2017 Focus Issue: Learning mathematics through reasoning and problem solving

2017 ◽  
Vol 24 (2) ◽  
pp. 71-72
Keyword(s):  
Problem Solving ◽  
Success For All ◽  
Solution Strategies ◽  
Learning Mathematics ◽  
Entry Points ◽  
Mathematical Success

Welcome to the 2017 Teaching Children Mathematics (TCM) Focus Issue. According to Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014, p. 23), for students to learn mathematics with understanding, they must have opportunities to engage on a regular basis with tasks that focus on reasoning and problem solving, have multiple entry points, and involve varied solution strategies. To solve such tasks, students must be able to understand and apply different tools and representations and move flexibly among them. Therefore, it is important for teachers to select and orchestrate discussions around highlevel tasks that provide opportunities for students to use different representations and apply their reasoning and problemsolving skills (5 Practices for Orchestrating Productive Mathematics Discussions, Margaret Schwan Smith and Mary Kay Stein. Reston, VA: NCTM, 2011).

Angle detectives

2017 ◽  
Vol 24 (3) ◽  
pp. 154-157
Author(s):  
Lisa Sherman
Keyword(s):  
Problem Solving ◽  
Effective Teaching ◽  
Teaching And Learning ◽  
Mathematical Reasoning ◽  
Success For All ◽  
Solution Strategies ◽  
Entry Points ◽  
Teaching Of Mathematics ◽  
Mathematical Success ◽  
Effective Teaching And Learning

NCTM's Principles to Actions: Ensuring Mathematical Success for All outlines eight mathematics teaching practices for effective teaching and learning of mathematics (NCTM 2014, p. 10). The second practice, Implement tasks that promote reasoning and problem solving, involves effective teaching of mathematics that engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Uncommon Partitions: Partitioning as a Problem-Solving Activity

2018 ◽  
Vol 24 (3) ◽  
pp. 164-171 ◽  
Author(s):  
Andrew Izsák ◽  
Sybilla Beckmann ◽  
Torrey Kulow
Keyword(s):  
Problem Solving ◽  
Teaching Practices ◽  
Common Factors ◽  
Success For All ◽  
The Third ◽  
Number Lines ◽  
Double Number ◽  
Mathematical Success

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series.

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).

Making Math Social

2019 ◽  
Vol 24 (4) ◽  
pp. 196
Author(s):  
Aaron Rumack ◽  
Rebecca Robichaux-Davis
Keyword(s):  
Mathematics Teaching ◽  
Success For All ◽  
Sense Making ◽  
Individual Study ◽  
Culture Of Learning ◽  
Foundational Principle ◽  
Learning Mathematics ◽  
Mathematical Success

Teachers, students, and parents might wonder: Why should we make mathematics a social pursuit? Although individual study and reflection are important parts of any discipline, providing a culture of learning mathematics socially enhances sense making for students. According to NCTM's Principles to Actions: Ensuring Mathematical Success for All (2014), learning through discourse, activity, and interaction related to meaningful problems is a foundational principle for effective mathematics teaching.

Two Instructional Moves to Promote Student Competence

2018 ◽  
Vol 24 (4) ◽  
pp. 244-249
Author(s):  
Jen Munson
Keyword(s):  
Problem Solving ◽  
State Standard ◽  
Fourth Graders ◽  
The State ◽  
Success For All ◽  
Reasoning Problem ◽  
Mathematical Success ◽  
Unit Conversion

Mrs. Hobbs's fourth graders are struggling. And it is working. This year, instead of teaching the state standard on unit conversion by showing students a procedure to follow, Hobbs asked her students to work in groups to develop a method. She is excited to promote more reasoning, problem solving, and use of varied solution pathways, in line with the NCTM's Principles to Actions: Ensuring Mathematical Success for All (2014). This is worthy work. But in some moments, for some students, the struggle does not feel productive. Several students are hesitant and lack confidence. A few give up easily. Hobbs does not want to go back to telling students a procedure, but she does not want to leave them to flounder.

Prove It to Me!

2019 ◽  
Vol 24 (7) ◽  
pp. 422-428
Author(s):  
Jo Boaler
Keyword(s):  
Problem Solving ◽  
Mathematics Teaching ◽  
Teaching Practices ◽  
Success For All ◽  
Mathematical Success ◽  
Mathematics Teaching Practices

Engage your learners through tasks proven to significantly promote reasoning and problem solving, which touch on many of the Mathematics Teaching Practices in Principles to Actions: Ensuring Mathematical Success for All. These tasks are discussed in this article, another installment in the series.

Hundred Chart Challenge

2015 ◽  
Vol 22 (2) ◽  
pp. 65-70
Author(s):  
J. Matt Switzer
Keyword(s):  
Problem Solving ◽  
Effective Teaching ◽  
Teaching Practices ◽  
Teaching And Learning ◽  
Success For All ◽  
Mathematical Representations ◽  
Mathematical Success ◽  
Effective Teaching And Learning

NCTM's Principles to Actions: Ensuring Mathematical Success for All (2014) outlines eight teaching practices for effective teaching and learning of mathematics. One of them, Use and connect mathematical representations, involves engaging students in “making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving” (p. 10).

Selecting and Sequencing Students' Solution Strategies

2016 ◽  
Vol 23 (4) ◽  
pp. 226-234 ◽  
Author(s):  
Erin M. Meikle
Keyword(s):  
Problem Solving ◽  
Solution Strategies ◽  
Class Discussions ◽  
Challenging Tasks ◽  
Whole Class ◽  
Fine Tune

For orchestrating whole-class discussions, note these suggestions to fine tune problem-solving techniques into cognitively challenging tasks.

Sign in / Sign up

Export Citation Format

Share Document