when students do not adequately master rational numbers. Purpose: The study provided a series of workshops organized…

Students' Recognition of Function Transformations' Themes Associated with the Algebraic Representation

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Anabousi, Anlam A.

2015-01-01

The topic of function transformations is a difficult mathematical topic for school and college students. This article examines how students conceive function transformations after working with GeoGebra, when this conceiving relates to the algebraic representation. The research participants were 19 ninth grade high achieving students who learned,…

Spontaneous Meta-Arithmetic as a First Step toward School Algebra

ERIC Educational Resources Information Center

Caspi, Shai; Sfard, Anna

2012-01-01

Taking as the point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following five pairs of 7th grade students as they progress in algebraic discourse during 24 months, from their informal algebraic talk to the formal algebraic discourse, as taught in school. Our analysis follows changes that…

Developing learning environments which support early algebraic reasoning: a case from a New Zealand primary classroom

NASA Astrophysics Data System (ADS)

Hunter, Jodie

2014-12-01

Current reforms in mathematics education advocate the development of mathematical learning communities in which students have opportunities to engage in mathematical discourse and classroom practices which underlie algebraic reasoning. This article specifically addresses the pedagogical actions teachers take which structure student engagement in dialogical discourse and activity which facilitates early algebraic reasoning. Using videotaped recordings of classroom observations, the teacher and researcher collaboratively examined the classroom practices and modified the participatory practices to develop a learning environment which supported early algebraic reasoning. Facilitating change in the classroom environment was a lengthy process which required consistent and ongoing attention initially to the social norms and then to the socio-mathematical norms. Specific pedagogical actions such as the use of specifically designed tasks, materials and representations and a constant press for justification and generalisation were required to support students to link their numerical understandings to algebraic reasoning.

Relationship between Instructional Strategies and Students' Performance in the New York State Regents Examination in Integrated Algebra in High Performing Suburban Districts

ERIC Educational Resources Information Center

Quintana, Elizabeth Ruiz

2015-01-01

This mixed method study explored and analyzed instructional strategies utilized by algebra teachers whose students' coursework culminated in the New York State Regents Examination in Integrated Algebra and for whom 50% of the tested cohort earned mastery level (85 or higher) on the examination. The targeted populations were eighth or ninth grade…

Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

ERIC Educational Resources Information Center

Wawro, Megan Jean

2011-01-01

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

A Study of Students' Achievement in Algebra: Considering the Effect of Gender and Types of Schools

ERIC Educational Resources Information Center

Saleh, Salmiza; Rahman, Muhamad Asyrah Abdul

2016-01-01

Algebra is a branch of mathematics that deals with symbols and also the rules for manipulating those symbols, which are used to represent numbers and quantities in mathematical formulae and equations. It is needed and used in our everyday lives. The purpose of this study was to examine students' performance in algebra related to gender and types…

Development of a Computerized Adaptive Testing for Diagnosing the Cognitive Process of Grade 7 Students in Learning Algebra, Using Multidimensional Item Response Theory

ERIC Educational Resources Information Center

Senarat, Somprasong; Tayraukham, Sombat; Piyapimonsit, Chatsiri; Tongkhambanjong, Sakesan

2013-01-01

The purpose of this research is to develop a multidimensional computerized adaptive test for diagnosing the cognitive process of grade 7 students in learning algebra by applying multidimensional item response theory. The research is divided into 4 steps: 1) the development of item bank of algebra, 2) the development of the multidimensional…

Case Studies Listening to Students Using Kinesthetic Movement While Learning to Graph Linear Functions

ERIC Educational Resources Information Center

Novak, Melissa A.

2017-01-01

The purpose of this qualitative practitioner research study was to describe middle school algebra students' experiences of learning linear functions through kinesthetic movement. Participants were comprised of 8th grade algebra students. Practitioner research was used because I wanted to improve my teaching so students will have more success in…

The Impact of Teachers' Characteristics and Self-Reported Practices on Students' Algebra Achievement

ERIC Educational Resources Information Center

Cope, Liza M.

2013-01-01

This study examined the impact of teachers' characteristics and self-reported practices on students' Algebra achievement while controlling for students' characteristics. This study is based on the secondary analysis of data collected from a nationally representative sample of 9 th grade students and their mathematics teachers during…

A Comparison Study of 9th Graders in the U.S. and Albania

ERIC Educational Resources Information Center

Garo, Sofokli

2008-01-01

The purpose of this research is to compare American and Albanian students' achievement in Algebra 1 and to identify the educational practices that influence students' achievement in each country. The study compared algebraic solving abilities of 242 ninth-grade American students in Grand Forks (U.S.) and 219 students in Durres (Albania). The data…

Constraint-Referenced Analytics of Algebra Learning

ERIC Educational Resources Information Center

Sutherland, Scot M.; White, Tobin F.

2016-01-01

The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…

Preparing Elementary Prospective Teachers to Teach Early Algebra

ERIC Educational Resources Information Center

Hohensee, Charles

2017-01-01

Researchers have argued that integrating early algebra into elementary grades will better prepare students for algebra. However, currently little research exists to guide teacher preparation programs on how to prepare prospective elementary teachers to teach early algebra. This study examines the insights and challenges that prospective teachers…

Difficulties in Initial Algebra Learning in Indonesia

ERIC Educational Resources Information Center

Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

2014-01-01

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…

Visual Salience of Algebraic Transformations

ERIC Educational Resources Information Center

Kirshner, David; Awtry, Thomas

2004-01-01

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

Cartooning in Algebra and Calculus

ERIC Educational Resources Information Center

Moseley, L. Jeneva

2014-01-01

This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

Situating Student Errors: Linguistic-to-Algebra Translation Errors

ERIC Educational Resources Information Center

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

2015-01-01

While it is well recognized that students are prone to difficulties when performing linguistic-to-algebra translations, the nature of students' difficulties remain an issue of contention. Moreover, the literature indicates that these difficulties are not easily remediated by domain-specific instruction. Some have opined that this is the case…

Relationships between Fractional Knowledge and Algebraic Reasoning: The Case of Willa

ERIC Educational Resources Information Center

Lee, Mi Yeon; Hackenberg, Amy J.

2014-01-01

To investigate relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The students were interviewed twice, once to explore their quantitative reasoning with fractions and once to explore their solutions of problems…

Strategies for Teaching Algebra to Students with Learning Disabilities: Making Research to Practice Connections

ERIC Educational Resources Information Center

Strickland, Tricia K.; Maccini, Paula

2010-01-01

To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic…

Developing Students' Functional Thinking in Algebra through Different Visualisations of a Growing Pattern's Structure

ERIC Educational Resources Information Center

Wilkie, Karina J.; Clarke, Doug M.

2016-01-01

Spatial visualisation of geometric patterns and their generalisation have become a recognised pathway to developing students' functional thinking and understanding of variables in algebra. This design-based research project investigated upper primary students' development of explicit generalisation of functional relationships and their…

Abstract Numeric Relations and the Visual Structure of Algebra

ERIC Educational Resources Information Center

Landy, David; Brookes, David; Smout, Ryan

2014-01-01

Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition,…

Abstract Algebra to Secondary School Algebra: Building Bridges

ERIC Educational Resources Information Center

Christy, Donna; Sparks, Rebecca

2015-01-01

The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

Assessing Mathematics Automatically Using Computer Algebra and the Internet

ERIC Educational Resources Information Center

Sangwin, Chris

2004-01-01

This paper reports some recent developments in mathematical computer-aided assessment which employs computer algebra to evaluate students' work using the Internet. Technical and educational issues raised by this use of computer algebra are addressed. Working examples from core calculus and algebra which have been used with first year university…

Learning algebra through MCREST strategy in junior high school students

NASA Astrophysics Data System (ADS)

Siregar, Nurfadilah; Kusumah, Yaya S.; Sabandar, J.; Dahlan, J. A.

2017-09-01

The aims of this paper are to describe the use of MCREST strategy in learning algebra and to obtain empirical evidence on the effect of MCREST strategy es specially on reasoning ability. Students in eight grade in one of schools at Cimahi City are chosen as the sample of this study. Using pre-test and post-test control group design, the data then analyzed in descriptive and inferential statistics. The results of this study show the students who got MCREST strategy in their class have better result in test of reasoning ability than students who got direct learning. It means that MCREST strategy gives good impact in learning algebra.

What Do the California Standards Test Results Reveal about the Movement toward Eighth-Grade Algebra for All?

ERIC Educational Resources Information Center

Liang, Jian-Hua; Heckman, Paul E.; Abedi, Jamal

2012-01-01

In California, an increasing number of 8th graders have taken algebra courses since 2003. This study examines students' California Standards Test (CST) results in grades 7 through 11, aiming to reveal who took the CST for Algebra I in 8th grade and whether the increase has led to a rise in students' taking higher-level mathematics CSTs and an…

Applied Algebra: The Modeling Technique of Least Squares

ERIC Educational Resources Information Center

Zelkowski, Jeremy; Mayes, Robert

2008-01-01

The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

The Effects of Schema-Broadening Instruction on Second Graders’ Word-Problem Performance and Their Ability to Represent Word Problems with Algebraic Equations: A Randomized Control Study

PubMed Central

Fuchs, Lynn S.; Zumeta, Rebecca O.; Schumacher, Robin Finelli; Powell, Sarah R.; Seethaler, Pamela M.; Hamlett, Carol L.; Fuchs, Douglas

2010-01-01

The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders’ word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which taught students to represent the structural, defining features of word problems with overarching equations. Intervention lasted 16 weeks. We pretested and posttested 270 students on measures of word-problem skill; analyses that accounted for the nested structure of the data indicated superior word-problem learning for SBI students. Descriptive analyses of students’ word-problem work indicated that SBI helped students represent the structure of word problems with algebraic equations, suggesting that SBI promoted this aspect of students’ emerging algebraic reasoning. PMID:20539822

Students' Comparison of Their Trigonometric Answers with the Answers of a Computer Algebra System in Terms of Equivalence and Correctness

ERIC Educational Resources Information Center

Tonisson, Eno; Lepp, Marina

2015-01-01

The answers offered by computer algebra systems (CAS) can sometimes differ from those expected by the students or teachers. The comparison of the students' answers and CAS answers could provide ground for discussion about equivalence and correctness. Investigating the students' comparison of the answers gives the possibility to study different…

Comparing Cognitive Models of Domain Mastery and Task Performance in Algebra: Validity Evidence for a State Assessment

ERIC Educational Resources Information Center

Warner, Zachary B.

2013-01-01

This study compared an expert-based cognitive model of domain mastery with student-based cognitive models of task performance for Integrated Algebra. Interpretations of student test results are limited by experts' hypotheses of how students interact with the items. In reality, the cognitive processes that students use to solve each item may be…

Programmed First Course in Algebra, Revised Form H, Student's Text, Part I, Unit 60.

ERIC Educational Resources Information Center

Buck, R. Creighton; And Others

This is part one of a two-part SMSG Programed Algebra Text for high school students. The general plan of the course is to build upon the student's experience with arithmetic. The student is initially led to extract from his or her experience the fundamental properties of addition and multiplication. The text then introduces negative real numbers…

I CAN Learn[R] Pre-Algebra and Algebra. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

The I CAN Learn[R] Education System is an interactive, self-paced, mastery-based software system that includes the I CAN Learn[R] Fundamentals of Math (5th-6th grade math) curriculum, the I CAN Learn[R] Pre-Algebra curriculum, and the I CAN Learn[R] Algebra curriculum. College algebra credit is also available to students in participating schools…

The Xs and Whys of Algebra: Key Ideas and Common Misconceptions

ERIC Educational Resources Information Center

Collins, Anne; Dacey, Linda

2011-01-01

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulations of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world. In the The Xs and Whys of Algebra: Key…

Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.

ERIC Educational Resources Information Center

Leitze, Annette Ricks; Kitt, Nancy A.

2000-01-01

Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)

Students' Use of Computational Thinking in Linear Algebra

ERIC Educational Resources Information Center

Bagley, Spencer; Rabin, Jeffrey M.

2016-01-01

In this work, we examine students' ways of thinking when presented with a novel linear algebra problem. Our intent was to explore how students employ and coordinate three modes of thinking, which we call computational, abstract, and geometric, following similar frameworks proposed by Hillel (2000) and Sierpinska (2000). However, the undergraduate…

Weaving Geometry and Algebra Together

ERIC Educational Resources Information Center

Cetner, Michelle

2015-01-01

When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…

Examining the Relationship between Class Scheduling and Student Achievement in College Algebra

ERIC Educational Resources Information Center

Gallo, Michael A.; Odu, Michael

2009-01-01

This study examines the relationship between scheduling (3-, 2-, and 1-day-per-week classes) and achievement in college algebra. The study is grounded in spacing effect theory, which examines how variations in the frequency and timing of instruction affect student learning, and involves 116 Florida community college students. Regression analyses…

Design-Based Research within the Constraints of Practice: AlgebraByExample

ERIC Educational Resources Information Center

Booth, Julie L.; Cooper, Laura A.; Donovan, M. Suzanne; Huyghe, Alexandra; Koedinger, Kenneth R.; Paré-Blagoev, E. Juliana

2015-01-01

Superintendents from districts in the Minority Student Achievement Network (MSAN) challenged the Strategic Education Research Partnership (SERP) to identify an approach to narrowing the minority student achievement gap in Algebra 1 without isolating minority students for intervention. SERP partnered with 8 MSAN districts and researchers from 3…

Support for Struggling Students in Algebra: Contributions of Incorrect Worked Examples

ERIC Educational Resources Information Center

Barbieri, Christina; Booth, Julie L.

2016-01-01

Middle school algebra students (N = 125) randomly assigned within classroom to a Problem-solving control group, a Correct worked examples control group, or an Incorrect worked examples group, completed an experimental classroom study to assess the differential effects of incorrect examples versus the two control groups on students' algebra…

Exploring Students' Understanding of Ordinary Differential Equations Using Computer Algebraic System (CAS)

ERIC Educational Resources Information Center

Maat, Siti Mistima; Zakaria, Effandi

2011-01-01

Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…

Algebra from Chips and Chopsticks

ERIC Educational Resources Information Center

Yun, Jeong Oak; Flores, Alfinio

2012-01-01

Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

Course Placement Series: Spotlight on Eighth Grade Algebra I. Policy Brief

ERIC Educational Resources Information Center

Tennessee Department of Education, 2015

2015-01-01

The Tennessee Department of Education explored course enrollment patterns in an effort to better understand in which courses students are enrolling and whether course enrollment policies and procedures are promoting students' interests. This report focuses on eighth grade Algebra I enrollment, which can propel students to take more rigorous math…

A Study of the Use of a Handheld Computer Algebra System in Discrete Mathematics

ERIC Educational Resources Information Center

Powers, Robert A.; Allison, Dean E.; Grassl, Richard M.

2005-01-01

This study investigated the impact of the TI-92 handheld Computer Algebra System (CAS) on student achievement in a discrete mathematics course. Specifically, the researchers examined the differences between a CAS section and a control section of discrete mathematics on students' in-class examinations. Additionally, they analysed student approaches…

An Authentic Task That Models Quadratics

ERIC Educational Resources Information Center

Baron, Lorraine M.

2015-01-01

As students develop algebraic reasoning in grades 5 to 9, they learn to recognize patterns and understand expressions, equations, and variables. Linear functions are a focus in eighth-grade mathematics, and by algebra 1, students must make sense of functions that are not linear. This article describes how students worked through a classroom task…

Superitem Test: An Alternative Assessment Tool to Assess Students' Algebraic Solving Ability

ERIC Educational Resources Information Center

Lian, Lim Hooi; Yew, Wun Thiam; Idris, Noraini

2010-01-01

Superitem test based on the SOLO model (Structure of the Observing Learning Outcome) has become a powerful alternative assessment tool for monitoring the growth of students' cognitive ability in solving mathematics problems. This article focused on developing a superitem test to assess students' algebraic solving ability through interview method.…

Algebra for Everyone? Student Perceptions of Tracking in Mathematics

ERIC Educational Resources Information Center

Spielhagen, Frances R.

2010-01-01

This research explored the experiences of students in a school district that limited early access to the study of algebra and to inform education policymakers of the impact of such tracking policies on the lives and futures of the students. Quantitative analysis had already yielded a snapshot of inequities deriving from the policies surrounding…

College Algebra I.

ERIC Educational Resources Information Center

Benjamin, Carl; And Others

Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra I. Topics covered include: sets; vocabulary; linear equations; inequalities; real numbers; operations; factoring; fractions; formulas; ratio, proportion, and…

Eighth Grade Algebra Placement Policies: Promoting Equity, Achievement, and Access

ERIC Educational Resources Information Center

Wambsgans, Cynthia

2014-01-01

This study was an investigation of a standardized 8th grade Algebra I placement policy across multiple educational districts. Researchers have documented benefits of students' 8th grade Algebra I education, while others have detailed the consequences of algebra enrollment without necessary prerequisite skills. The purpose of this study was to…

Designing Virtual Worlds for Use in Mathematics Education: The Example of Experiential Algebra.

ERIC Educational Resources Information Center

Winn, William; Bricken, William

1992-01-01

Discussion of the use of virtual reality (VR) to help students learn highlights the use of VR with elementary algebra. Learning theory is examined, including knowledge construction; knowledge representation is discussed, including the symbol systems of algebra; and spatial algebra is described and illustrated. (34 references) (LRW)

Assessing Elementary Algebra with STACK

ERIC Educational Resources Information Center

Sangwin, Christopher J.

2007-01-01

This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

Factors associated with middle-school mathematics achievement in Greece: the case of algebra

NASA Astrophysics Data System (ADS)

Skouras, A. S.

2014-01-01

This study presents a subset of factors and their association with students' achievement in school algebra. The participants were students who had enrolled in 2007 at the ninth year of Greek public education (third year of middle school). A total of 735 students participated (aged 14-15 years) from 37 public secondary schools. The sample consisted of 378 girls (51.4%) and 357 boys (48.6%). A written algebra test and a questionnaire including demographic survey items were used to collect data. The results show that attitude towards mathematics (ATM) and the current teacher rating of mathematics performance were identified as the more significant predictors of algebra achievement, contributing by 18.1% and 24.7%, respectively, in total variance of mean at the end of ninth grade.

Grouping Within Algebra I: A Structural Sieve With Powerful Effects for Low-Income, Minority, and Immigrant Students

ERIC Educational Resources Information Center

Paul, Faith G.

2005-01-01

A key element in educational reform has been to increase mathematical proficiency. We look at how five urban high schools with virtually all low-income, minority, and immigrant students have arranged for students to take algebra I, and we examine the course enrollments and grades of these student in the core college prep courses. Both preparation…

How Visual Imagery Contributed to College: A Case of How Visual Imagery Contributes to a College Algebra Student's Understanding of the Concept of Function in the United States

ERIC Educational Resources Information Center

Lane, Rebekah M.

2011-01-01

This investigation utilized the qualitative case study method. Seventy-one College Algebra students were given a mathematical processing instrument. This testing device measured a student's preference for visual thinking. Two students were purposefully selected using the instrument. The visual mathematical learner (VL) was discussed in this…

Pedagogical content knowledge: Knowledge of pedagogy novice teachers in mathematics learning on limit algebraic function

NASA Astrophysics Data System (ADS)

Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi

2017-02-01

Teacher is one of the key aspects of student's achievement. Teachers should master content material taught, how to teach it, and can interpret the students' thinking so that students easily understand the subject matter. This research was a qualitative research that aimed at describing profile of PCK's teachers in mathematics on limit algebraic functions in terms of the differences of teaching experience. Pedagogical Content Knowledge (PCK) and understanding of teachers is defined as involving the relationship between knowledge of teaching materials, how to transfer the subject matter, and the knowledge of students in mathematics on limit algebraic functions that the subject matter may be understood by students. The PCK components in this research were knowledge of subject matter, knowledge of pedagogy, and knowledge of students. Knowledge of pedagogy defines as knowledge and understanding of teachers about the planning and organization of the learning and teaching strategy of limit algebraic function. The subjects were two mathematics high school teachers who teach in class XI IPS. Data were collected through observation of learning during five meetings and interviews before and after the lesson continued with qualitative data analysis. Focus of this article was to describe novice teacher's knowledge of student in mathematics learning on limit algebraic function. Based on the results of the analysis of qualitative data the data concluded that novice teacher's knowledge of pedagogy in mathematics on limit algebraic function showed: 1) in teaching the definitions tend to identify prior knowledge of the student experience with the material to be studied, but not in the form of a problem, 2) in posing the questions tend to be monotonous non lead and dig, 3) in response to student questions preservice teachers do not take advantage of the characteristics or the potential of other students, 4) in addressing the problem of students, tend to use the drill approach and did not give illustrations easily to understand by students, 5) in teaching application concepts, tend to explain procedurally, without explaining the reasons why these steps are carried out, 6) less varied in the use of learning strategies.

Educational Outcomes of Synchronous and Asynchronous High School Students: A Quantitative Causal-Comparative Study of Online Algebra 1

ERIC Educational Resources Information Center

Berry, Sharon

2017-01-01

This study used a quantitative, causal-comparative design. It compared educational outcome data from online Algebra 1 courses to determine if a significant difference existed between synchronous and asynchronous students for end-of-course grades, state assessments scores, and student perceptions of their course. The study found that synchronous…

The Effect of Graphing Calculators on Student Achievement in College Algebra and Pre-Calculus Mathematics Courses

ERIC Educational Resources Information Center

Hatem, Neil

2010-01-01

This study investigates the relationship between the use of graphing calculators employed as Type II technology and student achievement, as determined by assessing students' problem solving skills associated with the concept of function, at the college algebra and pre-calculus level. In addition, this study explores the integration of graphing…

Reducing "Math Anxiety" in College Algebra Courses Including Comparisons with Elementary Statistics Courses.

ERIC Educational Resources Information Center

Bankhead, Mike

The high levels of anxiety, apprehension, and apathy of students in college algebra courses caused the instructor to create and test a variety of math teaching techniques designed to boost student confidence and enthusiasm in the subject. Overall, this proposal covers several different techniques, which have been evaluated by both students and the…

An Intervention Including an Online Game to Improve Grade 6 Students' Performance in Early Algebra

ERIC Educational Resources Information Center

Kolovou, Angeliki; van den Heuvel-Panhuizen, Marja; Koller, Olaf

2013-01-01

This study investigated whether an intervention including an online game contributed to 236 Grade 6 students' performance in early algebra, that is, solving problems with covarying quantities. An exploratory quasi-experimental study was conducted with a pretest-posttest-control-group design. Students in the experimental group were asked to solve…

Algebraic Reasoning: Professor Arbegla Introduces Variables and Functions. GEMS Teacher's Guide for Grades 3-5.

ERIC Educational Resources Information Center

Kopp, Jaine; Bergman, Lincoln

This teacher guide helps build a solid foundation in algebra for students in grades 3-5 in which students gain essential understanding of properties of numbers, variables, functions, equations, and formulas. Throughout the problem solving activities, students use computational skills and gain a deeper understanding of the number system. Students…

Teacher Self-Efficacy, Content and Pedagogical Knowledge, and Their Relationship to Student Achievement in Algebra I

ERIC Educational Resources Information Center

Fox, Antonia M.

2014-01-01

The purpose of this quantitative study was to explore the relationship between teacher self-efficacy beliefs and the level of student achievement their students obtain as evidenced by the Algebra I Virginia Standards of Learning (SOL) assessment. This study also explored teachers' mathematics content knowledge, mathematics pedagogical knowledge,…

Secondary School Students' Errors in the Translation of Algebraic Statements

ERIC Educational Resources Information Center

Molina, Marta; Rodríguez-Domingo, Susana; Cañadas, María Consuelo; Castro, Encarnación

2017-01-01

In this article, we present the results of a research study that explores secondary students' capacity to perform translations of algebraic statements between the verbal and symbolic representation systems through the lens of errors. We classify and compare the errors made by 2 groups of students: 1 at the beginning of their studies in school…

Student Accountability and Formative Assessment and Its Effects on Motivation and Academic Achievement in Developmental Mathematics

ERIC Educational Resources Information Center

Koukounas, Susan M.

2016-01-01

The purpose of this study was to investigate whether high student accountability and formative assessment affected student motivation, learning and resource management strategies, and achievement in developmental algebra I. The setting was a fifteen-week semester at a community college in suburban New York. Two sections of developmental algebra I…

Developing Students' Functional Thinking in Algebra through Different Visualisations of a Growing Pattern's Structure

ERIC Educational Resources Information Center

Wilkie, Karina J,; Clarke, Doug

2014-01-01

This design-based research project investigated the development of functional thinking in algebra for the upper primary years of schooling. Ten teachers and their students were involved in a sequence of five cycles of collaborative planning, team-teaching, evaluating and revising five lessons on functional thinking for their students over one…

Middle School Students' Conceptual Understanding of Equations: Evidence From Writing Story Problems. WCER Working Paper No. 2009-3

ERIC Educational Resources Information Center

Alibali, Martha W.; Kao, Yvonne S.; Brown, Alayna N.; Nathan, Mitchell J.; Stephens, Ana C.

2009-01-01

This study investigated middle school students' conceptual understanding of algebraic equations. Participants in the study--257 sixth- and seventh-grade students--were asked to solve one set of algebraic equations and to generate story problems corresponding with another set of equations. Structural aspects of the equations, including the number…

Student Learning of Basis, Span and Linear Independence in Linear Algebra

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.

2010-01-01

One of the earlier, more challenging concepts in linear algebra at university is that of basis. Students are often taught procedurally how to find a basis for a subspace using matrix manipulation, but may struggle with understanding the construct of basis, making further progress harder. We believe one reason for this is because students have…

Like Terms: What's in a Name?

ERIC Educational Resources Information Center

de Groot, Cornelis; Boyajian, Meredith

2015-01-01

In introductory algebra and later mathematics courses, students seem to struggle with the concepts of like terms and combining like terms with algebraic expressions. These ideas appear to be unfamiliar to students and do not seem to relate to any mathematics that they have done in the past. In an attempt to link with something that the students do…

Sense Making in the Context of Algebraic Activities

ERIC Educational Resources Information Center

Palatnik, Alik; Koichu, Boris

2017-01-01

This article concerns student sense making in the context of algebraic activities. We present a case in which a pair of middle-school students attempts to make sense of a previously obtained by them position formula for a particular numerical sequence. The exploration of the sequence occurred in the context of two-month-long student research…

The Development and Validation of a Diagnostic Assessment of Algebraic Thinking Skills for Students in the Elementary Grades

ERIC Educational Resources Information Center

Ralston, Nicole C.

2013-01-01

Elementary school students often exhibit a wide variety of different conceptions associated with algebraic thinking that their teachers fail to recognize or understand (Smith, diSessa, & Roschelle, 1994). It is crucial that elementary school teachers possess knowledge of the variety of different student conceptions and also boast abilities to…

The Nature of Student Predictions and Learning Opportunities in Middle School Algebra

ERIC Educational Resources Information Center

Kasmer, Lisa Anne; Kim, Ok-Kyeong

2012-01-01

In this article, we describe how using prediction during instruction can create learning opportunities to enhance the understanding and doing of mathematics. In doing so, we characterize the nature of the predictions students made and the levels of sophistication in students' reasoning within a middle school algebra context. In this study, when…

Error-Detecting Identification Codes for Algebra Students.

ERIC Educational Resources Information Center

Sutherland, David C.

1990-01-01

Discusses common error-detecting identification codes using linear algebra terminology to provide an interesting application of algebra. Presents examples from the International Standard Book Number, the Universal Product Code, bank identification numbers, and the ZIP code bar code. (YP)

Capitalizing on Basic Brain Processes in Developmental Algebra--Part 2

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

Basic brain function is not a mystery. Given that neuroscientists understand its basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain processes…

Capitalizing on Basic Brain Processes in Developmental Algebra--Part One

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

Basic brain function is not a mystery. Given that neuroscientists understand the brain's basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain…

Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2014-01-01

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

Relationships between Classroom Schedule Types and Performance on the Algebra I Criterion-Referenced Test

ERIC Educational Resources Information Center

Murray, Gregory V.; Moyer-Packenham, Patricia S.

2014-01-01

One option for length of individual mathematics class periods is the schedule type selected for Algebra I classes. This study examined the relationship between student achievement, as indicated by Algebra I Criterion-Referenced Test scores, and the schedule type for Algebra I classes. Data obtained from the Utah State Office of Education included…

A New Approach to an Old Order.

ERIC Educational Resources Information Center

Rambhia, Sanjay

2002-01-01

Explains the difficulties middle school students face in algebra regarding the order of operations. Describes a more visual approach to teaching the order of operations so that students can better solve complex problems and be better prepared for the rigors of algebra. (YDS)

Mathematical modelling in engineering: an alternative way to teach Linear Algebra

NASA Astrophysics Data System (ADS)

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-10-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014-2015 at the 'ETSEIB'of Universitat Politècnica de Catalunya (UPC).

Teaching Linear Functions in Context with Graphics Calculators: Students' Responses and the Impact of the Approach on Their Use of Algebraic Symbols

ERIC Educational Resources Information Center

Bardini, Caroline; Pierce, Robyn U.; Stacey, Kaye

2004-01-01

This study analyses some of the consequences of adopting a functional/modelling approach to the teaching of algebra. The teaching of one class of 17 students was observed over five weeks, with 15 students undertaking both pre- and post-tests and 6 students and the teacher being interviewed individually. Use of graphics calculators made the…

Learning algebra on screen and on paper: The effect of using a digital tool on students' understanding

NASA Astrophysics Data System (ADS)

Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

2016-02-01

The use of digital tools in algebra education is expected to not only contribute to master skill, but also to acquire conceptual understanding. The question is how digital tools affect students" thinking and understanding. This paper presents an analysis of data of one group of three grade seventh students (12-13 year-old) on the use of a digital tool for algebra, the Cover-up applet for solving equations in particular. This case study was part of a larger teaching experiment on initial algebra enriched with digital technology which aimed to improve students" conceptual understanding and skills in solving equations in one variable. The qualitative analysis of a video observation, digital and written work showed that the use of the applet affects student thinking in terms of strategies used by students while dealing with the equations. We conclude that the effects of the use of the digital tool can be traced from student problem solving strategies on paper-and-pencil environment which are similar to strategies while working with the digital tool. In future research, we recommend to use specific theoretical lenses, such as the theory of instrumental genesis and the onto-semiotic approach, to reveal more explicit relationships between students" conceptual understanding and the use of a digital tool.

Web Sitings.

ERIC Educational Resources Information Center

Lo, Erika

2001-01-01

Presents seven mathematics games, located on the World Wide Web, for elementary students, including: Absurd Math: Pre-Algebra from Another Dimension; The Little Animals Activity Centre; MathDork Game Room (classic video games focusing on algebra); Lemonade Stand (students practice math and business skills); Math Cats (teaches the artistic beauty…

Correlates of gender and achievement in introductory algebra based physics

NASA Astrophysics Data System (ADS)

Smith, Rachel Clara

The field of physics is heavily male dominated in America. Thus, half of the population of our country is underrepresented and underserved. The identification of factors that contribute to gender disparity in physics is necessary for educators to address the individual needs of students, and, in particular, the separate and specific needs of female students. In an effort to determine if any correlations could be established or strengthened between sex, gender identity, social network, algebra skill, scientific reasoning ability, and/or student attitude, a study was performed on a group of 82 students in an introductory algebra based physics course. The subjects each filled out a survey at the beginning of the semester of their first semester of algebra based physics. They filled out another survey at the end of that same semester. These surveys included physics content pretests and posttests, as well as questions about the students' habits, attitudes, and social networks. Correlates of posttest score were identified, in order of significance, as pretest score, emphasis on conceptual learning, preference for male friends, number of siblings (negatively correlated), motivation in physics, algebra score, and parents' combined education level. Number of siblings was also found to negatively correlate with, in order of significance, gender identity, preference for male friends, emphasis on conceptual learning, and motivation in physics. Preference for male friends was found to correlate with, in order of significance, emphasis on conceptual learning, gender identity, and algebra score. Also, gender identity was found to correlate with emphasis on conceptual learning, the strongest predictor of posttest score other than pretest score.

The Predictive Validity of Coordinate Algebra Common District Assessments on High-Stakes Coordinate Algebra End of Course Assessment

ERIC Educational Resources Information Center

Ainsworth, Jessica Marie

2016-01-01

Formative assessments have been deemed the key to effectively measuring if students have mastered the understanding of curriculum standards. Thus, allowing teachers to use the results to tailor remediation and use other efforts to support mastery of student learning before the end of the school year has positive effects on student achievement.…

"Double-Dose" Algebra as an Alternative Strategy to Remediation: Effects on Students' Academic Outcomes

ERIC Educational Resources Information Center

Nomi, Takako; Allensworth, Elaine

2009-01-01

Expanded instructional time has become increasingly popular as a strategy to improve the academic outcomes of low-skilled students, particularly in the 9th grade. We evaluate the efficacy of a double-period algebra policy initiated in the Chicago Public Schools in 2003. This policy required all students with 8th-grade test scores below the…

The Effects of Computer Algebra System on Undergraduate Students' Spatial Visualization Skills in a Calculus Course

ERIC Educational Resources Information Center

Karakus, Fatih; Aydin, Bünyamin

2017-01-01

This study aimed at determining the effects of using a computer algebra system (CAS) on undergraduate students' spatial visualization skills in a calculus course. This study used an experimental design. The "one group pretest-posttest design" was the research model. The participants were 41 sophomore students (26 female and 15 male)…

Longer Bars for Bigger Numbers? Children's Usage and Understanding of Graphical Representations of Algebraic Problems

ERIC Educational Resources Information Center

Lee, Kerry; Khng, Kiat Hui; Ng, Swee Fong; Ng Lan Kong, Jeremy

2013-01-01

In Singapore, primary school students are taught to use bar diagrams to represent known and unknown values in algebraic word problems. However, little is known about students' understanding of these graphical representations. We investigated whether students use and think of the bar diagrams in a concrete or a more abstract fashion. We also…

Tracking the Success of Pre-College Algebra Workshop Students in Subsequent College Mathematics Classes

ERIC Educational Resources Information Center

Fuller, Edgar; Deshler, Jessica M.; Kuhn, Betsy; Squire, Douglas

2014-01-01

In 2007 the Department of Mathematics at our institution began developing a placement process designed to identify at-risk students entering mathematics courses at the College Algebra and Calculus levels. Major changes in our placement testing process and the resulting interventions for at-risk students were put in place in Fall of 2008. At the…

Studying the Effectiveness of Online Homework for Different Skill Levels in a College Algebra Course

ERIC Educational Resources Information Center

Mathai, Elizabeth; Olsen, Darlene

2013-01-01

A comparison of the performance on the final exam for subpopulations of students in College Algebra was used to assess the effectiveness of online homework. Data was collected for two small groups of students, one with traditional paper homework and the other with online homework. The groups of students were further classified by incoming skill…

Mapping Conceptual Understanding of Algebraic Concepts: An Exploratory Investigation Involving Grade 8 Chinese Students

ERIC Educational Resources Information Center

Jin, Haiyue; Wong, Khoon Yoong

2015-01-01

Conceptual understanding is a major aim of mathematics education, and concept map has been used in non-mathematics research to uncover the relations among concepts held by students. This article presents the results of using concept map to assess conceptual understanding of basic algebraic concepts held by a group of 48 grade 8 Chinese students.…

The Effects of Migration to a Blended Self-Paced Format for a Remedial Pre-College Algebra Mathematics Course

ERIC Educational Resources Information Center

Deshler, Jessica; Fuller, Edgar

2016-01-01

Approximately 30% of students entering West Virginia University (WVU) are not ready for college mathematics. The WVU Department of Mathematics has been tasked with remediating these students and has worked over the last decade to find the most efficient way to teach the Pre-College Algebra Workshop; the prerequisite course students must complete…

Using Topic Order to Reinforce Student Algebra Skills in a Community College Introductory Chemistry Course

ERIC Educational Resources Information Center

Blakely, Alan W.

2011-01-01

This article describes the impact of starting with gases in an introductory chemistry course at a community college. Students in the author's class frequently are very weak in algebra skills, and this has a cumulative impact over time that culminates in student struggles when moles and reaction stoichiometry are discussed. The rationale behind…

Factors That Promote the Academic Success of African American Male Students in High School Math

ERIC Educational Resources Information Center

Allen, Tyrone J.

2014-01-01

Low performance of African American male students in high school math is an ongoing concern of Maryland's public schools. Because disproportionately large numbers of African American male students enroll in Algebra 2 in Grade 11, the use of early academic counseling to promote enrollment in Algebra 2 in Grade 9 and to increase self-regulation may…

Sources of Student Errors and Misconceptions in Algebra and Effectiveness of Classroom Practice Remediation in Machakos County--Kenya

ERIC Educational Resources Information Center

Mulungye, Mary M.; O'Connor, Miheso; Ndethiu, S.

2016-01-01

This paper is based on a study which sought to examine the various errors and misconceptions committed by students in algebra with the view to exposing the nature and origin of the errors and misconceptions in secondary schools in Machakos district. Teachers' knowledge on students' errors was investigated together with strategies for remedial…

A Method for Using Adjacency Matrices to Analyze the Connections Students Make within and between Concepts: The Case of Linear Algebra

ERIC Educational Resources Information Center

Selinski, Natalie E.; Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle

2014-01-01

The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation…

Factors Associated with Middle-School Mathematics Achievement in Greece: The Case of Algebra

ERIC Educational Resources Information Center

Skouras, A. S.

2014-01-01

This study presents a subset of factors and their association with students' achievement in school algebra. The participants were students who had enrolled in 2007 at the ninth year of Greek public education (third year of middle school). A total of 735 students participated (aged 14-15 years) from 37 public secondary schools. The sample consisted…

Effect of a Cooperative Learning Technique on the Academic Performance of High School Students in Mathematics

ERIC Educational Resources Information Center

Idowu, Olumuyiwa Ayodeji

2013-01-01

Over the past 2 years, almost 45% of the students attending a local suburban high school failed Algebra 2. The purpose of this study was to compare the impact of a cooperative instructional technique (student teams-achievement divisions [STAD]) to traditional instructional methods on performance in high school algebra. Motivational and cognitive…

Effects of Comparison and Game-Challenge on Sixth Graders' Algebra Variable Learning Achievement, Learning Attitude, and Meta-Cognitive Awareness

ERIC Educational Resources Information Center

Sun Lin, Hong-Zheng; Chiou, Guey-Fa

2017-01-01

This study examined the effects of comparison and game-challenge strategies on sixth graders' learning achievement of algebra variable, learning attitude towards algebra variable learning, and meta-cognitive awareness of algebra variable learning. A 2 × 2 factorial design was used, and 86 students were invited to participate in the experimental…

Middle School Math Acceleration and Equitable Access to Eighth-Grade Algebra: Evidence from the Wake County Public School System

ERIC Educational Resources Information Center

Dougherty, Shaun M.; Goodman, Joshua S.; Hill, Darryl V.; Litke, Erica G.; Page, Lindsay C.

2015-01-01

Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district's effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based…

It's a Wonderful Life: Using Public Domain Cinema Clips To Teach Affective Objectives and Illustrate Real-World Algebra Applications.

ERIC Educational Resources Information Center

Palmer, Loretta

A basic algebra unit was developed at Utah Valley State College to emphasize applications of mathematical concepts in the work world, using video and computer-generated graphics to integrate textual material. The course was implemented in three introductory algebra sections involving 80 students and taught algebraic concepts using such areas as…

Using Visualization to Generalize on Quadratic Patterning Tasks

ERIC Educational Resources Information Center

Kirwan, J. Vince

2017-01-01

Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…

A Learning Progression for Elementary Students' Functional Thinking

ERIC Educational Resources Information Center

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

2017-01-01

In this article we advance characterizations of and supports for elementary students' progress in generalizing and representing functional relationships as part of a comprehensive approach to early algebra. Our learning progressions approach to early algebra research involves the coordination of a curricular framework and progression, an…

Middle school students' reading comprehension of mathematical texts and algebraic equations

NASA Astrophysics Data System (ADS)

Duru, Adem; Koklu, Onder

2011-06-01

In this study, middle school students' abilities to translate mathematical texts into algebraic representations and vice versa were investigated. In addition, students' difficulties in making such translations and the potential sources for these difficulties were also explored. Both qualitative and quantitative methods were used to collect data for this study: questionnaire and clinical interviews. The questionnaire consisted of two general types of items: (1) selected-response (multiple-choice) items for which the respondent selects from multiple options and (2) open-ended items for which the respondent constructs a response. In order to further investigate the students' strategies while they were translating the given mathematical texts to algebraic equations and vice versa, five randomly chosen (n = 5) students were interviewed. Data were collected in the 2007-2008 school year from 185 middle-school students in five teachers' classrooms in three different schools in the city of Adıyaman, Turkey. After the analysis of data, it was found that students who participated in this study had difficulties in translating the mathematical texts into algebraic equations by using symbols. It was also observed that these students had difficulties in translating the symbolic representations into mathematical texts because of their weak reading comprehension. In addition, finding of this research revealed that students' difficulties in translating the given mathematical texts into symbolic representations or vice versa come from different sources.

Math remediation intervention for student success in the algebra-based introductory physics course

NASA Astrophysics Data System (ADS)

Forrest, Rebecca L.; Stokes, Donna W.; Burridge, Andrea B.; Voight, Carol D.

2017-12-01

Pretesting and early intervention measures to identify and remediate at-risk students were implemented in algebra-based introductory physics to help improve student success rates. Pretesting via a math and problem-solving diagnostic exam administered at the beginning of the course was employed to identify at-risk students based on their scores. At-risk students were encouraged to utilize an online math tutorial to increase their chances of passing the course. The tutorial covers the same math topics covered by the diagnostic exam. Results from 643 students enrolled in the course showed that the 61 at-risk students who successfully completed the math tutorial increased their odds of passing the course by roughly 4 times those of the at-risk students who did not. This intervention is easily implemented, short term, and can be administered concurrently with the course. Based on these results, the Department of Physics has implemented the math tutorials in all sections of the introductory algebra as well as the calculus-based physics courses.

Redesigning the Quantum Mechanics Curriculum to Incorporate Problem Solving Using a Computer Algebra System

NASA Astrophysics Data System (ADS)

Roussel, Marc R.

1999-10-01

One of the traditional obstacles to learning quantum mechanics is the relatively high level of mathematical proficiency required to solve even routine problems. Modern computer algebra systems are now sufficiently reliable that they can be used as mathematical assistants to alleviate this difficulty. In the quantum mechanics course at the University of Lethbridge, the traditional three lecture hours per week have been replaced by two lecture hours and a one-hour computer-aided problem solving session using a computer algebra system (Maple). While this somewhat reduces the number of topics that can be tackled during the term, students have a better opportunity to familiarize themselves with the underlying theory with this course design. Maple is also available to students during examinations. The use of a computer algebra system expands the class of feasible problems during a time-limited exercise such as a midterm or final examination. A modern computer algebra system is a complex piece of software, so some time needs to be devoted to teaching the students its proper use. However, the advantages to the teaching of quantum mechanics appear to outweigh the disadvantages.

The Effects of History of Mathematics on Attitudes Toward Mathematics of College Algebra Students

ERIC Educational Resources Information Center

McBride, Cecil; Rollins, James H.

1977-01-01

Two college algebra classes were exposed to items from mathematics history in their classroom instruction, while two other college algebra classes received no such exposure. Results showed a significant positive attitude change of the mathematics history group. (DT)

Earth Algebra: Real-Life Mathematics in Navajoland.

ERIC Educational Resources Information Center

Schaufele, Christopher; Srivastava, Ravindra

1995-01-01

An algebra class at Navajo Community College (Shiprock, New Mexico) uses traditional algebra topics to study real-life situations, focuses on environmental issues, encourages collaborative learning, uses modern technology, and promotes development of critical thinking and decision-making skills. Students follow principles of Dine educational…

Symbolic integration of a class of algebraic functions. [by an algorithmic approach

NASA Technical Reports Server (NTRS)

Ng, E. W.

1974-01-01

An algorithm is presented for the symbolic integration of a class of algebraic functions. This class consists of functions made up of rational expressions of an integration variable x and square roots of polynomials, trigonometric and hyperbolic functions of x. The algorithm is shown to consist of the following components:(1) the reduction of input integrands to conical form; (2) intermediate internal representations of integrals; (3) classification of outputs; and (4) reduction and simplification of outputs to well-known functions.

Towards Student Instrumentation of Computer-Based Algebra Systems in University Courses

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.; Hannah, John

2005-01-01

There are many perceived benefits of using technology, such as computer algebra systems, in undergraduate mathematics courses. However, attaining these benefits sometimes proves elusive. Some of the key variables are the teaching approach and the student instrumentation of the technology. This paper considers the instrumentation of computer-based…

Processes and Reasoning in Representations of Linear Functions

ERIC Educational Resources Information Center

Adu-Gyamfi, Kwaku; Bossé, Michael J.

2014-01-01

This study examined student actions, interpretations, and language in respect to questions raised regarding tabular, graphical, and algebraic representations in the context of functions. The purpose was to investigate students' interpretations and specific ways of working within table, graph, and the algebraic on notions fundamental to a…

Factors Shaping Students' Opportunities to Engage in Argumentative Activity

ERIC Educational Resources Information Center

Ayalon, Michal; Even, Ruhama

2016-01-01

This study examines how students' opportunities to engage in argumentative activity are shaped by the teacher, the class, and the mathematical topic. It compares the argumentative activity between two classes taught by the same teacher using the same textbook and across two beginning algebra topics--investigating algebraic expressions and…

Effect of Worked Examples and Cognitive Tutor Training on Constructing Equations

ERIC Educational Resources Information Center

Reed, Stephen K.; Corbett, Albert; Hoffman, Bob; Wagner, Angela; MacLaren, Ben

2013-01-01

Algebra students studied either static-table, static-graphics, or interactive-graphics instructional worked examples that alternated with Algebra Cognitive Tutor practice problems. A control group did not study worked examples but solved both the instructional and practice problems on the Cognitive Tutor (CT). Students in the control group…

Monitoring Student Learning in Algebra

ERIC Educational Resources Information Center

Accardo, Amy L.; Kuder, S. Jay

2017-01-01

Mr. Perez and Mrs. Peterson co-teach a ninth-grade algebra class. Perez and Peterson's class includes four students with individualized education programs (IEPs). In response to legislation, such as the No Child Left Behind (NCLB) Act (2001) and the Individuals with Disabilities Education Improvement Act (2006), an increasing number of students…

Teaching Algebraic Equations to Middle School Students with Intellectual Disabilities

ERIC Educational Resources Information Center

Baker, Joshua N.; Rivera, Christopher J.; Morgan, Joseph John; Reese, Noelle

2015-01-01

The purpose of this study was to replicate similar instructional techniques of Jimenez, Browder, and Courtade (2008) using a single-subject multiple-probe across participants design to investigate the effects of task analytic instruction coupled with semi-concrete representations to teach linear algebraic equations to middle school students with…

Solving Optimization Problems with Spreadsheets

ERIC Educational Resources Information Center

Beigie, Darin

2017-01-01

Spreadsheets provide a rich setting for first-year algebra students to solve problems. Individual spreadsheet cells play the role of variables, and creating algebraic expressions for a spreadsheet to perform a task allows students to achieve a glimpse of how mathematics is used to program a computer and solve problems. Classic optimization…

Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving

ERIC Educational Resources Information Center

Engerman, Jason; Rusek, Matthew; Clariana, Roy

2014-01-01

This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…

Fixing Ganache: Another Real-Life Use for Algebra

ERIC Educational Resources Information Center

Kalman, Adam M.

2011-01-01

This article presents a real-world application of proportional reasoning and equation solving. The author describes how students adjust ingredient amounts in a recipe for chocolate ganache. Using this real-world scenario provided students an opportunity to solve a difficult and nonstandard algebra problem, a lot of practice with fractions, a…

Algebra Students' Difficulty with Fractions: An Error Analysis

ERIC Educational Resources Information Center

Brown, George; Quinn, Robert J.

2006-01-01

An analysis of the 1990 National Assessment of Educational Progress (NAEP) found that only 46 percent of all high school seniors demonstrated success with a grasp of decimals, percentages, fractions and simple algebra. This article investigates error patterns that emerge as students attempt to answer questions involving the ability to apply…

Elementary Algebra Connections to Precalculus

ERIC Educational Resources Information Center

Lopez-Boada, Roberto; Daire, Sandra Arguelles

2013-01-01

This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

The Impact of Teacher Perception of Professional Learning Communities on Student Algebraic Achievement

ERIC Educational Resources Information Center

John, Tyrone Ahson

2017-01-01

In this study, I investigate the impact of teachers' perceptions of professional learning communities on student algebraic achievement. Furthermore, I also investigate whether these relationships manifest differently for males compared to females. Research indicates that teacher quality and professionalism are considered the most critical factors…

A Flexible, Extensible Online Testing System for Mathematics

ERIC Educational Resources Information Center

Passmore, Tim; Brookshaw, Leigh; Butler, Harry

2011-01-01

An online testing system developed for entry-skills testing of first-year university students in algebra and calculus is described. The system combines the open-source computer algebra system "Maxima" with computer scripts to parse student answers, which are entered using standard mathematical notation and conventions. The answers can…

Middle Grade Students' Concept Images of Algebraic Concepts

ERIC Educational Resources Information Center

Tekin-Sitrava, Reyhan

2017-01-01

This study investigates middle school students' concept images of algebraic concepts which are term, constant term, variable, and coefficient. Also, the study aimed to explore their performances in defining these concepts correctly. A phenomenological method was used to support methodological perspective and to reveal the findings of the study.…

78 FR 24393 - Agency Information Collection Activities; Comment Request; Promoting Student Success in Algebra I...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-04-25

... learning/ double-dose algebra can serve as possible avenues for improving student success in mathematics... needs in mathematics. This work will make an important contribution by producing actionable information... Common Core State Standards for Mathematics (CCSSM). The study centers around three major research...

Thinking Visually about Algebra

ERIC Educational Resources Information Center

Baroudi, Ziad

2015-01-01

Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

Development of abstract mathematical reasoning: the case of algebra.

PubMed

Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja

2014-01-01

Algebra typically represents the students' first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students' ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16-17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15-16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students' transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.

Perceptions of 9th and 10th Grade Students on How Their Environment, Cognition, and Behavior Motivate Them in Algebra and Geometry Courses

ERIC Educational Resources Information Center

Harootunian, Alen

2012-01-01

In this study, relationships were examined between students' perception of their cognition, behavior, environment, and motivation. The purpose of the research study was to explore the extent to which 9th and 10th grade students' perception of environment, cognition, and behavior can predict their motivation in Algebra and Geometry courses. A…

Effects of Using a Computer Algebra System (CAS) on Junior College Students' Attitudes towards CAS and Achievement in Mathematics

ERIC Educational Resources Information Center

Leng, Ng Wee; Choo, Kwee Tiow; Soon, Lau Hock; Yi-Huak, Koh; Sun, Yap Yew

2005-01-01

This study examines the effects of using Texas Instruments' Voyage 200 calculator (V200), a graphing calculator with a built-in computer algebra system (CAS), on attitudes towards CAS and achievement in mathematics of junior college students (17 year olds). Students' attitudes towards CAS were examined using a 40-item Likert-type instrument…

Mixing Microworld and CAS Features in Building Computer Systems that Help Students Learn Algebra

ERIC Educational Resources Information Center

Nicaud, Jean-Francois; Bouhineau, Denis; Chaachoua, Hamid

2004-01-01

We present the design principles for a new kind of computer system that helps students learn algebra. The fundamental idea is to have a system based on the microworld paradigm that allows students to make their own calculations, as they do with paper and pencil, without being obliged to use commands, and to verify the correctness of these…

The Great Debate: Should All 8th Graders Take Algebra?

ERIC Educational Resources Information Center

McKibben, Sarah

2009-01-01

While 8th grade algebra was once reserved as a course for the gifted, today, more U.S. 8th graders take algebra than any other math course. This article discusses a report from the Brookings Institution which chronicles the history of the 8th-grade algebra surge and its impact on today's low-performing students. The report indicates that many of…

Change in Peer Ability as a Mediator and Moderator of the Effect of the Algebra-For-All Policy on Ninth Graders' Math Outcomes

ERIC Educational Resources Information Center

Hong, Guanglei; Nomi, Takako

2011-01-01

A recent report by the Mathematics Advisory Panel referred to algebra as a "gateway" to later achievement (National Mathematics Advisory Panel, 2008). To address the problem of low academic performance in algebra, an increasing number of states and districts have started to implement a policy of requiring algebra for all students in…

The analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference

NASA Astrophysics Data System (ADS)

Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi

2017-08-01

The aim of this study was to describe the analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference. The purpose of this study is to describe the analysis of mathematics teacher's learning on limit algebraic functions in terms of the differences of teaching experience. Learning analysis focused on Pedagogical Content Knowledge (PCK) of teachers in mathematics on limit algebraic functions related to the knowledge of pedagogy. PCK of teachers on limit algebraic function is a type of specialized knowledge for teachers on how to teach limit algebraic function that can be understood by students. Subjects are two high school mathematics teacher who has difference of teaching experience they are one Novice Teacher (NP) and one Experienced Teacher (ET). Data are collected through observation of learning in the class, videos of learning, and then analyzed using qualitative analysis. Teacher's knowledge of Pedagogic defined as a knowledge and understanding of teacher about planning and organizing of learning, and application of learning strategy. The research results showed that the Knowledge of Pedagogy on subject NT in mathematics learning on the material of limit function algebra showed that the subject NT tended to describe procedurally, without explaining the reasons why such steps were used, asking questions which tended to be monotonous not be guiding and digging deeper, and less varied in the use of learning strategies while subject ET gave limited guidance and opportunities to the students to find their own answers, exploit the potential of students to answer questions, provide an opportunity for students to interact and work in groups, and subject ET tended to combine conceptual and procedural explanation.

Algebra for All: California's Eighth-Grade Algebra Initiative as Constrained Curricula.

PubMed

Domina, Thurston; Penner, Andrew M; Penner, Emily K; Conley, Annemarie

2014-08-01

Across the United States, secondary school curricula are intensifying as a growing proportion of students enroll in high-level academic math courses. In many districts, this intensification process occurs as early as eighth grade, where schools are effectively constraining their mathematics curricula by restricting course offerings and placing more students into Algebra I. This paper provides a quantitative single-case research study of policy-driven curricular intensification in one California school district. (1a) What effect did 8th eighth grade curricular intensification have on mathematics course enrollment patterns in Towering Pines Unified schools? (2b) How did the distribution of prior achievement in Towering Pines math classrooms change as the district constrained the curriculum by universalizing 8th eighth grade Algebra? (3c) Did 8th eighth grade curricular intensification improve students' mathematics achievement? Towering Pines is an immigrant enclave in the inner-ring suburbs of a major metropolitan area. The district's 10 middle schools together enroll approximately 4,000 eighth graders each year. The districts' students are ethnically diverse and largely economically disadvantaged. The study draws upon administrative data describing 8th eighth graders in the district in the 2004-20-05 through 2007-20-08 school years. During the study period, Towering Pines dramatically intensified middle school students' math curricula: In the 2004-20-05 school year 32% of the district's 8th eighth graders enrolled in Algebra or a higher- level mathematics course; by the 2007-20-08 school year that proportion had increased to 84%. We use an interrupted time-series design, comparing students' 8th eighth grade math course enrollments, 10th grade math course enrollments, and 10th grade math test scores across the four cohorts, controlling for demographics and prior achievement. We find that students' odds of taking higher level mathematics courses increased as this district implemented the state's Algebra mandate. However, even as the district implemented a constrained curriculum strategy, mathematics achievement growth between 6th sixth and 10th grade slowed and the achievement advantages associated with 8th eighth grade Algebra declined. Our analyses suggest that curricular intensification increased the inclusiveness and decreased the selectivity of the mathematics tracking regime in Towering Pines middle schools. However, the findings suggest that this constrained curriculum strategy may have may have unintended negative consequences for student achievement.

Focus on Fractions to Scaffold Algebra

ERIC Educational Resources Information Center

Ooten, Cheryl Thomas

2013-01-01

Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…

The Algebra of Complex Numbers.

ERIC Educational Resources Information Center

LePage, Wilbur R.

This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

Cognitive Tutor[R] Algebra I. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

The "Cognitive Tutor[R] Algebra I" curriculum, published by Carnegie Learning, is an approach that combines algebra textbooks with interactive software. The software is developed around an artificial intelligence model that identifies strengths and weaknesses in each individual student's mastery of mathematical concepts. It then customizes prompts…

Who Takes College Algebra?

ERIC Educational Resources Information Center

Herriott, Scott R.; Dunbar, Steven R.

2009-01-01

The common understanding within the mathematics community is that the role of the college algebra course is to prepare students for calculus. Though exceptions are emerging, the curriculum of most college algebra courses and the content of most textbooks on the market both reflect that assumption. This article calls that assumption into question…

An Analysis of Content Knowledge and Cognitive Abilities as Factors That Are Associated with Algebra Performance

ERIC Educational Resources Information Center

McLean, Tamika Ann

2017-01-01

The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational…

Measuring the Readability of Elementary Algebra Using the Cloze Technique.

ERIC Educational Resources Information Center

Kulm, Gerald

The relationship to readability of ten variables characterizing structural properties of mathematical prose was investigated in elementary algebra textbooks. Readability was measured by algebra student's responses to two forms of cloze tests. Linear and currilinear correlations were calculated between each structural variable and the cloze test.…

Promoting Quantitative Literacy in an Online College Algebra Course

ERIC Educational Resources Information Center

Tunstall, Luke; Bossé, Michael J.

2016-01-01

College algebra (a university freshman level algebra course) fulfills the quantitative literacy requirement of many college's general education programs and is a terminal course for most who take it. An online problem-based learning environment provides a unique means of engaging students in quantitative discussions and research. This article…

Teaching Annuities to Mathematics Majors.

ERIC Educational Resources Information Center

Smart, James R.

1980-01-01

This article contains a sequence of topics from the mathematics of annuities presented in a way that can be used as a brief unit on business applications at the level of intermediate or college algebra. (Author/MK)

A Structural Model of Algebra Achievement: Computational Fluency and Spatial Visualisation as Mediators of the Effect of Working Memory on Algebra Achievement

ERIC Educational Resources Information Center

Tolar, Tammy Daun; Lederberg, Amy R.; Fletcher, Jack M.

2009-01-01

The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…

Understanding the Algebraic Variable: Comparative Study of Mexican and Spanish Students

ERIC Educational Resources Information Center

Álvarez, Isabel; Gómez-Chacón, Inés Mª

2015-01-01

Students' difficulty in learning and suitably understanding the concept of the algebraic variable has been studied with a number of tools and documented for several populations. Little research has been conducted, however, using the same tool to explore understanding of the notion among populations from different countries in an attempt to…

Effects of Graphic Organiser on Students' Achievement in Algebraic Word Problems

ERIC Educational Resources Information Center

Owolabi, Josiah; Adaramati, Tobiloba Faith

2015-01-01

This study investigated the effects of graphic organiser and gender on students' academic achievement in algebraic word problem. Three research questions and three null hypotheses were used in guiding this study. Quasi experimental research was employed and Non-equivalent pre and post test design was used. The study involved the Senior Secondary…

Computer-Aided College Algebra: Learning Components that Students Find Beneficial

ERIC Educational Resources Information Center

Aichele, Douglas B.; Francisco, Cynthia; Utley, Juliana; Wescoatt, Benjamin

2011-01-01

A mixed-method study was conducted during the Fall 2008 semester to better understand the experiences of students participating in computer-aided instruction of College Algebra using the software MyMathLab. The learning environment included a computer learning system for the majority of the instruction, a support system via focus groups (weekly…

"Playing the Game" of Story Problems: Coordinating Situation-Based Reasoning with Algebraic Representation

ERIC Educational Resources Information Center

Walkington, Candace; Sherman, Milan; Petrosino, Anthony

2012-01-01

This study critically examines a key justification used by educational stakeholders for placing mathematics in context--the idea that contextualization provides students with access to mathematical ideas. We present interviews of 24 ninth grade students from a low-performing urban school solving algebra story problems, some of which were…

The Role of Technology in Increasing Preservice Teachers' Anticipation of Students' Thinking in Algebra

ERIC Educational Resources Information Center

Rhine, Steve; Harrington, Rachel; Olszewski, Brandon

2015-01-01

The collision between a growing, inexperienced teaching force and students' algebra struggles should be one of great concern. A collaboration of four public and private universities in Oregon restructured mathematics methods courses for preservice teacher candidates by using the affordances of technology to counteract this loss of experience. Over…

Classroom Connectivity and Algebra 1 Achievement: A Three-Year Longitudinal Study

ERIC Educational Resources Information Center

Irving, Karen E.; Pape, Stephen J.; Owens, Douglas T.; Abrahamson, Louis; Silver, David; Sanalan, Vehbi A.

2016-01-01

Findings from three years of a longitudinal randomized control trial involving a national U.S. sample of Algebra 1 teachers and students are reported. The study examines the effects of a connected classroom technology (CCT) professional development and classroom intervention on student achievement when compared to classroom instruction with…

Examining the Implementation of Technology-Based Blended Algebra I Curriculum at Scale

ERIC Educational Resources Information Center

Karam, Rita; Pane, John F.; Griffin, Beth Ann; Robyn, Abby; Phillips, Andrea; Daugherty, Lindsay

2017-01-01

Studies on blended education pay little attention to implementation, thus limiting the understanding of how such programs contribute to student math learning. This article examines the implementation of a widely used blended algebra curriculum and the relationship between implementation and student outcomes. The study was conducted in 74 middle…

Online Homework Effectiveness for Underprepared and Repeating College Algebra Students

ERIC Educational Resources Information Center

Brewer, David Shane; Becker, Kurt

2010-01-01

This research compared the effectiveness, in terms of mathematical achievement, of online homework to textbook homework over an entire semester for 145 students enrolled in multiple sections of college algebra at a large community college. A quasi-experimental, posttest design was used to analyze the effect on mathematical achievement, as measured…

Graphs in Kinematics--A Need for Adherence to Principles of Algebraic Functions

ERIC Educational Resources Information Center

Sokolowski, Andrzej

2017-01-01

Graphs in physics are central to the analysis of phenomena and to learning about a system's behavior. The ways students handle graphs are frequently researched. Students' misconceptions are highlighted, and methods of improvement suggested. While kinematics graphs are to represent a real motion, they are also algebraic entities that must satisfy…

A Third Grader's Way of Thinking about Linear Function Tables

ERIC Educational Resources Information Center

Martinez, Mara; Brizuela, Barbara M.

2006-01-01

This paper is inscribed within the research effort to produce evidence regarding primary school students' learning of algebra. Given the results obtained so far in the research community, we are convinced that young elementary school students can successfully learn algebra. Moreover, children this young can make use of different representational…

Investigating the Relationship between Fraction Proficiency and Success in Algebra

ERIC Educational Resources Information Center

Brown, George; Quinn, Robert J.

2007-01-01

Teachers all over the world are aware that students struggle with fractional concepts and with elementary algebra. Support for this assertion can be found in a variety of research reports. The National Assessment of Educational Progress (NAEP), a United States report, indicates that students have recurrently demonstrated a lack of proficiency in…

Lack of Set Theory Relevant Prerequisite Knowledge

ERIC Educational Resources Information Center

Dogan-Dunlap, Hamide

2006-01-01

Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students' mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a…

Mat-Rix-Toe: Improving Writing through a Game-Based Project in Linear Algebra

ERIC Educational Resources Information Center

Graham-Squire, Adam; Farnell, Elin; Stockton, Julianna Connelly

2014-01-01

The Mat-Rix-Toe project utilizes a matrix-based game to deepen students' understanding of linear algebra concepts and strengthen students' ability to express themselves mathematically. The project was administered in three classes using slightly different approaches, each of which included some editing component to encourage the…

Using Cognitive Tutor Software in Learning Linear Algebra Word Concept

ERIC Educational Resources Information Center

Yang, Kai-Ju

2015-01-01

This paper reports on a study of twelve 10th grade students using Cognitive Tutor, a math software program, to learn linear algebra word concept. The study's purpose was to examine whether students' mathematics performance as it is related to using Cognitive Tutor provided evidence to support Koedlinger's (2002) four instructional principles used…

Student Reactions to Learning Theory Based Curriculum Materials in Linear Algebra--A Survey Analysis

ERIC Educational Resources Information Center

Cooley, Laurel; Vidakovic, Draga; Martin, William O.; Dexter, Scott; Suzuki, Jeff

2016-01-01

In this report we examine students' perceptions of the implementation of carefully designed curriculum materials (called modules) in linear algebra courses at three different universities. The curricular materials were produced collaboratively by STEM and mathematics education faculty as members of a professional learning community (PLC) over…

Definitions Are Important: The Case of Linear Algebra

ERIC Educational Resources Information Center

Berman, Abraham; Shvartsman, Ludmila

2016-01-01

In this paper we describe an experiment in a linear algebra course. The aim of the experiment was to promote the students' understanding of the studied concepts focusing on their definitions. It seems to be a given that students should understand concepts' definitions before working substantially with them. Unfortunately, in many cases they do…

Proof in Algebra: Reasoning beyond Examples

ERIC Educational Resources Information Center

Otten, Samuel; Herbel-Eisenmann, Beth A.; Males, Lorraine M.

2010-01-01

The purpose of this article is to provide an image of what proof could look like in beginning algebra, a course that nearly every secondary school student encounters. The authors present an actual classroom vignette in which a rich opportunity for student reasoning arose. After analyzing the proof schemes at play, the authors provide a…

Tasks That Promote Functional Reasoning in Early Elementary School Students

ERIC Educational Resources Information Center

Payne, Nancy Tilley

2012-01-01

Algebra is often described as the gateway to higher mathematics (Carpenter, Franke, & Levi, 2003; Kaput, 2008; Kaput & Blanton, 2001; Mason, 2008). Unfortunately, many students do not navigate this gateway successfully. Kaput (2008) and Mason (2008) suggested that this is due in part to the abrupt switch from arithmetic to algebra that…

Student academic achievement in college chemistry

NASA Astrophysics Data System (ADS)

Tabibzadeh, Kiana S.

General Chemistry is required for variety of baccalaureate degrees, including all medical related fields, engineering, and science majors. Depending on the institution, the prerequisite requirement for college level General Chemistry varies. The success rate for this course is low. The purpose of this study is to examine the factors influencing student academic achievement and retention in General Chemistry at the college level. In this study student achievement is defined by those students who earned grades of "C" or better. The dissertation contains in-depth studies on influence of Intermediate Algebra as a prerequisite compared to Fundamental Chemistry for student academic achievement and student retention in college General Chemistry. In addition the study examined the extent and manner in which student self-efficacy influences student academic achievement in college level General Chemistry. The sample for this part of the study is 144 students enrolled in first semester college level General Chemistry. Student surveys determined student self-efficacy level. The statistical analyses of study demonstrated that Fundamental Chemistry is a better prerequisite for student academic achievement and student retention. The study also found that student self-efficacy has no influence on student academic achievement. The significance of this study will be to provide data for the purpose of establishing a uniform and most suitable prerequisite for college level General Chemistry. Finally the variables identified to influence student academic achievement and enhance student retention will support educators' mission to maximize the students' ability to complete their educational goal at institutions of higher education.

Analysis of algebraic reasoning ability of cognitive style perspectives on field dependent field independent and gender

NASA Astrophysics Data System (ADS)

Rosita, N. T.

2018-03-01

The purpose of this study is to analyse algebraic reasoning ability using the SOLO model as a theoretical framework to assess students’ algebraic reasoning abilities of Field Dependent cognitive (FD), Field Independent (FI) and Gender perspectives. The method of this study is a qualitative research. The instrument of this study is the researcher himself assisted with algebraic reasoning tests, the problems have been designed based on NCTM indicators and algebraic reasoning according to SOLO model. While the cognitive style of students is determined using Group Embedded Figure Test (GEFT), as well as interviews on the subject as triangulation. The subjects are 15 female and 15 males of the sixth semester students of mathematics education, STKIP Sebelas April. The results of the qualitative data analysis is that most subjects are at the level of unistructural and multi-structural, subjects at the relational level have difficulty in forming a new linear pattern. While the subjects at the extended abstract level are able to meet all the indicators of algebraic reasoning ability even though some of the answers are not perfect yet. Subjects of FI tend to have higher algebraic reasoning abilities than of the subject of FD.

The VATES-Diamond as a Verifier's Best Friend

NASA Astrophysics Data System (ADS)

Glesner, Sabine; Bartels, Björn; Göthel, Thomas; Kleine, Moritz

Within a model-based software engineering process it needs to be ensured that properties of abstract specifications are preserved by transformations down to executable code. This is even more important in the area of safety-critical real-time systems where additionally non-functional properties are crucial. In the VATES project, we develop formal methods for the construction and verification of embedded systems. We follow a novel approach that allows us to formally relate abstract process algebraic specifications to their implementation in a compiler intermediate representation. The idea is to extract a low-level process algebraic description from the intermediate code and to formally relate it to previously developed abstract specifications. We apply this approach to a case study from the area of real-time operating systems and show that this approach has the potential to seamlessly integrate modeling, implementation, transformation and verification stages of embedded system development.

Astronomy Education using the Web and a Computer Algebra System

NASA Astrophysics Data System (ADS)

Flurchick, K. M.; Culver, Roger B.; Griego, Ben

2013-04-01

The combination of a web server and a Computer Algebra System to provide students the ability to explore and investigate astronomical concepts presented in a class can help student understanding. This combination of technologies provides a framework to extend the classroom experience with independent student exploration. In this presentation we report on the developmen of this web based material and some initial results of students making use of the computational tools using webMathematica^TM. The material developed allow the student toanalyze and investigate a variety of astronomical phenomena, including topics such as the Runge-Lenz vector, descriptions of the orbits of some of the exo-planets, Bode' law and other topics related to celestial mechanics. The server based Computer Algebra System system allows for computations without installing software on the student's computer but provides a powerful environment to explore the various concepts. The current system is installed at North Carolina A&T State University and has been used in several undergraduate classes.

Capitalizing on Basic Brain Processes in Developmental Algebra--Part 3

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

In Part Three, the author reviews the basic ideas presented in Parts One and Two while arguing why the traditional equation-solving developmental algebra curricula is not a good choice for implementing neural response strategies presented in the first two parts. He continues by showing that the developmental algebra student audience is simply…

Linear Algebra and Image Processing

ERIC Educational Resources Information Center

Allali, Mohamed

2010-01-01

We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

Carnegie Learning Curricula and Cognitive Tutor™. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2013

2013-01-01

"Carnegie Learning Curricula and Cognitive Tutor"®, published by Carnegie Learning, is a secondary math curricula that offers textbooks and interactive software to provide individualized, self-paced instruction based on student needs. The program includes pre-Algebra, Algebra I, Algebra II, and Geometry, as well as a three-course series…

Catching Up on Algebra

ERIC Educational Resources Information Center

Cavanagh, Sean

2008-01-01

A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…

Concreteness Fading of Algebraic Instruction: Effects on Learning

ERIC Educational Resources Information Center

Ottmar, Erin; Landy, David

2017-01-01

Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

The Algebra of the Arches

ERIC Educational Resources Information Center

Buerman, Margaret

2007-01-01

Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…

Success after Failure: Academic Effects and Psychological Implications of Early Universal Algebra Policies

ERIC Educational Resources Information Center

Howard, Keith A.; Scott, Allison; Romero, Martin; Saddler, Derrick

2015-01-01

In this article, the authors use the High School Longitudinal Study 2009 (HSLS:09) national database to analyze the relationships between algebra failure, subsequent performance, motivation, and college readiness. Students who failed eighth-grade Algebra I did not differ significantly in mathematics proficiency from those who passed lower-level…

A Comparison of Web-Based and Paper-and-Pencil Homework on Student Performance in College Algebra

ERIC Educational Resources Information Center

Hauk, Shandy; Powers, Robert A.; Segalla, Angelo

2015-01-01

College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods: "WeBWorK," an open-source system for web-based homework, or traditional…

Just Say Yes to Early Algebra!

ERIC Educational Resources Information Center

Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy

2015-01-01

Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…

An Emoji Is Worth a Thousand Variables

ERIC Educational Resources Information Center

McCaffrey, Tony; Matthews, Percival G.

2017-01-01

In this article, the authors discuss the potential of the icon-based mathematical games, emoji math and mobile math, to promote student engagement with and understanding of algebra. They describe how these games serve as accessible entry points for algebraic thinking and that, in contrast to traditional symbolic algebra, the use of these…

Foundations of Algebra: 2009-10. Implementation Insights. E&R Report No. 10.28

ERIC Educational Resources Information Center

Paeplow, Colleen

2010-01-01

This report examined the implementation of Foundations of Algebra, a course designed to provide high school students with low mathematics performance an extra opportunity to review and study foundational mathematics concepts prior to enrolling in Introductory Mathematics and subsequently Algebra I. In the fall of 2009, 877 high school students…

The Algebra Initiative Colloquium. Volume 2: Working Group Papers.

ERIC Educational Resources Information Center

Lacampagne, Carole B., Ed.; And Others

This volume presents recommendations from four working groups at a conference on reform in algebra held in Leesburg, Virginia, December 9-12, 1993. Working Group 1: Creating an Appropriate Algebra Experience for All Grades K-12 Students produced the following papers: (1) "Report" (A. H. Schoenfeld); (2) "Five Questions About Algebra…

Examining Heterogeneity in the Effect of Taking Algebra in Eighth Grade

ERIC Educational Resources Information Center

Rickles, Jordan H.

2013-01-01

Increased access to algebra was a focal point of the National Mathematics Advisory Panel's 2008 report on improving mathematics learning in the United States. Past research found positive effects for early access to algebra, but the focus on average effects may mask important variation across student subgroups. The author addresses whether these…

Designing Algebraic Tasks for 7-Year-Old Students--A Pilot Project Inspired by Davydov's "Learning Activity" Concept

ERIC Educational Resources Information Center

Eriksson, Inger; Jansson, Anders

2017-01-01

The issue of this article is to identify and discuss what conditions may be necessary to build into tasks to make it likely for students to be involved in an algebraic Learning Activity inspired by Davydov. Data from a pilot study was used in which a group of students (N = 28) in grade 1 (7-year-olds) were invited to participate in discussions and…

Graphs in kinematics—a need for adherence to principles of algebraic functions

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej

2017-11-01

Graphs in physics are central to the analysis of phenomena and to learning about a system’s behavior. The ways students handle graphs are frequently researched. Students’ misconceptions are highlighted, and methods of improvement suggested. While kinematics graphs are to represent a real motion, they are also algebraic entities that must satisfy conditions for being algebraic functions. To be algebraic functions, they must pass certain tests before they can be used to infer more about motion. A preliminary survey of some physics resources has revealed that little attention is paid to verifying if the position, velocity and acceleration versus time graphs, that are to depict real motion, satisfy the most critical condition for being an algebraic function; the vertical line test. The lack of attention to this adherence shows as vertical segments in piecewise graphs. Such graphs generate unrealistic interpretations and may confuse students. A group of 25 college physics students was provided with such a graph and asked to analyse its adherence to reality. The majority of the students (N  =  16, 64%) questioned the graph’s validity. It is inferred that such graphs might not only jeopardize the function principles studied in mathematics but also undermine the purpose of studying these principles. The aim of this study was to bring this idea forth and suggest a better alignment of physics and mathematics methods.

Relating Understanding of Inverse and Identity to Engagement in Proof in Abstract Algebra

ERIC Educational Resources Information Center

Plaxco, David

2015-01-01

In this research, I set out to elucidate the relationships that might exist between students' conceptual understanding upon which they draw in their proof activity. I explore these relationships using data from individual interviews with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of…

Design of Teacher Assistance Tools in an Exploratory Learning Environment for Algebraic Generalization

ERIC Educational Resources Information Center

Gutierrez-Santos, S.; Geraniou, E.; Pearce-Lazard, D.; Poulovassilis, A.

2012-01-01

The MiGen project is designing and developing an intelligent exploratory environment to support 11-14-year-old students in their learning of algebraic generalization. Deployed within the classroom, the system also provides tools to assist teachers in monitoring students' activities and progress. This paper describes the design of these Teacher…

Counter Conjectures: Using Manipulatives to Scaffold the Development of Number Sense and Algebra

ERIC Educational Resources Information Center

West, John

2016-01-01

This article takes the position that teachers can use simple manipulative materials to model relatively complex situations and in doing so scaffold the development of students' number sense and early algebra skills. While students' early experiences are usually dominated by the cardinal aspect of number (i.e., counting the number of items in a…

An Insurrectionary Generation: Young People, Poverty, Education, and Obama

ERIC Educational Resources Information Center

Gillen, Jay

2009-01-01

The Baltimore Algebra Project is a student-run, student-staffed nonprofit that employs public high schoolers and recent graduates as math study group leaders and as organized advocates for quality education as a constitutional right. In this essay Jay Gillen draws on his experiences as a facilitator of the Algebra Project to argue that only a…

The Effects of the Elevate Math Summer Program on Math Achievement and Algebra Readiness

ERIC Educational Resources Information Center

Snipes, Jason; Huang, Chun-Wei; Jaquet, Karina; Finkelstein, Neal

2016-01-01

To raise math success rates in middle school, many schools and districts have implemented summer math programs designed to improve student preparation for algebra content in grade 8. However, little is known about the effectiveness of these programs. While students who participate typically experience learning gains, there is little rigorous…

The Effect of Worked Examples on Student Learning and Error Anticipation in Algebra

ERIC Educational Resources Information Center

Booth, Julie L.; Begolli, Kreshnik N.; McCann, Nicholas

2016-01-01

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with reform textbooks either containing the original practice problems or in which a portion of those problems were converted into…

Computers in the Classroom: Teacher's Resource Manual for Algebra.

ERIC Educational Resources Information Center

Koetke, Walter

Demonstration programs, possible assignments for students (with solutions), and remedial drill programs for students to use are presented to aid teachers using a computer or a computer terminal in the teaching of algebra. The text can be followed page by page or used as a well-indexed reference work, and specific suggestions are made on how and…

Meta-Representation in an Algebra I Classroom

ERIC Educational Resources Information Center

Izsak, Andrew; Caglayan, Gunhan; Olive, John

2009-01-01

We describe how 1 Algebra I teacher and her 8th-grade students used meta-representational knowledge when generating and evaluating equations to solve word problems. Analyzing data from a sequence of 4 lessons, we found that the teacher and her students used criteria for evaluating equations, in addition to other types of knowledge (e.g., different…

Should All Students Be Required to Take Algebra? Are Any Two Snowflakes Alike?

ERIC Educational Resources Information Center

Morgatto, Sara Festa

2008-01-01

In this article, the author explores the "algebra for all" issue to raise awareness about the many facets of this dilemma facing educators at the middle and high school levels. She discusses both sides of this controversial issue, especially regarding its impact on students' futures relative to higher education and employment. The author concludes…

A Computer Program To Increase Comprehension of the Cartesian Rectangular Coordinate System in High School Pre-Algebra Students.

ERIC Educational Resources Information Center

Exley, I. Sheck

The high percentage of high school pre-algebra students having difficulty learning the abstract concept of graphing ordered pairs on the Cartesian rectangular coordinate system was addressed by the creation and implementation of a computer-managed instructional program. Modules consisted of a pretest, instruction, two practice sessions, and a…

Algebra I Achievement of Eighth Grade Mexican American Students Using Cooperative Learning versus Traditional Instruction

ERIC Educational Resources Information Center

Bunrasi, John Bosco Tuptip

2012-01-01

The purpose of this study was to examine constructivist-based algebra lessons and a cooperative construct to address the achievement gap between White (non-Hispanic) and Mexican American 8th grade students at a southern California middle school. The lessons were designed to facilitate social interdependence which promoted peer-to-peer interaction…

Computer Algebra Systems: Permitted but Are They Used?

ERIC Educational Resources Information Center

Pierce, Robyn; Bardini, Caroline

2015-01-01

Since the 1990s, computer algebra systems (CAS) have been available in Australia as hand-held devices designed for students with the expectation that they will be used in the mathematics classroom. The data discussed in this paper was collected as part of a pilot study that investigated first year university mathematics and statistics students'…

The Effects of Online Homework on Achievement and Self-Efficacy of College Algebra Students

ERIC Educational Resources Information Center

Brewer, David Shane

2009-01-01

This study compared the effectiveness, in terms of mathematical achievement and mathematics self-efficacy, of online homework to textbook homework over an entire semester for 145 students enrolled in multiple sections of college algebra at a large community college. A quasi-experimental, posttest design was used to analyze the effect on…

Students' Use of Variables and Multiple Representations in Generalizing Functional Relationships Prior to Secondary School

ERIC Educational Resources Information Center

Wilkie, Karina J.

2016-01-01

Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 12-13-year-old Australian students' algebraic thinking in a hybrid environment of functional and equation-based approaches to…

Functional Thinking Ways in Relation to Linear Function Tables of Elementary School Students

ERIC Educational Resources Information Center

Tanisli, Dilek

2011-01-01

One of the basic components of algebraic thinking is functional thinking. Functional thinking involves focusing on the relationship between two (or more) varying quantities and such thinking facilitates the studies on both algebra and the notion of function. The development of functional thinking of students should start in the early grades and it…

Writing to Promote and Assess Conceptual Understanding in College Algebra

ERIC Educational Resources Information Center

Gay, A. Susan; Peterson, Ingrid

2014-01-01

Concept-focused quiz questions required College Algebra students to write about their understanding. The questions can be viewed in three broad categories: a focus on sense-making, a focus on describing a mathematical object such as a graph or an equation, and a focus on understanding vocabulary. Student responses from 10 classes were analyzed.…

Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course

ERIC Educational Resources Information Center

Cook, John Paul

2015-01-01

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

Developing Conceptual Understanding and Definitional Clarity in Linear Algebra through the Three Worlds of Mathematical Thinking

ERIC Educational Resources Information Center

Hannah, John; Stewart, Sepideh; Thomas, Michael

2016-01-01

Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…

Strategies Utilized by Superintendents and Mathematics District Personnel That Impact Minority Student Outcomes in Algebra

ERIC Educational Resources Information Center

DuPree, Jared Bernard

2013-01-01

This study applies the constructs from effective instruction from the literature on teacher education to understand the impact of school district strategies on algebra outcomes for minority students. The purpose of this study was to examine the strategies utilized by superintendents and district personnel and the impact of these identified…

Proof and Reasoning in Secondary School Algebra Textbooks

ERIC Educational Resources Information Center

Dituri, Philip

2013-01-01

The purpose of this study was to determine the extent to which the modeling of deductive reasoning and proof-type thinking occurs in a mathematics course in which students are not explicitly preparing to write formal mathematical proofs. Algebra was chosen because it is the course that typically directly precedes a student's first formal…

From rational numbers to algebra: separable contributions of decimal magnitude and relational understanding of fractions.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2015-05-01

To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuring multiple aspects of knowledge about rational numbers. Because fractions are the first numbers that are relational expressions to which students are exposed, we investigated how understanding the relational bipartite format (a/b) of fractions might connect to later algebra performance. We presented middle school students with a battery of tests designed to measure relational understanding of fractions, procedural knowledge of fractions, and placement of fractions, decimals, and whole numbers onto number lines as well as algebra performance. Multiple regression analyses revealed that the best predictors of algebra performance were measures of relational fraction knowledge and ability to place decimals (not fractions or whole numbers) onto number lines. These findings suggest that at least two specific components of knowledge about rational numbers--relational understanding (best captured by fractions) and grasp of unidimensional magnitude (best captured by decimals)--can be linked to early success with algebraic expressions. Copyright © 2015 Elsevier Inc. All rights reserved.

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.

Hypotetical learning trajectory to anticipate mathematics anxiety in algebra learning based on the perspective of didactical situation theory

NASA Astrophysics Data System (ADS)

Yuliani, R. E.; Suryadi, D.; Dahlan, J. A.

2018-05-01

The objective of this research is to design an alleged teacher learning path or Hypotetical Learning Trajectory (HLT) to anticipate mathematics anxiety of students in learning algebra. HLT loads expected mathematics learning objectives, estimates the level of knowledge and understanding of the students, as well as the selection of mathematical activity in accordance with the learning competencies. This research uses educational design research method. The research steps consist of a preliminary design, experimental and retrospective analysis. Data were gathered from various sources, such as data is written during the research process of test results, documentation, sheet results of students' work, results of interviews, questionnaires, and video recordings. The subjects of the study were 10 junior high school students. Based on the research identified 2 students at the level of high anxiety, 7 people at medium anxiety level and 1 student at low anxiety level. High anxiety levels about 20%, was approximately 70% and approximately 10% lower. These results can be used as an evaluation and reflection for designing materials that can anticipate mathematics anxiety of students learning algebra concepts.

An Early Algebra Approach to Pattern Generalisation: Actualising the Virtual through Words, Gestures and Toilet Paper

ERIC Educational Resources Information Center

Ferrara, Francesca; Sinclair, Nathalie

2016-01-01

This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based…

Implementing Computer Algebra Enabled Questions for the Assessment and Learning of Mathematics

ERIC Educational Resources Information Center

Sangwin, Christopher J.; Naismith, Laura

2008-01-01

We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education. The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.…

Advanced Mathematics Online: Assessing Particularities in the Online Delivery of a Second Linear Algebra Course

ERIC Educational Resources Information Center

Montiel, Mariana; Bhatti, Uzma

2010-01-01

This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…

The Aftermath of Accelerating Algebra: Evidence from District Policy Initiatives

ERIC Educational Resources Information Center

Clotfelter, Charles T.; Ladd, Helen F.; Vigdor, Jacob L.

2014-01-01

In 2008, the California State Board of Education voted to require all students to enroll in algebra by 8th grade. This policy initiative, yet to be actually implemented, represents the culmination of a decades-long movement toward offering algebra instruction before the traditional high school years. Nationally, the proportion of 8th grade…

Paper 3: Content and Rigor of Algebra Credit Recovery Courses

ERIC Educational Resources Information Center

Walters, Kirk; Stachel, Suzanne

2014-01-01

This paper describes the content, organization and rigor of the f2f and online summer algebra courses that were delivered in summers 2011 and 2012. Examining the content of both types of courses is important because research suggests that algebra courses with certain features may be better than others in promoting success for struggling students.…

The Impact of Technology-Enhanced Curriculum on Learning Advanced Algebra in US High School Classrooms

ERIC Educational Resources Information Center

Hegedus, Stephen J.; Dalton, Sara; Tapper, John R.

2015-01-01

We report on two large studies conducted in advanced algebra classrooms in the US, which evaluated the effect of replacing traditional algebra 2 curriculum with an integrated suite of dynamic interactive software, wireless networks and technology-enhanced curriculum on student learning. The first study was a cluster randomized trial and the second…

Introduction to Algebra Curriculum Guide, Grade 8, 1987. Bulletin 1802.

ERIC Educational Resources Information Center

Louisiana State Dept. of Education, Baton Rouge. Div. of Academic Programs.

Because of the high incidence of failure in algebra I among ninth-grade students, the Louisiana State Board of Elementary and Secondary Education requested the development of this guide with the intention of providing a good pre-algebra foundation. The purposes of the guide are to recognize standards that involve the application of mathematical…

Sowing the Seeds of Algebraic Generalization: Designing Epistemic Affordances for an Intelligent Microworld

ERIC Educational Resources Information Center

Mavrikis, M.; Noss, R.; Hoyles, C.; Geraniou, E.

2013-01-01

This paper describes the design of a mathematical microworld to tackle the persistent difficulties that secondary school students have with the idea of algebraic generalization, which is a key stumbling block in secondary-school mathematics classrooms. Our focus is to characterize algebraic ways of thinking and to design both affordances of the…

Lisa's Lemonade Stand: Exploring Algebraic Ideas.

ERIC Educational Resources Information Center

Billings, Esther M. H.; Lakatos, Tracy

2003-01-01

Presents an activity, "Lisa's Lemonade Stand," that actively engages students in algebraic thinking as they analyze change by investigating relationships between variables and gain experience describing and representing these relationships graphically. (YDS)

Visualizing the inner product space ℝm×n in a MATLAB-assisted linear algebra classroom

NASA Astrophysics Data System (ADS)

Caglayan, Günhan

2018-05-01

This linear algebra note offers teaching and learning ideas in the treatment of the inner product space ? in a technology-supported learning environment. Classroom activities proposed in this note demonstrate creative ways of integrating MATLAB technology into various properties of Frobenius inner product as visualization tools that complement the algebraic approach. As implemented in linear algebra lessons in a university in the Unites States, the article also incorporates algebraic and visual work of students who experienced these activities with MATLAB software. The connection between the Frobenius norm and the Euclidean norm is also emphasized.

A Symbolic Dance: The Interplay between Movement, Notation, and Mathematics on a Journey toward Solving Equations

ERIC Educational Resources Information Center

Hewitt, Dave

2014-01-01

This article analyzes the use of the software Grid Algebra with a mixed ability class of 21 nine-to-ten-year-old students who worked with complex formal notation involving all four arithmetic operations. Unlike many other models to support learning, Grid Algebra has formal notation ever present and allows students to "look through" that…

Determining the Numeracy and Algebra Errors of Students in a Two-Year Vocational School

ERIC Educational Resources Information Center

Akyüz, Gözde

2015-01-01

The goal of this study was to determine the mathematics achievement level in basic numeracy and algebra concepts of students in a two-year program in a technical vocational school of higher education and determine the errors that they make in these topics. The researcher developed a diagnostic mathematics achievement test related to numeracy and…

Investigating the Use of Mastery-Style Online Homework Exercises in Introductory Algebra-Based Mechanics in a Controlled Clinical Study

ERIC Educational Resources Information Center

Evans, William R.; Selen, Mats A.

2017-01-01

Homework in introductory physics represents an important part of a student's learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs. traditional-style homework with students in both algebra-based and…

Effects of Argumentation on Group Micro-Creativity: Statistical Discourse Analyses of Algebra Students' Collaborative Problem Solving

ERIC Educational Resources Information Center

Chiu, Ming Ming

2008-01-01

The micro-time context of group processes (such as argumentation) can affect a group's micro-creativity (new ideas). Eighty high school students worked in groups of four on an algebra problem. Groups with higher mathematics grades showed greater micro-creativity, and both were linked to better problem solving outcomes. Dynamic multilevel analyses…

School and District Policies and Strategies That Impact Student Performance on the Missouri End-of-Course Algebra 1 NCLB Assessment

ERIC Educational Resources Information Center

Nevels, Nevels

2012-01-01

The dissertation study reported here describes various policies and strategies used by school districts that impact student performance on the Missouri Algebra 1 End-of- Course (EOC) assessment. Analysis of state testing data, teacher survey data, and interview data were used to describe policies and strategies used by 42 teachers and…

Effect of Self-Instruction Strategy on the Achievement in Algebra of Students with Learning Difficulty in Mathematics

ERIC Educational Resources Information Center

Adani, Anthony; Eskay, Michael; Onu, Victoria

2012-01-01

This quasi-experimental study examined the effect of self-instruction strategy on the achievement in algebra of students with learning difficulty in mathematics. Two research questions and one null hypothesis were formulated to guide the study. The study adopted a non-randomized pre-test and post-test control group design with one experimental…

The Effects of Cognitive Style and Piagetian Logical Reasoning on Solving a Propositional Relation Algebra Word Problem.

ERIC Educational Resources Information Center

Nasser, Ramzi; Carifio, James

The purpose of this study was to find out whether students perform differently on algebra word problems that have certain key context features and entail proportional reasoning, relative to their level of logical reasoning and their degree of field dependence/independence. Field-independent students tend to restructure and break stimuli into parts…

Who Repeats Algebra, and How Does Initial Performance Relate to Improvement When the Course Is Repeated?

ERIC Educational Resources Information Center

Fong, Anthony; Jaquet, Karina; Finkelstein, Neal

2016-01-01

The information provided in this report shows how students perform when they repeat algebra I and how the level of improvement varies depending on initial course performance and the academic measure (course grades or CST scores). This information can help inform decisions and policies regarding whether and under what circumstances students should…

Competence with Fractions in Fifth or Sixth Grade as a Unique Predictor of Algebraic Thinking?

ERIC Educational Resources Information Center

Pearn, Catherine; Stephens, Max

2016-01-01

Researchers have argued that there are strong links between primary school students' competence with fraction concepts and operations and their algebraic readiness. This study involving 162 Years 5/6 students in three primary schools examined the strength of that relationship using a test based on familiar fraction tasks and a test of algebraic…

Using Technology to Optimize and Generalize: The Least-Squares Line

ERIC Educational Resources Information Center

Burke, Maurice J.; Hodgson, Ted R.

2007-01-01

With the help of technology and a basic high school algebra method for finding the vertex of a quadratic polynomial, students can develop and prove the formula for least-squares lines. Students are exposed to the power of a computer algebra system to generalize processes they understand and to see deeper patterns in those processes. (Contains 4…

What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra

ERIC Educational Resources Information Center

Christou, Konstantinos P.; Vosniadou, Stella

2012-01-01

Three experiments used multiple methods--open-ended assessments, multiple-choice questionnaires, and interviews--to investigate the hypothesis that the development of students' understanding of the concept of real variable in algebra may be influenced in fundamental ways by their initial concept of number, which seems to be organized around the…

The Northwest Guilford High School Heterogeneous Grouping, Algebra IA and IB, and Guided Studies Programs. Evaluation Report.

ERIC Educational Resources Information Center

Harman, Patrick; And Others

Northwest Guilford High School, Guilford County (North Carolina), is an essentially rural, largely white school that serves about 1,200 students from all socioeconomic levels. An evaluation was conducted of a heterogeneous grouping project involving students in a 2-year sequence of algebra for those who scored below the 40th percentile on a…

Effects of Multimedia-Based Instructional Technology on African American Ninth Grade Students' Mastery of Algebra Concepts

ERIC Educational Resources Information Center

Malik, Ishan Z.

2011-01-01

Urban African American students lack an abstract understanding of algebra and are below their academic level in comparison to other ethnic groups, and this is a pervasive problem (McKinney, Chappell, Berry, & Hickman, 2009). The purpose of this quantitative study using a quasi-experimental design was to determine whether the use of…

Students' Use of CAS Calculators--Effects on the Trustworthiness and Fairness of Mathematics Assessments

ERIC Educational Resources Information Center

Pantzare, Anna Lind

2012-01-01

Calculators with computer algebra systems (CAS) are powerful tools when working with equations and algebraic expressions in mathematics. When calculators are allowed to be used during assessments but are not available or provided to every student, they may cause bias. The CAS calculators may also have an impact on the trustworthiness of results.…

A REPORT ON EXPERIMENTATION IN THE TEACHING OF THE FIRST COURSE IN ALGEBRA AT EL CAMINO COLLEGE.

ERIC Educational Resources Information Center

MANSFIELD, HENRY, JR.

AN INITIAL ATTEMPT TO EVALUATE PROGRAMED INSTRUCTIONAL MATERIAL IN ALGEBRA CLASSES LED TO FURTHER EXPERIMENTATION WITH A VARIETY OF PROCEDURES. IN 1964-65, NO SIGNIFICANT DIFFERENCES WERE FOUND IN THE PERCENT OF STUDENTS SUCCEEDING IN PROGRAMED AND CONVENTIONAL CLASSES, THOUGH STUDENTS IN PROGRAMED SECTIONS DID NOT SEEM MOTIVATED TO WORK AT THEIR…

High-School Students' Approaches to Solving Algebra Problems that Are Posed Symbolically: Results from an Interview Study

ERIC Educational Resources Information Center

Huntley, Mary Ann; Davis, Jon D.

2008-01-01

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are…

The Relationship between Multiplication Fact Speed-Recall and Fluency and Higher Level Mathematics Learning with Eighth Grade Middle School Students

ERIC Educational Resources Information Center

Curry, Steven James

2012-01-01

This quantitative study investigated relationships between higher level mathematics learning and multiplication fact fluency, multiplication fact speed-recall, and reading grade equivalency of eighth grade students in Algebra I and Pre-Algebra. Higher level mathematics learning was indicated by an average score of 80% or higher on first and second…

Pion and Kaon Lab Frame Differential Cross Sections for Intermediate Energy Nucleus-Nucleus Collisions

NASA Technical Reports Server (NTRS)

Norbury, John W.; Blattnig, Steve R.

2008-01-01

Space radiation transport codes require accurate models for hadron production in intermediate energy nucleus-nucleus collisions. Codes require cross sections to be written in terms of lab frame variables and it is important to be able to verify models against experimental data in the lab frame. Several models are compared to lab frame data. It is found that models based on algebraic parameterizations are unable to describe intermediate energy differential cross section data. However, simple thermal model parameterizations, when appropriately transformed from the center of momentum to the lab frame, are able to account for the data.

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.

Analysis of Newton's Third Law Questions on the Force Concepts Inventory at Georgia State University

NASA Astrophysics Data System (ADS)

Oakley, Christopher; Thoms, Brian

2012-03-01

A major emphasis of the Physics Education Research program at Georgia State University is an effort to assess and improve students' understanding of Newton's Laws concepts. As part of these efforts the Force Concepts Inventory (FCI) has been given to students in both the algebra-based and calculus-based introductory physics sequences. In addition, the algebra-based introductory physics sequence is taught in both a SCALE-UP and a traditional lecture format. The results of the FCI have been analyzed by individual question and also as categorized by content. The analysis indicates that students in both algebra and calculus-based courses are successful at overcoming Aristotelian misconceptions regarding Newton's Third Law (N3) in the context of a stationary system. However, students are less successful on N3 questions involving objects in constant motion or accelerating. Interference between understanding of Newton's Second and Third Laws as well as other possible explanations for lower student performance on N3 questions involving non-stationary objects will be discussed.

A Comparison of Success and Failure Rates between Computer-Assisted and Traditional College Algebra Sections

ERIC Educational Resources Information Center

Herron, Sherry; Gandy, Rex; Ye, Ningjun; Syed, Nasser

2012-01-01

A unique aspect of the implementation of a computer algebra system (CAS) at a comprehensive university in the U.S. allowed us to compare the student success and failure rates to the traditional method of teaching college algebra. Due to space limitations, the university offered sections of both CAS and traditional simultaneously and, upon…

Opening a Gateway to College Access: Algebra at the Right Time. Research Brief

ERIC Educational Resources Information Center

Snipes, Jason; Finkelstein, Neal

2015-01-01

Four years of math in high school, with a strong foundation in algebra that builds from middle school, is key to higher education access. Therefore, ensuring that middle and high school students succeed in math--and in algebra in particular--is an important issue for policy and practice. This research brief examines three recent Regional…

Using Example Generation to Explore Students' Understanding of the Concepts of Linear Dependence/Independence in Linear Algebra

ERIC Educational Resources Information Center

Aydin, Sinan

2014-01-01

Linear algebra is a basic mathematical subject taught in mathematics and science depar-tments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing…

The Aftermath of Accelerating Algebra: Evidence from a District Policy Initiative. Working Paper 69

ERIC Educational Resources Information Center

Clotfelter, Charles T.; Ladd, Helen F.; Vigdor, Jacob L.

2012-01-01

In 2002/03, the Charlotte-Mecklenburg Schools initiated a broad program of accelerating entry into algebra coursework. The proportion of moderately-performing students taking 8th grade algebra increased from less than half to nearly 90%, then reverted to baseline levels, in the span of just six age cohorts. We use this policy-induced variation to…

The Aftermath of Accelerating Algebra: Evidence from a District Policy Initiative. Working Paper 18161

ERIC Educational Resources Information Center

Clotfelter, Charles T.; Ladd, Helen F.; Vigdor, Jacob L.

2012-01-01

In 2002/03, the Charlotte-Mecklenburg Schools in North Carolina initiated a broad program of accelerating entry into algebra coursework. The proportion of moderately-performing students taking algebra in 8th grade increased from half to 85%, then reverted to baseline levels, in the span of just five years. We use this policy-induced variation to…

An Intensification Approach to Double-Block Algebra: A Pilot Implementation of Intensified Algebra in A Large Urban School District

ERIC Educational Resources Information Center

Tidd, Simon T.; Stoelinga, Timothy M.; Bush-Richards, Angela M.; De Sena, Donna L.; Dwyer, Theodore J.

2018-01-01

Double-block instruction has become a popular strategy for supporting struggling mathematics students in algebra I. Despite its widespread adoption, little consistent evidence supports the attributes of a successful double-block design or the effectiveness of this instructional strategy. In this study, the authors examine a pilot implementation of…

The Linear Algebra Curriculum Study Group Recommendations for the First Course in Linear Algebra.

ERIC Educational Resources Information Center

Carlson, David; And Others

1993-01-01

Presents five recommendations of the Linear Algebra Curriculum Study Group: (1) The syllabus must respond to the client disciplines; (2) The first course should be matrix oriented; (3) Faculty should consider the needs and interests of students; (4) Faculty should use technology; and (5) At least one follow-up course should be required. Provides a…

Mobile Learning: Integrating Text Messaging into a Community College Pre-Algebra Course

ERIC Educational Resources Information Center

Bull, Prince; McCormick, Carlos

2012-01-01

This study investigated the use of text messaging as an educational tool in a pre-algebra course at a community college in the central region of North Carolina. The research was conducted in two pre-algebra classes with thirty-three students and one instructor. Data were gathered using qualitative and quantitative methods. A mixed method design…

Using Standardized Tests to Identify Prior Knowledge Necessary for Success in Algebra: A Predictive Analysis

ERIC Educational Resources Information Center

Jensen, Jennifer

2014-01-01

This study sought to determine if there is a relationship between students' scores on the eighth-grade Indiana State Test of Education Progress Plus (ISTEP+) exam and success on Indiana's Algebra End-of-Course Assessment (ECA). Additionally, it sought to determine if algebra success could be significantly predicted by the achievement in one or…

Diagrams benefit symbolic problem-solving.

PubMed

Chu, Junyi; Rittle-Johnson, Bethany; Fyfe, Emily R

2017-06-01

The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic equations can benefit problem-solving performance as well. We tested the impact of diagram presence on students' performance on algebra equation problems to determine whether diagrams increase problem-solving success. We also examined the influence of item- and student-level factors to test the robustness of the diagram effect. We worked with 61 seventh-grade students who had received 2 months of pre-algebra instruction. Students participated in an experimenter-led classroom session. Using a within-subjects design, students solved algebra problems in two matched formats (equation and equation-with-diagram). The presence of diagrams increased equation-solving accuracy and the use of informal strategies. This diagram benefit was independent of student ability and item complexity. The benefits of diagrams found previously for story problems generalized to symbolic problems. The findings are consistent with cognitive models of problem-solving and suggest that diagrams may be a useful additional representation of symbolic problems. © 2017 The British Psychological Society.

The Perspectives of Twelfth-Grade Students toward the Acquisition of Algebraic Skills throughout High School

ERIC Educational Resources Information Center

Johnson, Melloney W. A.

2017-01-01

Too many students do not learn algebra and therefore do not graduate from high school. This basic qualitative study conducted in a large suburban public school district explored the perspectives of high school seniors who were at least 18 years old and at risk for not graduating from high school because they had not demonstrated an adequate…

An Examination in Turkey: Error Analysis of Mathematics Students on Group Theory

ERIC Educational Resources Information Center

Arikan, Elif Esra; Ozkan, Ayten; Ozkan, E. Mehmet

2015-01-01

The aim of this study is to analyze the mistakes that have been made in the group theory underlying the algebra mathematics. The 100 students taking algebra math 1 class and studying at the 2nd grade at a state university in Istanbul participated in this study. The related findings were prepared as a classical exam of 6 questions which have been…

Computer Aided Instruction for a Course in Boolean Algebra and Logic Design. Final Report (Revised).

ERIC Educational Resources Information Center

Roy, Rob

The use of computers to prepare deficient college and graduate students for courses that build upon previously acquired information would solve the growing problem of professors who must spend up to one third of their class time in review of material. But examination of students who were taught Boolean Algebra and Logic Design by means of Computer…

Effects of Modified Schema-Based Instruction on Real-World Algebra Problem Solving of Students with Autism Spectrum Disorder and Moderate Intellectual Disability

ERIC Educational Resources Information Center

Root, Jenny Rose

2016-01-01

The current study evaluated the effects of modified schema-based instruction (SBI) on the algebra problem solving skills of three middle school students with autism spectrum disorder and moderate intellectual disability (ASD/ID). Participants learned to solve two types of group word problems: missing-whole and missing-part. The themes of the word…

Algebra? There's an App for That: Florida Goes Online with Math Support for Teachers and Students

ERIC Educational Resources Information Center

Schackow, Joy Bronston; Cugini, Stephanie

2016-01-01

The transition to Common Core State Standards for Mathematics has created a need for high-quality professional learning on content and pedagogy. This is especially true for algebra 1 teachers in Florida, where students must pass a standards-based exam as a requirement to earning a high school diploma. Time, distance, and cost constraints can get…

"Menos y menos da Mas": Using Spanish as the Language of Instruction with English Learners in Algebra 1

ERIC Educational Resources Information Center

Diaz, Marco Antonio

2013-01-01

This study examines the use of Spanish as the language of instruction with Spanish dominant EL students in a 9th grade Algebra 1 classroom. The study documents conceptions of mathematical symbols at the start and at the end of the academic year of two groups of students; one receiving primary language instruction and another receiving sheltered…

The Effect of Using the TI-92 on Basic College Algebra Students' Ability To Solve Word Problems.

ERIC Educational Resources Information Center

Runde, Dennis C.

As part of an effort to improve community college algebra students' ability to solve word problems, a study was undertaken at Florida's Manatee Community College to determine the effects of using heuristic instruction (i.e., providing general rules for solving different types of math problems) in combination with the TI-92 calculator. The TI-92…

Teaching Basic Algebra Courses at the College Level

ERIC Educational Resources Information Center

Mallenby, Michel L.; Mallenby, Douglas W.

2004-01-01

Three dysfunctional behaviors of basic algebra students are described: Silence as Camouflage, Wing and a Prayer, and Ignorance is OK. These behavior patterns are explained, and beneficial teaching methods that address the weaknesses are presented.

Paving the Way To Algebraic Thought Using Residue Designs.

ERIC Educational Resources Information Center

Johnson, Iris DeLoach

1998-01-01

Presents a brief definition and examples of residue designs while sharing some of the algebraic thought that a student used to form generalizations about the patterns discovered during the investigations of residue designs. (ASK)

Visual Thinking, Algebraic Thinking, and a Full Unit-Circle Diagram.

ERIC Educational Resources Information Center

Shear, Jonathan

1985-01-01

The study of trigonometric functions in terms of the unit circle offer an example of how students can learn algebraic relations and operations while using visually oriented thinking. Illustrations are included. (MNS)

Developing CORE model-based worksheet with recitation task to facilitate students’ mathematical communication skills in linear algebra course

NASA Astrophysics Data System (ADS)

Risnawati; Khairinnisa, S.; Darwis, A. H.

2018-01-01

The purpose of this study was to develop a CORE model-based worksheet with recitation task that were valid and practical and could facilitate students’ communication skills in Linear Algebra course. This study was conducted in mathematics education department of one public university in Riau, Indonesia. Participants of the study were media and subject matter experts as validators as well as students from mathematics education department. The objects of this study are students’ worksheet and students’ mathematical communication skills. The results of study showed that: (1) based on validation of the experts, the developed students’ worksheet was valid and could be applied for students in Linear Algebra courses; (2) based on the group trial, the practicality percentage was 92.14% in small group and 90.19% in large group, so the worksheet was very practical and could attract students to learn; and (3) based on the post test, the average percentage of ideals was 87.83%. In addition, the results showed that the students’ worksheet was able to facilitate students’ mathematical communication skills in linear algebra course.

Algebraic model checking for Boolean gene regulatory networks.

PubMed

Tran, Quoc-Nam

2011-01-01

We present a computational method in which modular and Groebner bases (GB) computation in Boolean rings are used for solving problems in Boolean gene regulatory networks (BN). In contrast to other known algebraic approaches, the degree of intermediate polynomials during the calculation of Groebner bases using our method will never grow resulting in a significant improvement in running time and memory space consumption. We also show how calculation in temporal logic for model checking can be done by means of our direct and efficient Groebner basis computation in Boolean rings. We present our experimental results in finding attractors and control strategies of Boolean networks to illustrate our theoretical arguments. The results are promising. Our algebraic approach is more efficient than the state-of-the-art model checker NuSMV on BNs. More importantly, our approach finds all solutions for the BN problems.

The Effects of the Elevate Math Summer Program on Math Achievement and Algebra Readiness. REL 2015-096

ERIC Educational Resources Information Center

Snipes, Jason; Huang, Chun-Wei; Jaquet, Karina; Finkelstein, Neal

2015-01-01

The Effects of the Elevate Math summer program on math achievement and algebra readiness: This randomized trial examined the effects of the Elevate Math summer program on math achievement and algebra readiness, as well as math interest and self-efficacy, among rising 8th grade students in California's Silicon Valley. The Elevate Math summer math…

Using the Interactive Learning Environment Aplusix for Teaching and Learning School Algebra: A Research Experiment in a Middle School

ERIC Educational Resources Information Center

Hadjerrouit, Said

2011-01-01

Most software tools that have been developed with the aim of helping students to learn school algebra have not yet achieved successful results in classroom. Almost all of them are menu-based systems that provide transformation rules in menus and buttons. Aplusix is a new interactive software tool for learning school algebra. In contrast to…

Algebra for All and Its Relationship to English Language Learner's Opportunity-to-Learn and Algebra I Success Rates

ERIC Educational Resources Information Center

Veith, Velma

2013-01-01

English as a Second Language (ESL) learners' access and achievement in Algebra I was examined to determine whether ESL students continue to be denied equal opportunity-to-learn (OTL) as a result of unnecessary tracking practices. In this quasi-experiment, a pre-post retrospective comparison group design was used to determine the effects of the…

An Application of Cartesian Graphing to Seismic Exploration.

ERIC Educational Resources Information Center

Robertson, Douglas Frederick

1992-01-01

Describes how college students enrolled in a course in elementary algebra apply graphing and algebra to data collected from a seismic profile to uncover the structure of a subterranean rock formation. Includes steps guiding the activity. (MDH)

The Conservation Principles and Kepler's Laws of Planetary Motion

ERIC Educational Resources Information Center

Motz, Lloyd

1975-01-01

Derives Kepler's three laws of planetary motion algebraically from conservation principles without introducing Newton's law of force explicitly. This procedure can be presented to students who have had no more than high school algebra. (Author)

Tracking problem solving by multivariate pattern analysis and Hidden Markov Model algorithms.

PubMed

Anderson, John R

2012-03-01

Multivariate pattern analysis can be combined with Hidden Markov Model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application involves using fMRI activity to track what students are doing as they solve a sequence of algebra problems. The methodology achieves considerable accuracy at determining both what problem-solving step the students are taking and whether they are performing that step correctly. The second "model discovery" application involves using statistical model evaluation to determine how many substates are involved in performing a step of algebraic problem solving. This research indicates that different steps involve different numbers of substates and these substates are associated with different fluency in algebra problem solving. Copyright © 2011 Elsevier Ltd. All rights reserved.

Possibility of Engineering Education That Makes Use of Algebraic Calculators by Various Scenes

NASA Astrophysics Data System (ADS)

Umeno, Yoshio

Algebraic calculators are graphing calculators with a feature of computer algebra system. It can be said that we can solve mathematics only by pushing some keys of these calculators in technical colleges or universities. They also possess another feature, so we can make extensive use in engineering education. For example, we can use them for a basic education, a programming education, English education, and creative thinking tools for excellent students. In this paper, we will introduce the summary of algebraic calculators, then, consider how we utilize them in engineer education.

The Relationship between School-Facilitated Parental Involvement and Academic Math Achievement of High School Students in Virginia Who Receive Special Education Services

ERIC Educational Resources Information Center

Stein, Allison

2017-01-01

This study examined how school-facilitated parental involvement affects Standards of Learning (SOL) end-of-course exams for high school students in Virginia who are receiving special education services. This study examined test results from the 2012-2013, 2013-2014, and 2014-2015 school years for the Algebra I, Geometry, and Algebra II SOL exams,…

A Quantitative Study Analyzing Predictive Factors That Affect Achievement on Florida's Algebra I End-of-Course Exam (EOC)

ERIC Educational Resources Information Center

Holley, Hope D.

2017-01-01

Despite research that high-stakes tests do not improve knowledge, Florida requires students to pass an Algebra I End-of-Course exam (EOC) to earn a high school diploma. Test passing scores are determined by a raw score to t-score to scale score analysis. This method ultimately results as a comparative test model where students' passage is…

Procedures for, and Experiences in, Introducing Algebra in New South Wales.

ERIC Educational Resources Information Center

Pegg, John; Redden, Edward

1990-01-01

Discussed are the philosophy and procedures behind the introduction of algebra to students in grade 7 in Australia. Included are the importance of concrete experiences, language development, and the consequences involved in this procedure. (CW)

Scaffolding the Mathematical "Connections": A New Approach to Preparing Teachers for the Teaching of Lower Secondary Algebra

ERIC Educational Resources Information Center

Ormond, Christine A.

2016-01-01

This paper discusses the results of a three-year mixed methods study into the effectiveness of a mathematics education unit. This was written for both pre-service primary education students and re-training in-service teachers, to prepare them for the teaching of pre-algebra and early algebra. The unit was taught rom 2013 to 2015 inclusively in a…

Impact of Providing Information to Parents in Texas about the Role of Algebra II in College Admission. REL 2018-290

ERIC Educational Resources Information Center

Stoker, Ginger; Mellor, Lynn

2018-01-01

This study examines the impact of providing parents with an informational brochure about the role of algebra II in college access on students' grade 11 algebra II completion rates in Texas. One hundred nine schools, covering all 20 Educational Service Center regions in Texas, participated in the study. Parents in the 54 treatment schools were…

The Perceptions of the Self-Efficacy of 9th Grade Algebra 1 Students at an Urban High School in New England Based on Their Placement in Low, On, or above Level Algebra Classes

ERIC Educational Resources Information Center

Lopes, Manuel J.

2017-01-01

At a time of persistent unemployment, especially among the less skilled, many wonder whether our schools are adequately preparing students for the 21st-century global economy. Despite above average employment rates, firms are experiencing shortages of educated workers, outsourcing professional-level work to workers abroad, and competing for the…

Using Technology to Balance Algebraic Explorations

ERIC Educational Resources Information Center

Kurz, Terri L.

2013-01-01

In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

The Role of Proof in Comprehending and Teaching Elementary Linear Algebra.

ERIC Educational Resources Information Center

Uhlig, Frank

2002-01-01

Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)

Constructive Learning in Undergraduate Linear Algebra

ERIC Educational Resources Information Center

Chandler, Farrah Jackson; Taylor, Dewey T.

2008-01-01

In this article we describe a project that we used in our undergraduate linear algebra courses to help our students successfully master fundamental concepts and definitions and generate interest in the course. We describe our philosophy and discuss the projects overall success.

Remarks on a one-parameter family of singular matrices

NASA Astrophysics Data System (ADS)

Sharma, Ramesh; Pariso, Chris; Duda, Michelle

2015-01-01

This short article will present to the reader a family of matrices that form an algebra over the reals. This presentation provides both current and former students of modern abstract algebra a better illustration of the concepts of rings, fields, and algebra itself. In addition, this article relates eigenspaces of 3×3 matrices with the arithmetic-geometric mean equality, an attribute that teachers might enjoy utilizing as a teaching tool in their classes.

Without derivatives or limits: from visual and geometrical points of view to algebraic methods for identifying tangent lines

NASA Astrophysics Data System (ADS)

Vivier, L.

2013-07-01

Usually, the tangent line is considered to be a calculus notion. However, it is also a graphical and an algebraic notion. The graphical frame, where our primary conceptions are conceived, could give rise to algebraic methods to obtain the tangent line to a curve. In this pre-calculus perspective, two methods are described and discussed according to their potential for secondary students and teacher training.

Connecting Functions in Geometry and Algebra

ERIC Educational Resources Information Center

Steketee, Scott; Scher, Daniel

2016-01-01

One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

Integrals of motion from quantum toroidal algebras

NASA Astrophysics Data System (ADS)

Feigin, B.; Jimbo, M.; Mukhin, E.

2017-11-01

We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors. That allows us to prove the Litvinov conjectures on the Intermediate Long Wave model. We also discuss the ({gl_m, {gl_n) duality of XXZ models in quantum toroidal setting and the implications for the quantum KdV model. In particular, we conjecture that the spectrum of non-local integrals of motion of Bazhanov, Lukyanov, and Zamolodchikov is described by Gaudin Bethe ansatz equations associated to affine {sl}2 . Dedicated to the memory of Petr Petrovich Kulish.

Investigating the use of mastery-style online homework exercises in introductory algebra-based mechanics in a controlled clinical study

NASA Astrophysics Data System (ADS)

Evans, William R.; Selen, Mats A.

2017-12-01

Homework in introductory physics represents an important part of a student's learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs traditional-style homework with students in both algebra-based and calculus-based introductory mechanics. Results indicate a benefit from mastery-style over traditional-style homework, principally for weaker students who are less familiar with the material being covered and on questions that are nearer transfer to the study materials.

Journal Writing: Enlivening Elementary Linear Algebra.

ERIC Educational Resources Information Center

Meel, David E.

1999-01-01

Examines the various issues surrounding the implementation of journal writing in an undergraduate linear algebra course. Identifies the benefits of incorporating journal writing into an undergraduate mathematics course, which are supported with students' comments from their journals and their reflections on the process. Contains 14 references.…

Algebraic Thinking in Solving Linier Program at High School Level: Female Student’s Field Independent Cognitive Style

NASA Astrophysics Data System (ADS)

Hardiani, N.; Budayasa, I. K.; Juniati, D.

2018-01-01

The aim of this study was to describe algebraic thinking of high school female student’s field independent cognitive style in solving linier program problem by revealing deeply the female students’ responses. Subjects in this study were 7 female students having field independent cognitive style in class 11. The type of this research was descriptive qualitative. The method of data collection used was observation, documentation, and interview. Data analysis technique was by reduction, presentation, and conclusion. The results of this study showed that the female students with field independent cognitive style in solving the linier program problem had the ability to represent algebraic ideas from the narrative question that had been read by manipulating symbols and variables presented in tabular form, creating and building mathematical models in two variables linear inequality system which represented algebraic ideas, and interpreting the solutions as variables obtained from the point of intersection in the solution area to obtain maximum benefit.

The development and nature of problem-solving among first-semester calculus students

NASA Astrophysics Data System (ADS)

Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving performance, we observe that current instruction requires ongoing refinement to help students develop multi-register fluency and the ability to model quantitatively, as is called for in current US standards for mathematical instruction.

A structural equation modeling analysis of students' understanding in basic mathematics

NASA Astrophysics Data System (ADS)

Oktavia, Rini; Arif, Salmawaty; Ferdhiana, Ridha; Yuni, Syarifah Meurah; Ihsan, Mahyus

2017-11-01

This research, in general, aims to identify incoming students' understanding and misconceptions of several basic concepts in mathematics. The participants of this study are the 2015 incoming students of Faculty of Mathematics and Natural Science of Syiah Kuala University, Indonesia. Using an instrument that were developed based on some anecdotal and empirical evidences on students' misconceptions, a survey involving 325 participants was administered and several quantitative and qualitative analysis of the survey data were conducted. In this article, we discuss the confirmatory factor analysis using Structural Equation Modeling (SEM) on factors that determine the new students' overall understanding of basic mathematics. The results showed that students' understanding on algebra, arithmetic, and geometry were significant predictors for their overall understanding of basic mathematics. This result supported that arithmetic and algebra are not the only predictors of students' understanding of basic mathematics.

Developing students' functional thinking in algebra through different visualisations of a growing pattern's structure

NASA Astrophysics Data System (ADS)

Wilkie, Karina J.; Clarke, Doug M.

2016-06-01

Spatial visualisation of geometric patterns and their generalisation have become a recognised pathway to developing students' functional thinking and understanding of variables in algebra. This design-based research project investigated upper primary students' development of explicit generalisation of functional relationships and their representation descriptively, graphically and symbolically. Ten teachers and their classes were involved in a sequence of tasks involving growing patterns and geometric structures over 1 year. This article focuses on two aspects of the study: visualising the structure of a geometric pattern in different ways and using this to generalise the functional relationship between two quantifiable aspects (variables). It was found that in an initial assessment task ( n = 222), students' initial visualisations could be categorised according to different types and some of these were more likely to lead either to recursive or explicit generalisation. In a later task, a small number of students demonstrated the ability to find more than one way to visualise the same geometric structure and thus represent their explicit generalisations as different but equivalent symbolic equations (using pronumerals). Implications for the teaching of functional thinking in middle-school algebra are discussed.

The Visual Syntax of Algebra.

ERIC Educational Resources Information Center

Kirshner, David

1989-01-01

A structured system of visual features is seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Women more than men were found to depend on these visual cues. Possible causes and consequences are discussed. Subjects were secondary and college students. (Author/DC)

Algebra, Home Mortgages, and Recessions

ERIC Educational Resources Information Center

Mariner, Jean A. Miller; Miller, Richard A.

2009-01-01

The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…

Applications of Maple To Algebraic Cryptography.

ERIC Educational Resources Information Center

Sigmon, Neil P.

1997-01-01

Demonstrates the use of technology to enhance the appreciation of applications involving abstract algebra. The symbolic manipulator Maple can perform computations required for a linear cryptosystem. One major benefit of this process is that students can encipher and decipher messages using a linear cryptosystem without becoming confused and…

Alternative Delivery Systems for Introductory Algebra.

ERIC Educational Resources Information Center

Keating, John; And Others

Since 1988, Massachusetts' Massasoit Community College has offered two alternative introductory algebra courses for students receiving low scores on mathematics admission tests. One alternative course provides 5 hours of instruction per week, rather than the 3 hours per week in the traditional course, while the other segments the traditional…

Teaching Algebra to Students With Learning Disabilities: Where Have We Come and Where Should We Go?

PubMed

Watt, Sarah J; Watkins, Jessie R; Abbitt, Jason

2016-07-01

This review investigates effective interventions for teaching algebra to students with learning disabilities and evaluates the complexity and alignment of skills with the Common Core State Standards in math. The review includes the results of 10 experimental and 5 single-subject designs (N = 15) producing a moderate overall effect size (g = 0.48). A total of five interventions were identified and analyzed across the studies using effect size data. © Hammill Institute on Disabilities 2014.

Assessing the Effectiveness of Studio Physics in Introductory-Level Courses at Georgia State University

NASA Astrophysics Data System (ADS)

Upton, Brianna; Evans, John; Morrow, Cherilynn; Thoms, Brian

2009-11-01

Previous studies have shown that many students have misconceptions about basic concepts in physics. Moreover, it has been concluded that one of the challenges lies in the teaching methodology. To address this, Georgia State University has begun teaching studio algebra-based physics. Although many institutions have implemented studio physics, most have done so in calculus-based sequences. The effectiveness of the studio approach in an algebra-based introductory physics course needs further investigation. A 3-semester study assessing the effectiveness of studio physics in an algebra-based physics sequence has been performed. This study compares the results of student pre- and post-tests using the Force Concept Inventory. Using the results from this assessment tool, we will discuss the effectiveness of the studio approach to teaching physics at GSU.

Effects of the Good Behavior Game on classwide off-task behavior in a high school basic algebra resource classroom.

PubMed

Flower, Andrea; McKenna, John; Muething, Colin S; Bryant, Diane Pedrotty; Bryant, Brian R

2014-01-01

This study investigated the effects of the Good Behavior Game (GBG) on classwide off-task behavior in two ninth-grade basic algebra resource classes. Ten students with a variety of disabilities, in two classrooms, and their special education resource teacher participated in this study. A reversal design was employed, in which the special education teacher implemented GBG compared to typical practice-algebra readiness instruction. Results showed that classwide off-task behavior decreased in the GBG conditions compared to the baseline and reversal conditions. Fidelity measures indicated that the teacher implemented GBG with fidelity. Students and the teacher rated GBG favorably. Overall findings support the use of GBG for reducing classwide off-task behavior. Implications for practice and future research directions are presented.

Algebra. A Guidebook for Teaching.

ERIC Educational Resources Information Center

Goodman, Terry A.; And Others

This book provides a general framework for organizing the instructional program in algebra. For each topic, a general approach for instruction, together with specific strategies, activities, and resources that can be used daily, are provided. Also included are worksheet pages that can be used with students. Most activities provide for student…

Algebra for All: California's Eighth-Grade Algebra Initiative as Constrained Curricula

ERIC Educational Resources Information Center

Domina, Thurston; Penner, Andrew M.; Penner, Emily K.; Conley, AnneMarie

2014-01-01

Background/Context: Across the United States, secondary school curricula are intensifying as a growing proportion of students enroll in high-level academic math courses. In many districts, this intensification process occurs as early as eighth grade, where schools are effectively constraining their mathematics curricula by restricting course…

The Leap from Patterns to Formulas

ERIC Educational Resources Information Center

Beigie, Darin

2011-01-01

Initial exposure to algebraic thinking involves the critical leap from working with numbers to thinking with variables. The transition to thinking mathematically using variables has many layers, and for all students an abstraction that is clear in one setting may be opaque in another. Geometric counting and the resulting algebraic patterns provide…

Assessing Formal Knowledge of Math Equivalence among Algebra and Pre-Algebra Students

ERIC Educational Resources Information Center

Fyfe, Emily R.; Matthews, Percival G.; Amsel, Eric; McEldoon, Katherine L.; McNeil, Nicole M.

2018-01-01

A central understanding in mathematics is knowledge of "math equivalence," the relation indicating that 2 quantities are equal and interchangeable. Decades of research have documented elementary-school (ages 7 to 11) children's (mis)understanding of math equivalence, and recent work has developed a construct map and comprehensive…

The Progressive Development of Early Embodied Algebraic Thinking

ERIC Educational Resources Information Center

Radford, Luis

2014-01-01

In this article I present some results from a 5-year longitudinal investigation with young students about the genesis of embodied, non-symbolic algebraic thinking and its progressive transition to culturally evolved forms of symbolic thinking. The investigation draws on a cultural-historical theory of teaching and learning--the theory of…

Effects of Computer Algebra System (CAS) with Metacognitive Training on Mathematical Reasoning.

ERIC Educational Resources Information Center

Kramarski, Bracha; Hirsch, Chaya

2003-01-01

Describes a study that investigated the differential effects of Computer Algebra Systems (CAS) and metacognitive training (META) on mathematical reasoning. Participants were 83 Israeli eighth-grade students. Results showed that CAS embedded within META significantly outperformed the META and CAS alone conditions, which in turn significantly…

The Jukes-Cantor Model of Molecular Evolution

ERIC Educational Resources Information Center

Erickson, Keith

2010-01-01

The material in this module introduces students to some of the mathematical tools used to examine molecular evolution. This topic is standard fare in many mathematical biology or bioinformatics classes, but could also be suitable for classes in linear algebra or probability. While coursework in matrix algebra, Markov processes, Monte Carlo…

Studies in Mathematics, Volume X. Applied Mathematics in the High School.

ERIC Educational Resources Information Center

Schiffer, Max M.

This publication contains a sequence of lectures given to high school mathematics teachers by the author. Applications of mathematics emphasized are elementary algebra, geometry, and matrix algebra. Included are: (1) an introduction concerning teaching applications of mathematics; (2) Chapter 1: Mechanics for the High School Student; (3) Chapter…

A Guided Reinvention of Ring, Integral Domain, and Field

ERIC Educational Resources Information Center

Cook, John Paul

2012-01-01

Abstract algebra enjoys a prestigious position in mathematics and the undergraduate mathematics curriculum. A typical abstract algebra course aims to provide students with a glimpse into the elegance of mathematics by exposing them to structures that form its foundation--it arguably approximates the actual practice of mathematics better than any…

International Inequalities: Algebraic Investigations into Health and Economic Development

ERIC Educational Resources Information Center

Staats, Susan; Robertson, Douglas

2009-01-01

The Millennium Project is an international effort to improve the health, economic status, and environmental resources of the world's most vulnerable people. Using data associated with the Millennium Project, students use algebra to explore international development issues including poverty reduction and the relationship between health and economy.…

Math 3008--Developmental Mathematics II. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course designed to develop student proficiency in the basic algebraic skills. This is designed as the second of a two-semester sequence. Topics include performing operations with radicals and exponents; learning to solve equations;…

Math 3007--Developmental Mathematics I. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course designed to develop student proficiency in the basic algebraic skills. This course is designed as the first of a two-semester sequence. Topics include operations with signed numbers; simple operations on monomials and…

Alternative Representations for Algebraic Problem Solving: When Are Graphs Better than Equations?

ERIC Educational Resources Information Center

Mielicki, Marta K.; Wiley, Jennifer

2016-01-01

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

The Transformation App Redux: The Notion of Linearity

ERIC Educational Resources Information Center

Domenick, Anthony

2015-01-01

The notion of linearity is perhaps the most fundamental idea in algebraic thinking. It sets the transition to functions and culminates with the instantaneous rate of change in calculus. Despite its simplicity, this concept poses complexities to a considerable number of first semester college algebra students. The purpose of this observational…

Algebraic Procedures and Creative Thinking

ERIC Educational Resources Information Center

Tabach, Michal; Friedlander, Alex

2017-01-01

Simplifying symbolic expressions is usually perceived in middle school algebra as an algorithmic activity, achieved by performing sequences of short drill-and-practice tasks, which have little to do with conceptual learning or with creative mathematical thinking. The aim of this study is to explore possible ways by which ninth-grade students can…

Computer Algebra Systems and Theorems on Real Roots of Polynomials

ERIC Educational Resources Information Center

Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.

2010-01-01

A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)

Embodied, Symbolic and Formal Thinking in Linear Algebra

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.

2007-01-01

Students often find their first university linear algebra experience very challenging. While coping with procedural aspects of the subject, solving linear systems and manipulating matrices, they may struggle with crucial conceptual ideas underpinning them, making it very difficult to progress in more advanced courses. This research has sought to…

Inequalities, Assessment and Computer Algebra

ERIC Educational Resources Information Center

Sangwin, Christopher J.

2015-01-01

The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

Staircases, Towers, and Castles

ERIC Educational Resources Information Center

Kara, Melike; Eames, Cheryl L.; Miller, Amanda L.; Chieu, Annie

2015-01-01

The very nature of algebra concerns the generalization of patterns (Lee 1996). Patterning activities that are geometric in nature can serve as powerful contexts that engage students in algebraic thinking and visually support them in constructing a variety of generalizations and justifications (e.g., Healy and Hoyles 1999; Lannin 2005). In this…

Computer Algebra System Calculators: Gender Issues and Teachers' Expectations

ERIC Educational Resources Information Center

Forgasz, Helen J.; Griffith, Shirly

2006-01-01

In this paper we present findings from two studies focusing on computer algebra system (CAS) calculators. In Victoria, Australia, it is currently mandatory for students to use graphics calculators in some grade 12 mathematics examinations. Since 2001, a pilot study has been conducted involving Victorian Certificate of Education (VCE) students…

Mathematics Placement at Cottey College.

ERIC Educational Resources Information Center

Callahan, Susan

In response to the large numbers of students who were failing or dropping out of basic algebra and calculus classes, Cottey College, in Missouri, developed a math placement program in 1982 using Basic Algebra (BA) and Calculus Readiness (CR) tests from the Mathematical Association of America's Placement Testing Program. Cut off scores for the…

Using an Online Tool for Learning about and Implementing Algebra Progress Monitoring

ERIC Educational Resources Information Center

Foegen, Anne; Stecker, Pamela M.; Genareo, Vincent R.; Lyons, Renée; Olson, Jeannette R.; Simpson, Amber; Romig, John Elwood; Jones, Rachel

2016-01-01

Research supports special educators' use of progress-monitoring data for instructional decision-making purposes as an evidence-based practice for improving student achievement. This article describes the Professional Development for Algebra Progress Monitoring (PD-APM) system. PD-APM, is an online system that includes two "hubs" that…

Titration Calculations with Computer Algebra Software

ERIC Educational Resources Information Center

Lachance, Russ; Biaglow, Andrew

2012-01-01

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

Adventures in Flipping College Algebra

ERIC Educational Resources Information Center

Van Sickle, Jenna

2015-01-01

This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…

Using e-Learning Platforms for Mastery Learning in Developmental Mathematics Courses

ERIC Educational Resources Information Center

Boggs, Stacey; Shore, Mark; Shore, JoAnna

2004-01-01

Many colleges and universities have adopted e-learning platforms to utilize computers as an instructional tool in developmental (i.e., beginning and intermediate algebra) mathematics courses. An e-learning platform is a computer program used to enhance course instruction via computers and the Internet. Allegany College of Maryland is currently…

A New Age for Algebra

ERIC Educational Resources Information Center

Oishi, Lindsay

2011-01-01

"Solve for x." While many people first encountered this enigmatic instruction in high school, the last 20 years have seen a strong push to get students to take algebra in eighth grade or even before. Today, concerns about the economy highlight a familiar worry: American eighth-graders trailed their peers in five Asian countries on the…

High Level Technology in a Low Level Mathematics Course.

ERIC Educational Resources Information Center

Schultz, James E.; Noguera, Norma

2000-01-01

Describes a teaching experiment in which spreadsheets and computer algebra systems were used to teach a low-level college consumer mathematics course. Students were successful in using different types of functions to solve a variety of problems drawn from real-world situations. Provides an existence proof that computer algebra systems can assist…

Algebraic Functions, Computer Programming, and the Challenge of Transfer

ERIC Educational Resources Information Center

Schanzer, Emmanuel Tanenbaum

2015-01-01

Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems.…

Examples in College Algebra Textbooks: Opportunities for Students' Learning

ERIC Educational Resources Information Center

Mesa, Vilma; Suh, Heejoo; Blake, Tyler; Whittemore, Timothy

2012-01-01

We present an analysis of several characteristics of examples in 10 college algebra textbooks used in community colleges or 4-year institutions. We analyzed the examples along four dimensions: cognitive demand, the responses expected, the use of representations, and the strategies available for verifying the correctness of the solutions. We found…

Exploring Concepts from Abstract Algebra Using Variations of Generalized Woven Figure Eights

ERIC Educational Resources Information Center

Taylor, Tara; Knoll, Eva; Landry, Wendy

2016-01-01

Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…

Some Unexpected Results Using Computer Algebra Systems.

ERIC Educational Resources Information Center

Alonso, Felix; Garcia, Alfonsa; Garcia, Francisco; Hoya, Sara; Rodriguez, Gerardo; de la Villa, Agustin

2001-01-01

Shows how teachers can often use unexpected outputs from Computer Algebra Systems (CAS) to reinforce concepts and to show students the importance of thinking about how they use the software and reflecting on their results. Presents different examples where DERIVE, MAPLE, or Mathematica does not work as expected and suggests how to use them as a…

Designing Tasks for Math Modeling in College Algebra: A Critical Review

ERIC Educational Resources Information Center

Staats, Susan; Robertson, Douglas

2014-01-01

Over the last decade, the pedagogical approach known as mathematical modeling has received increased interest in college algebra classes in the United States. Math modeling assignments ask students to develop their own problem-solving tools to address non-routine, realistic scenarios. The open-ended quality of modeling activities creates dilemmas…

Validating Cognitive Models of Task Performance in Algebra on the SAT®. Research Report No. 2009-3

ERIC Educational Resources Information Center

Gierl, Mark J.; Leighton, Jacqueline P.; Wang, Changjiang; Zhou, Jiawen; Gokiert, Rebecca; Tan, Adele

2009-01-01

The purpose of the study is to present research focused on validating the four algebra cognitive models in Gierl, Wang, et al., using student response data collected with protocol analysis methods to evaluate the knowledge structures and processing skills used by a sample of SAT test takers.

Student Connections of Linear Algebra Concepts: An Analysis of Concept Maps

ERIC Educational Resources Information Center

Lapp, Douglas A.; Nyman, Melvin A.; Berry, John S.

2010-01-01

This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud's theory of conceptual fields and Pirie and Kieren's model for the growth of mathematical understanding.…

All Talk and More Action

ERIC Educational Resources Information Center

Williams-Candek, Maryellen

2016-01-01

How better to begin the study of linear equations in an algebra class than to determine what students already know about the subject? A seventh-grade algebra class in a suburban school undertook a project early in the school year that was completed before they began studying linear relations and functions. The project, which might have been…

Transforming an Introductory Linear Algebra Course with a TI-92 Hand-Held Computer.

ERIC Educational Resources Information Center

Quesada, Antonio R.

2003-01-01

Describes how the introduction of the TI-92 transformed a traditional first semester linear algebra course into a matrix-oriented course that emphasized conceptual understanding, relevant applications, and numerical issues. Indicates an increase in students' overall performance as they found the calculator very useful, believed it helped them…

The Effect of Online Tasks for Algebra on Student Achievement in Grade 8

ERIC Educational Resources Information Center

Drijvers, Paul; Doorman, Michiel; Kirschner, Paul; Hoogveld, Bert; Boon, Peter

2014-01-01

Online resources are widely used for educational purposes, such as the training of skills. For algebra education in particular, online resources are expected to contribute to skill mastery in an efficient and effective way. However, studies that underpin these claims through a randomized experiment are scarce. To experimentally investigate the…

Design Research on Personalized Problem Posing in Algebra

ERIC Educational Resources Information Center

Walkington, Candace

2017-01-01

Algebra is an area of pressing national concern around issues of equity and access in education. Recent theories and research suggest that personalization of instruction can allow students to activate their funds of knowledge and can elicit interest in the content to be learned. This paper examines the results of a large-scale teaching experiment…