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Maria Blanton; Angela Murphy Gardiner; Ingrid Ristroph; Ana Stephens; Eric Knuth; Rena Stroud – Mathematical Thinking and Learning: An International Journal, 2024
Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about parity arguments for sums of evens and odds, as well as underlying…
Descriptors: Persuasive Discourse, Algebra, Learning Processes, Elementary School Students
Erbilgin, Evrim; Gningue, Serigne M. – Educational Studies in Mathematics, 2023
Representations are key to mathematical activities and meaning-making processes as they are part of modeling, connecting, communicating, and understanding mathematical ideas and concepts. The current study sought to examine a group of novice algebra learners' interactions with different representations from an onto-semiotic approach. A case study…
Descriptors: Novices, Algebra, Learning Processes, Mathematics Instruction
Philip Slobodsky; Mariana Durcheva – International Journal for Technology in Mathematics Education, 2023
The mode of assessment is one of the most important factors influencing learning. E-assessment usually includes only checking the final answer, thus limiting teacher's ability to check the complete solution, and it does not allow inclusion of math proofs problems that constitute an important part of math content. The e-assessment module of Halomda…
Descriptors: Mathematics Instruction, Learning Processes, Algebra, Validity
Stewart, Sepideh; Andrews-Larson, Christine; Zandieh, Michelle – ZDM: The International Journal on Mathematics Education, 2019
In this survey paper, we describe the state of the field on linear algebra research. We synthesize themes, questions, results, and perspectives emphasized in the papers that appear in this issue, as well as a selection of those published between 2008 and 2017. We highlight the extensive base of empirical research detailing how students reason…
Descriptors: Mathematics Instruction, Mathematical Logic, Teaching Methods, Mathematics Achievement
Elizabeth Wrightsman; Cody L. Patterson – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
We investigate teacher beliefs about discourses for equation solving and the challenges these beliefs might pose for the implementation of instructional practices that promote deductive reasoning in algebra. To uncover these beliefs, we recorded three video explanations of solutions to the same linear equation with distinct discursive…
Descriptors: Teacher Attitudes, Mathematics Instruction, Logical Thinking, Teaching Methods
Graf, Edith Aurora; Peters, Stephanie; Fife, James H.; van Rijn, Peter W.; Arieli-Attali, Meirav; Marquez, Elizabeth – ETS Research Report Series, 2019
Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…
Descriptors: Mathematical Concepts, Learning Processes, Sequential Approach, Student Development
Hurst, Chris; Hurrell, Derek – Australian Primary Mathematics Classroom, 2016
Multiplicative thinking is accepted as a "big idea" of mathematics that underpins important mathematical concepts such as fraction understanding, proportional reasoning, and algebraic thinking. It is characterised by understandings such as the multiplicative relationship between places in the number system, basic and extended number…
Descriptors: Multiplication, Mathematics Instruction, Algebra, Mathematical Logic
Fonger, Nicole L.; Stephens, Ana; Blanton, Maria; Isler, Isil; Knuth, Eric; Gardiner, Angela Murphy – Cognition and Instruction, 2018
Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked…
Descriptors: Academic Achievement, Mathematics Education, Algebra, Research and Development
Selter, Christoph; Prediger, Susanne; Nuhrenborger, Marcus; Hussmann, Stephan – Educational Studies in Mathematics, 2012
Subtraction can be understood by two basic models--taking away (ta) and determining the difference (dd)--and by its inverse relation to addition. Epistemological analyses and empirical examples show that the two models are not relevant only in single-digit arithmetic. As curricula should be developed in a longitudinal perspective on mathematics…
Descriptors: Equations (Mathematics), Mathematics Instruction, Learning Processes, Subtraction
Güler, Gürsel; Dikici, Ramazan – International Journal of Mathematical Education in Science and Technology, 2014
The aim of this study was to examine prospective mathematics teachers' proof processes for algebraic concepts. The study was conducted with 10 prospective teachers who were studying at the department of secondary mathematics teaching and who volunteered to participate in the study. The data were obtained via task-based clinical interviews…
Descriptors: Algebra, Preservice Teachers, Mathematics Teachers, Mathematical Concepts
Star, Jon R.; Foegen, Anne; Larson, Matthew R.; McCallum, William G.; Porath, Jane; Zbiek, Rose Mary; Caronongan, Pia; Furgeson, Joshua,; Keating, Betsy; Lyskawa, Julia – What Works Clearinghouse, 2015
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…
Descriptors: Algebra, Mathematics Instruction, Secondary School Mathematics, Teaching Methods
Howell, Tracey H. – ProQuest LLC, 2013
In an era of new standards and emerging accountability systems, an understanding of the supports needed to aid teachers and students in making necessary transitions in mathematics teaching and learning is critical. Given the established research base demonstrating the importance of justification and reasoning in students' mathematics learning and…
Descriptors: High School Students, Persuasive Discourse, Mathematical Logic, Teacher Expectations of Students
Tabach, Michal; Hershkowitz, Rina; Arcavi, Abraham – Journal of Mathematical Behavior, 2008
This study is part of a large research and development project aimed at observing, describing and analyzing the learning processes of two seventh grade classes during a yearlong beginning algebra course in a computer intensive environment (CIE). The environment includes carefully designed algebra learning materials with a functional approach, and…
Descriptors: Spreadsheets, Mathematics Instruction, Secondary School Mathematics, Computer Assisted Instruction

Bonsangue, Martin V.; Gannon, Gerald E,; Pheifer, Laura J. – Mathematics Teacher, 2002
Reports findings from the team teaching of a course in mathematical problem solving designed for secondary and community college teachers to clarify the concept of ."ecessary and sufficient" conditions. Discusses assigned problems and students' incorrect interpretations. Student interpretations showed how simple mistakes can often lead to rich…
Descriptors: Algebra, Elementary Secondary Education, Learning Problems, Learning Processes
Endress, Ansgar D.; Scholl, Brian J.; Mehler, Jacques – Journal of Experimental Psychology: General, 2005
Recent research suggests that humans and other animals have sophisticated abilities to extract both statistical dependencies and rule-based regularities from sequences. Most of this research stresses the flexibility and generality of such processes. Here the authors take up an equally important project, namely, to explore the limits of such…
Descriptors: Algebra, Cognitive Ability, Generalization, Infants
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