It's a Home Run! Using Mathematical Discourse to Support the Learning of Statistics

2007 ◽  
Vol 101 (4) ◽  
pp. 250-256 ◽  
Author(s):  
Kathleen S. Himmelberger ◽  
Daniel L. Schwartz
Keyword(s):  
Mathematics Classroom ◽  
Mathematical Thinking ◽  
National Council ◽  
Instructional Programs ◽  
Group Discussions ◽  
Good Communication ◽  
Mathematical Ideas ◽  
Positive Effects ◽  
Procedural Fluency ◽  
Learning Mathematics

The Standards developed by the National Council of Teachers of Mathematics (2000) state that instructional programs should enable all students to communicate mathematical ideas. The Standards indicate that good communication includes the ability to express organized and precise ideas as well as the ability to analyze and evaluate the mathematical thinking of others. Learning mathematics goes beyond procedural fluency; it also includes learning to discuss mathematical ideas. For this purpose, small groups have become a frequent configuration in the mathematics classroom. When combined with a suitable exercise, small-group discussions can have positive effects on mathematical understanding.

Technology in the Mathematics Classroom

2011 ◽  
pp. 114-133 ◽  
Author(s):  
Robin J. Ittigson ◽  
John G. Zewe
Keyword(s):  
Decision Making ◽  
Teaching And Learning ◽  
Mathematics Classroom ◽  
Information Support ◽  
Visual Images ◽  
National Council ◽  
Problem Solving Skills ◽  
Mathematical Ideas ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics

According to the National Council of Teachers of Mathematics, technology is essential in teaching and learning mathematics. It influences how mathematics should be taught and enhances what students learn. Calculators and computers present visual images of mathematical ideas for students. They help students organize information, support investigations, and develop decision-making, reflection, reasoning, and problem-solving skills.

New Challenges to the Research Community: Reflections of the Research Advisory Committee

1998 ◽  
Vol 29 (5) ◽  
pp. 499-502
Keyword(s):  
Teaching Practice ◽  
Mathematics Classroom ◽  
Mathematics Learning ◽  
Research Community ◽  
National Council ◽  
Mathematical Ideas ◽  
Education Community ◽  
Research Findings ◽  
New Challenges ◽  
Children’S Thinking

Drawing on several decades of research findings, the National Council of Teachers of Mathematics (NCTM) produced, between 1989 and 1995, three volumes of Standards in which members of the mathematics education community formulated new visions of mathematics learning, teaching, and assessment. These new visions comprise an ambitious agenda for the mathematics classroom—one that includes, but surpasses, mastery of facts and procedures, the mainstay of extant practice—designed to engage students in the exploration of mathematical ideas and their interrelationships. Students would now be invited to articulate their ideas, and teachers to identify and mobilize those elements in children's thinking upon which stronger conceptions can be built. Paralleling this ambitious departure in teaching practice, new means of assessment were proposed to capture progress toward these far-reaching goals.

On Blocks, Stairs, and Beyond: Learning about the Significance of Representations

2007 ◽  
Vol 101 (5) ◽  
pp. 340-344
Author(s):  
Laurie H. Rubel ◽  
Betina A. Zolkower
Keyword(s):  
National Council ◽  
Classroom Activity ◽  
Instructional Programs ◽  
Mathematical Representations ◽  
Mathematical Ideas ◽  
Grade Levels

The National Council of Teachers of Mathematics (2000) recommends that students at all grade levels be provided with instructional programs that enable them to “create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; and use representations to model and interpret physical, social, and mathematical phenomena” (p. 67). This article describes a particular classroom activity used to highlight the significance of mathematical representations.

Links to Literature: A Remainder of One: Exploring Partitive Division

2000 ◽  
Vol 6 (8) ◽  
pp. 517-521
Author(s):  
Patricia Seray Moyer
Keyword(s):  
Children's Literature ◽  
Mathematical Knowledge ◽  
Mathematics Classroom ◽  
Children’S Literature ◽  
National Council ◽  
Mathematical Concepts ◽  
Mathematical Ideas ◽  
Mathematics Problems ◽  
Mathematical Symbols ◽  
Everyday Experiences

Children's literature can be a springboard for conversations about mathematical concepts. Austin (1998) suggests that good children's literature with a mathematical theme provides a context for both exploring and extending mathematics problems embedded in stories. In the context of discussing a story, children connect their everyday experiences with mathematics and have opportunities to make conjectures about quantities, equalities, or other mathematical ideas; negotiate their understanding of mathematical concepts; and verbalize their thinking. Children's books that prompt mathematical conversations also lead to rich, dynamic communication in the mathematics classroom and develop the use of mathematical symbols in the context of communicating. The National Council of Teachers of Mathematics (1989) emphasizes the importance of communication in helping children both construct mathematical knowledge and link their informal notions with the abstract symbols used to express mathematical ideas.

Examining Graphing Calculator Affordances in Learning Pre-Calculus among Undergraduate Students

2016 ◽  
Vol 12 (2) ◽  
pp. 35-50 ◽  
Author(s):  
Francis Nzuki
Keyword(s):  
Cognitive Load ◽  
Undergraduate Students ◽  
Cognitive Load Theory ◽  
Mathematics Classroom ◽  
Graphing Calculator ◽  
Mathematical Ideas ◽  
Extraneous Cognitive Load ◽  
Load Theory ◽  
Learning Mathematics ◽  
Intelligent Technology

This study examines graphing calculator affordances in learning mathematics among college precalculus students. The study draws from the Cognitive Load Theory (CLT) and the “Intelligent Technology” theoretical framework proposed by Salomon, Perkins, and Globerson (1991). From these perspectives the effects “with” the graphing calculator technology include the potential for this technology to offload students' extraneous cognitive load (e.g., the presence of unwieldy numbers), and in turn optimize their germane cognitive load (e.g., freeing students to focus on the key mathematical ideas). To examine students' perceptions on the adoption of the graphing calculator instructional approach a questionnaire was administered towards the end of the semester. The findings showed that the graphing calculator afforded students' learning in a variety of ways. Also considered is the challenge for educators to develop strategies that encourage appropriate use of graphing calculators in mathematics classroom in order to ensure that their integration is effective in instruction.

Improving Data Analysis through Discourse

2000 ◽  
Vol 5 (8) ◽  
pp. 548-553
Author(s):  
Kay McClain ◽  
Maggie McGatha ◽  
Lynn L. Hodge
Keyword(s):  
Data Analysis ◽  
Mathematics Classroom ◽  
Effective Communication ◽  
National Council ◽  
Classroom Norms ◽  
Mathematical Ideas ◽  
Mathematical Arguments ◽  
Teacher’S Role ◽  
Mathematical Discussions ◽  
Asking Questions

The National Council of Teachers of Mathematics has been advocating the importance of effective communication in classrooms since the release of its Standards documents (NCTM 1989, 1991). This emphasis is echoed in Richards's (1991) description of an inquiry classroom (see also, e.g., Ball [1993]; Cobb, Wood, and Yackel [1991]; Lampert [1990]). In this setting, the teacher's role is to guide the negotiation of classroom norms to enable the teacher and students together to engage in meaningful mathematical discussions, which include asking questions, solving problems, posing conjectures, and formulating and critiquing mathematical arguments. An increased emphasis on communication in the mathematics classroom allows students the opportunity to discuss and validate mathematical ideas and to make and evaluate conjectures and arguments.

Advance care planning: a personal view and stories from the frontline

2018 ◽  
Author(s):  
Tony Bonser
Keyword(s):  
Advance Care Planning ◽  
Good Practice ◽  
Societal Implications ◽  
National Council ◽  
Care Planning ◽  
Personal View ◽  
Positive Effects ◽  
Health And Social Care ◽  
Advance Care ◽  
High Level

This chapter includes a personal view of advance care planning (ACP) from Tony Bonser, whose son, Neil died aged 35 and who now works for the National Council for Palliative Care, with examples from others. It describes the importance and impact of ACP on people nearing the end of life and their families, and recommends that ACP should be mainstreamed across health and social care as part of good practice, and become part of the public debate through movements like Dying Matters. It affirms that ACP: enables a dialogue to be started; must be centred on patients and enable the implementation of patient wishes; will centre on giving advice rather than prescribing outcomes; has positive effects; needs high-level communication skills; helps restore control; and has societal implications.

scholarly journals Mathematical Thinking Styles—The Advantage of Analytic Thinkers When Learning Mathematics

2021 ◽  
Vol 11 (6) ◽  
pp. 289
Author(s):  
Jaime Huincahue ◽  
Rita Borromeo-Ferri ◽  
Pamela Reyes-Santander ◽  
Viviana Garrido-Véliz
Keyword(s):  
Mathematical Thinking ◽  
Quantitative Approach ◽  
Mathematical Tasks ◽  
Thinking Styles ◽  
Mathematical Performance ◽  
Test Instrument ◽  
Analytical Thinking ◽  
Learning Mathematics ◽  
Valid Test ◽  
Insight Into

School is a space where learning mathematics should be accompanied by the student’s preferences; however, its valuation in the classroom is not necessarily the same. From a quantitative approach, we ask from the mathematical thinking styles (MTS) theory about the correlations between preferences of certain MTS and mathematical performance. For this, a valid test instrument and a sample of 275 16-year-old Chilean students were used to gain insight into their preferences, beliefs and emotions when solving mathematical tasks and when learning mathematics. The results show, among other things, a clear positive correlation between mathematical performance and analytical thinking style, and also evidence the correlation between self-efficacy, analytical thinking and grades. It is concluded that students who prefer the analytical style are more advantageous in school, since the evaluation processes have a higher valuation of analytic mathematical thinking.

Mathematical ideas and indigenous languages

2021 ◽  
Author(s):  
Bill Barton ◽  
Roslyn M Frank
Keyword(s):  
Cognitive Linguistics ◽  
Mathematical Thinking ◽  
Human Experience ◽  
Indigenous Languages ◽  
Mathematical Ideas ◽  
Cultural Activities ◽  
Recent Interest ◽  
Formal Mathematics ◽  
Different Types ◽  
And Linguistics

Recent interest in how anthropology and linguistics relates to mathematics has led to recognition that mathematical thinking is a function of language in ways not previously recognised. Ethnomathematics, cognitive linguistics, and anthropology are all pointing to a way of understanding mathematical ideas based on human experience and cultural activities. Formal mathematics can be seen to have developed from metaphors deeply embedded in our languages. This raises the question of relativity in mathematics. Do different languages embody different types of mathematics? This chapter examines some emerging evidence in the grammar and syntax of indigenous languages, i.e. languages structurally very different from the Indo-European linguistic tradition. The educational consequences of the possibility of different mathematical thinking is briefly discussed.

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.

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