Early Secondary Mathematics: The Use of Intrigue to Enhance Mathematical Thinking and Motivation in Beginning Algebra

2003 ◽  
Vol 96 (2) ◽  
pp. 92-96
Author(s):  
Marjorie L. Lewkowicz
Keyword(s):  
Conceptual Understanding ◽  
Mathematical Thinking ◽  
Secondary Mathematics ◽  
Algebra Students ◽  
Beginning Algebra

IN AN EFFORT TO HELP MY BEGINNING ALGEBRA STUDENTS further develop their conceptual understanding of variables, the language of algebra, and other important topics,

The Use of the Concrete-representational-abstract (CRA) Sequence to Improve Mathematical Outcomes for Elementary Students with Emotional Behavioral Disorders

2021 ◽  
Author(s):  
Margaret M Flores ◽  
Vanessa M Hinton
Keyword(s):  
Elementary Students ◽  
Behavioral Disorders ◽  
Conceptual Understanding ◽  
Mathematical Thinking ◽  
Emotional Behavioral Disorders ◽  
Teaching Mathematics ◽  
Teaching Sequence ◽  
Positive Effects ◽  
Students With Ebd

The concrete-representational-abstract (CRA) sequence is an explicit methodology for teaching mathematics that has been shown to have positive effects for students with EBD. This teaching sequence fosters conceptual understanding and mathematical thinking. This article describes how a teacher used explicit CRA instruction with two elementary students with EBD. Its aims are to describe and provide rationale for CRA instruction. We will describe lesson activities, methods, materials, and procedures. Finally, we will offer suggestions for implementation.

A Framework for Computational Thinking Dispositions in Mathematics Education

2018 ◽  
Vol 49 (4) ◽  
pp. 424-461 ◽  
Author(s):  
Arnulfo Pérez
Keyword(s):  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Relevant Literature ◽  
Computational Thinking ◽  
Secondary Mathematics ◽  
Mathematical Concepts ◽  
Thinking Dispositions ◽  
Secondary Mathematics Teachers ◽  
Tolerance For Ambiguity ◽  
Epistemic Frame

This theoretical article describes a framework to conceptualize computational thinking (CT) dispositions—tolerance for ambiguity, persistence, and collaboration—and facilitate integration of CT in mathematics learning. CT offers a powerful epistemic frame that, by foregrounding core dispositions and practices useful in computer science, helps students understand mathematical concepts as outward oriented. The article conceptualizes the characteristics of CT dispositions through a review of relevant literature and examples from a study that explored secondary mathematics teachers' engagement with CT. Discussion of the CT framework highlights the complementary relationship between CT and mathematical thinking, the relevance of mathematics to 21st-century professions, and the merit of CT to support learners in experiencing these connections.

An Excel–lent Card Trick

2011 ◽  
Vol 104 (7) ◽  
pp. 526-530
Author(s):  
Holly S. Zullo
Keyword(s):  
Mathematical Explanation ◽  
Microsoft Excel ◽  
Mathematical Ideas ◽  
Algebra Students ◽  
Beginning Algebra ◽  
Composite Functions ◽  
Floor Function

Card tricks based on mathematical principles can be a great way to get students interested in exploring some important mathematical ideas. Bonomo (2008) describes several variations of a card trick that rely on nested floor functions, but these generally go beyond the reach of beginning algebra students. However, a simple spreadsheet implementation shows students why the card trick works and allows them to explore several variations. As an added bonus, students are introduced to composite functions, the floor function, and iteration, and they learn how to use formulas and the INT function in Microsoft Excel. The depth of the mathematical explanation can be varied according to students' background.

Mathematical Conversations to Transform Algebra Class

2015 ◽  
Vol 108 (9) ◽  
pp. 656-661
Author(s):  
Jennifer Earles Szydlik
Keyword(s):  
Classroom Discussions ◽  
Algebra Students ◽  
Beginning Algebra ◽  
Algebra Class

Three topics worthy of classroom discussions help beginning algebra students create meaning and build understanding as a community.

scholarly journals Special Issue on Digital Games for Learning Mathematics

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Alessandro De Gloria
Keyword(s):  
Conceptual Understanding ◽  
Mathematical Thinking ◽  
Leading Edge ◽  
Digital Games ◽  
Online Games ◽  
Special Issue ◽  
Learning Mathematics ◽  
Games For Learning ◽  
Thinking Processes

Given the huge relevance of mathematics, for both reasoning and applications, it is important to develop more engaging and effective methods that can be used to enhance children’s conceptual understanding of mathematics, develop mathematical thinking processes and improve arithmetical skills. Digital games provide interesting possibilities to support these goals and one can easily find great deal of online games and apps targeted for learning mathematics. This spoecial issue is devoted to present leading-edge research and perspectives in the field.

scholarly journals Challenges in mathematical cognition: A collaboratively-derived research agenda

2016 ◽  
Vol 2 (1) ◽  
pp. 20-41 ◽  
Author(s):  
Lara Alcock ◽  
Daniel Ansari ◽  
Sophie Batchelor ◽  
Marie-Josée Bisson ◽  
Bert De Smedt ◽  
...  
Keyword(s):  
Conceptual Understanding ◽  
Research Agenda ◽  
Mathematical Thinking ◽  
Developmental Trajectories ◽  
Mathematical Cognition ◽  
Established Method ◽  
Effective Interventions ◽  
Research Questions ◽  
Education Psychology ◽  
Initial List

This paper reports on a collaborative exercise designed to generate a coherent agenda for research on mathematical cognition. Following an established method, the exercise brought together 16 mathematical cognition researchers from across the fields of mathematics education, psychology and neuroscience. These participants engaged in a process in which they generated an initial list of research questions with the potential to significantly advance understanding of mathematical cognition, winnowed this list to a smaller set of priority questions, and refined the eventual questions to meet criteria related to clarity, specificity and practicability. The resulting list comprises 26 questions divided into six broad topic areas: elucidating the nature of mathematical thinking, mapping predictors and processes of competence development, charting developmental trajectories and their interactions, fostering conceptual understanding and procedural skill, designing effective interventions, and developing valid and reliable measures. In presenting these questions in this paper, we intend to support greater coherence in both investigation and reporting, to build a stronger base of information for consideration by policymakers, and to encourage researchers to take a consilient approach to addressing important challenges in mathematical cognition.

Supporting Preservice Secondary Mathematics Teachers’ Professional Judgment Around Digital Technology Use

2021 ◽  
Vol 9 (2) ◽  
pp. 145-159
Author(s):  
Charmaine Mangram ◽  
Kathy Liu Sun
Keyword(s):  
Preservice Teachers ◽  
Digital Technology ◽  
Technology Use ◽  
Teacher Educators ◽  
Mathematical Thinking ◽  
Mathematical Practice ◽  
Secondary Mathematics ◽  
Ease Of Use ◽  
Professional Judgment ◽  
Mathematics Methods

The pervasiveness of digital technology creates an imperative for mathematics teacher educators to prepare preservice teachers (PSTs) to select technology to support students’ mathematical development. We report on research conducted on an assignment created for and implemented in secondary mathematics methods courses requiring PSTs to select and evaluate digital mathematics tools. We found that PSTs primarily focused on pedagogical fidelity (ease of use), did not consider mathematical fidelity (accuracy), and at times superficially attended to cognitive fidelity (how well the tool reflects students’ mathematical thinking processes) operationalized as the CCSS for Mathematical Practice and Five Strands of Mathematical Proficiency. We discuss implications for implementing the assignment and suggestions for addressing PSTs’ challenges with identifying the mathematical practices and five strands.

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