Promoting Mathematical Connections Using Three-Dimensional Manipulatives

2017 ◽  
Vol 22 (8) ◽  
pp. 488-492
Author(s):  
Farshid Safi ◽  
Siddhi Desai
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Three Dimensional ◽  
Mathematical Understanding ◽  
Success For All ◽  
Sense Making ◽  
Problem Solving Skills ◽  
Mathematical Ideas ◽  
Mathematical Connections ◽  
Mathematical Success

Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of representations should continually develop in complexity and scope. “[Students] will need to be able to convert flexibly among these representations. Much of the power of mathematics comes from being able to view and operate on objects from different perspectives” (NCTM 2000, p. 361). In fact, when students represent, discuss, and make connections among different mathematical ideas by using different methods, they engage in deeper sense making and improve their problem-solving skills while refining their mathematical understanding (Fuson, Kalchman, and Bransford 2005; Lesh, Post, and Behr 1987).

Using Tools to Make Sense of Right Triangles

2018 ◽  
Vol 23 (4) ◽  
pp. 226-230
Author(s):  
Terri L. Kurz ◽  
Mi Yeon Lee
Keyword(s):  
Conceptual Understanding ◽  
Three Dimensional ◽  
Mathematical Understanding ◽  
Sense Making ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Mathematical Ideas

Sometimes, teaching mathematics with a focus on conceptual understanding can be challenging. With the advent of standards and principles (CCSSI 2010; NCTM 2014) an emphasis has been placed on using tools for deeper mathematical understanding and learning with understanding. Specifically, there has been a movement to include opportunities for learners to engage in sense-making activities when exploring mathematical concepts (Schoenfeld 1992). Tools can be used to support sense making and the development of mathematical ideas, and numerous tools can support learning in geometry (e.g., geoboards, pattern blocks, three-dimensional shapes, and linking cubes). We focus on AngLegs®, which are linking rods that are becoming more common in the classroom.

Improving Mathematics Discourse through Action Research

2019 ◽  
Vol 112 (4) ◽  
pp. 302-306 ◽  
Author(s):  
Christopher W. Parrish ◽  
Ruby L. Ellis ◽  
W. Gary Martin
Keyword(s):  
Mathematics Teaching ◽  
Mathematics Classroom ◽  
Central Element ◽  
Success For All ◽  
Mathematical Ideas ◽  
Mathematical Connections ◽  
Mathematics Discourse ◽  
Mathematics Educators ◽  
Mathematical Success ◽  
Support Students

NCTM identified eight Mathematics Teaching Practices within its reform-oriented text, Principles to Actions: Ensuring Mathematical Success for All (2014). These practices include research-informed, high-leverage processes that support the in-depth learning of mathematics by all students. Discourse within the mathematics classroom is a central element in these practices. The goal of implementing the practice facilitate meaningful discourse is to give students the opportunity to “share ideas and clarify understandings, construct convincing arguments regarding why and how things work, develop a language for expressing mathematical ideas, and learn to see things from other perspectives” (NCTM 2014, p. 29). To further support implementing meaningful discourse, mathematics educators must become adept at posing questions that require student explanation and reflection, hence, pose purposeful questions, which is another of the eight practices. Posing purposeful questions allows “teachers to discern what students know and adapt lessons to meet varied levels of understanding, help students make important mathematical connections, and support students in posing their own questions” (NCTM 2014, pp. 35-36).

scholarly journals Improving Problem-Solving Skills with the Help of Plane-Space Analogies

2013 ◽  
Vol 3 (4) ◽  
pp. 79-98
Author(s):  
László Budai
Keyword(s):  
High School Students ◽  
Problem Solving ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Spatial Thinking ◽  
Great Promise ◽  
School Students ◽  
Problem Solving Skills ◽  
Plane Space

We live our lives in three-dimensional space and encounter geometrical problems (equipment instructions, maps, etc.) every day. Yet there are not sufficient opportunities for high school students to learn geometry. New teaching methods can help remedy this. Specifically our experience indicates that there is great promise for use of geometry programs, GeoGebra and DGS, combined with plane space analogies for the development of spatial thinking and problem-solving skills in the three dimensions of solid geometry.

Implementing the Standards: Developing Communication Skills in Mathematics for Students with Limited English Proficiency

1991 ◽  
Vol 84 (3) ◽  
pp. 186-189
Author(s):  
Gilbert J. Cuevas
Keyword(s):  
Problem Solving ◽  
Communication Skills ◽  
Limited English Proficiency ◽  
English Proficiency ◽  
Mathematical Understanding ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Listening And Speaking

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) emphasizes the need to address communication skills. These skills, including reading, writing, listening, and speaking, enhance mathematical understanding and problem-solving ability. Moreover, to communicate effectively, one must be able to interpret and analyze mathematical ideas. The curriculum and evaluation standards recommend that opportunities be afforded students to “use language to communicate their mathematical ideas” (NCTM 1989, 78). Although these recommendations are valuable, teachers may find them difficult to implement with students who are not proficient in English.

An Experiment in Using Portfolios in the Middle School Classroom

2008 ◽  
Vol 13 (7) ◽  
pp. 404-409
Author(s):  
Vicki L. Maxwell ◽  
Marshall B. Lassak
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Assessment Tool ◽  
Real Life ◽  
Eighth Grade ◽  
Mathematical Connections ◽  
School Classroom ◽  
Subject Areas ◽  
Over Time

Standard classroom tests tend to showcase what students know at that point in time and do not usually reflect real-life mathematics. They are not always accurate indicators of what students understand and how they understand it. I wanted to use an assessment tool that would allow students a better opportunity to exhibit mathematical growth in understanding and attitude over time. This tool should also give students the chance to show that they could communicate in a mathematical context, exhibit problem-solving techniques, and make mathematical connections to other subject areas. From these ideas and my review of the research on assessment, I decided to use portfolios as an assessment tool in one of my eighth-grade prealgebra classes.

A Popcorn Project for All Students

1997 ◽  
Vol 90 (3) ◽  
pp. 194-200
Author(s):  
Lydotta M. Taylor ◽  
Joann L. King
Keyword(s):  
Problem Solving ◽  
Cooperative Learning ◽  
Real World ◽  
Data Gathering ◽  
School Mathematics ◽  
Combine Data ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematical Connections ◽  
Reasoning Problem

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) encourages teachers to include activities that help students “construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations” (p. 167) and “express mathematical ideas orally and in writing” (p. 140). The following activities combine data gathering and analysis with cooperative learning, mathematical connections, reasoning, problem solving, and communication.

Launching mathematical success

2019 ◽  
Vol 25 (4) ◽  
pp. 249-252
Author(s):  
Dittika Gupta ◽  
Lara K. Dick
Keyword(s):  
Real World ◽  
Success For All ◽  
Design Task ◽  
Mathematical Ideas ◽  
Mathematical Success ◽  
Paper Airplane

Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014) calls for integrating into the classroom real-world activities that connect mathematical ideas to other subjects and contexts. Motivated by the desire to make these connections, we devised a paper airplane design task to engage students in various STEM concepts.

scholarly journals IMPROVING STUDENTS' MATHEMATICAL UNDERSTANDING AND PROBLEM SOLVING SKILLS AND THEIR LEARNING INTERESTS IN MTS THROUGH CONTEXTUAL TEACHING AND LEARNING LEARNING (CTL)

2018 ◽  
Vol 1 (2) ◽  
pp. 130
Author(s):  
Rina Yustinawati ◽  
Jozua Sabandar
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Mathematical Problem ◽  
Mathematical Understanding ◽  
Problem Solving Skills ◽  
Parametric Statistics ◽  
Contextual Teaching ◽  
Learning Mathematic ◽  
Quasi Experiment Study

This article is derived from the results of research entitled "Improving Students' Mathematical Understanding and Problem Solving Skills and Their Learning Interests in MTs through Contextual Teaching and Learning Learning (CTL)" which aims to see not only the influence of Contextual Teaching and Learning (CTL) in increasing students' mathematical understanding and problems solving skills, but also to see their interests in learning mathematic as well. This research is a quasi-experiment study. The population in this study is all students of MTs Cianjur district. The sample in this research are 36 students of class VII A as experiment class and 36 students of class VII B as control class. The data in this study was analyzed using parametric and non parametric statistics. The results of this study indicate that students' mathematical understanding and problem solving skills, as well as their learning interests when using the approach of Contextual Teaching and Learning Learning (CTL), is better than the students using conventional learning. There is an association between the quality of students' mathematical understanding skill and their mathematical problem solving skill with high enough criteria. There is an association between the quality of students' understanding and their interest in learning mathematic with high criteria. There is an association between students' problem-solving skill and learning interests with fairly high criteria.

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