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Townsend, Cynthia; Slavit, David; McDuffie, Amy Roth – Mathematics Teaching in the Middle School, 2018
In "Principles to Actions: Ensuring Mathematical Success for All," NCTM (2014) defines productive struggle as students delving "more deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions" (p. 48). Hiebert and Grouws (2007, p. 387)…
Descriptors: Mathematics Instruction, Mathematics Achievement, Problem Solving, Algebra
Cho, Peter; Nagle, Courtney – North American Chapter of the International Group for the Psychology of Mathematics Education, 2017
This study extends past research on students' understanding of slope by analyzing college students' mistakes on routine tasks involving slope. We conduct quantitative and qualitative analysis of students' mistakes to extract information regarding slope conceptualizations described in prior research. Results delineate procedural proficiencies and…
Descriptors: Task Analysis, College Students, Error Correction, Error Patterns
Stephens, Ana; Strachota, Susanne; Knuth, Eric; Blanton, Maria; Isler, Isil; Gardiner, Angela – North American Chapter of the International Group for the Psychology of Mathematics Education, 2017
This research explores the interplay between students' understandings of proportional and functional relationships. Approximately 90 students participated in an early algebra intervention in Grades 3- 5. Before the intervention and after each year of the intervention, we evaluated their understandings of proportional and functional relationships.…
Descriptors: Algebra, Early Intervention, Grade 3, Grade 4
Ioannou, Marios – Mathematics Education Research Group of Australasia, 2016
Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…
Descriptors: Undergraduate Students, Mathematics Education, Problem Solving, Student Reaction
Walick, Christopher M.; Burns, Matthew K. – Assessment for Effective Intervention, 2017
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.…
Descriptors: Algebra, Mathematics Instruction, Secondary School Mathematics, Mathematical Aptitude
Kolovou, Angeliki; van den Heuvel-Panhuizen, Marja; Koller, Olaf – Journal for Research in Mathematics Education, 2013
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…
Descriptors: Intervention, Algebra, Student Improvement, Problem Solving
Lian, Lim Hooi; Yew, Wun Thiam; Idris, Noraini – International Journal for Mathematics Teaching and Learning, 2010
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.…
Descriptors: Alternative Assessment, Mathematics Instruction, Cognitive Ability, Algebra
Ross, Dan; Reys, Robert; Chavez, Oscar; McNaught, Melissa D.; Grouws, Douglas A. – School Science and Mathematics, 2011
A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th-, 9th-, and 10th-grade students in five different school systems over three consecutive…
Descriptors: Algebra, Problem Sets, Problem Solving, Mathematical Applications
Samo, Mashooque Ali – International Journal for Mathematics Teaching and Learning, 2009
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…
Descriptors: Student Attitudes, Word Problems (Mathematics), Algebra, Misconceptions
Arizpe, Omar; Dwyer, Jerry; Stevens, Tara – International Journal for Mathematics Teaching and Learning, 2009
A solution to the Rubik's Cube was introduced to an eighth grade mathematics class. The purpose of this study was to determine if an introduction to a solution to the Rubik's Cube could enhance students' problem-solving abilities, increase their general interest in mathematics, and enhance students' problem solving self-efficacy. Pre and Post…
Descriptors: Self Efficacy, Problem Solving, Grade 8, Problem Sets
Koedinger, Kenneth R.; Nathan, Mitchell J. – Journal of the Learning Sciences, 2004
This article explores how differences in problem representations change both the performance and underlying cognitive processes of beginning algebra students engaged in quantitative reasoning. Contrary to beliefs held by practitioners and researchers in mathematics education, students were more successful solving simple algebra story problems than…
Descriptors: Mathematics Education, Algebra, Problem Solving, Cognitive Processes

Berner, Leslie; McLaughlin, Patrick; Verzoni, Kathryn A. – Mathematics Teaching in the Middle School, 1997
Discusses mathematical thinking and problems posed by seventh- grade students as part of a unit on the study of algebraic ideas. The unit involves showing how variables cause changes and also incorporates the solving of systems of equations by constructing line-graph drawings and combination charts. (AIM)
Descriptors: Algebra, Equations (Mathematics), Graphs, Junior High Schools
Talbi, Mohamed T. – International Journal of Mathematical Education in Science and Technology, 2003
This study deals with the demand of a task. A theoretical background shows the difficulty of applying the idea of demand (as established in the literature) to the data. This has been confirmed in the preliminary study of this paper, which deals with the analysis of university examinations. Some factors that affect the demand of a task have been…
Descriptors: Teacher Attitudes, Mathematics Anxiety, Mathematical Aptitude, Problem Solving
Brizuela, Barbara; Schliemann, Analucia – For the Learning of Mathematics, 2004
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…
Descriptors: Equations (Mathematics), Elementary School Mathematics, Elementary School Students, Problem Solving