Why Is Teaching With Problem Solving Important to Student Le

Why Is Teaching With Problem Solving Important to Student Learning?

Additional Resources:

Henningsen, Marjorie, and Mary Stein. "Mathematical Tasks and Student Cognition: Classroom-Based Factors That Support and Inhibit High-Level Mathematical Thinking and Reasoning." Journal for Research in Mathematics Education 28.5 (1997): 524. National Council of Teachers of Mathematics, 26 Sept. 2014. Web. 02 Oct. 2015.

http://jwilson.coe.uga.edu/EMAT7050/articles/HenningsenStein.pdf

Small, Marian. "Chapter 3: Focus On Problem SOlving." Making Math Meaningful to Canadian Students, K-8. Toronto: Nelson Education, 2009. N. pag. Print.

Chang, Kuo-En, Lin-Jung Wu, Sheng-En Weng, and Yao-Ting Sung. "Embedding Game-based Problem-solving Phase into Problem-posing System for Mathematics Learning." Computers & Education 58.2 (2012): 775-86. Elsevier. Web. 4 Oct. 2016.

Steps of Problem Solving:

• understanding the problem
• making a plan
• carrying out the plan
• reflecting on the solution

Discuss

Should problem solving be taught as a separate topic or should it be integrated throughout the curriculum?

Share

What kinds of problem-solving activities should students be given?

In teaching through problem solving, learning takes place during the process of attempting to solve problems in which relevant mathematics concepts and skills are embedded

(Lester & Charles, 2003; Schoen & Charles, 2003).

• the problem has important, useful mathematics embedded in it

• the problem requires higher level thinking and problem solving

• the problem contributes to the conceptual development of students

• the problem creates opportunity for the teacher to assess what his/her students are learning and where they are experiencing difficulty

"The term "problem solving" refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development"

(p. 1)

24 + 37 = ?

Group 1

_____ +____ = 61

Group 2

The answer is 61. What's the question?

Group 3

Shalini believes the answer to 24 + 37 is 51, but Nayab is almost positive it must be 511.

Who is correct? Explain your thinking in writing.

Discuss:

How does your question fit the criteria for a good problem as outlined by the article?

How can teachers orchestrate pedagogically sound, active problem solving in the classroom?

"Picking the problem or task is only one part of teaching with problem solving [...] Students' actual learning also depends on the classroom discourse that takes place during problem solving." p. 3

Cai, Janifa, and Frank Lester. "Why Is Teaching With Problem Solving Important to Student Learning?" Problem Solving. Ed. Judith R. Quander. National Council of Teachers of Mathematics, 8 Apr. 2010. Web. 03 Oct. 2016.

Images from:

Cai, Janifa, and Frank Lester. "Why Is Teaching With Problem Solving Important to Student Learning?" Problem Solving. Ed. Judith R. Quander. National Council of Teachers of Mathematics, 8 Apr. 2010. Web. 03 Oct. 2016.

• T2 was more consistent in probing the students
• T2 and students explain justify their thinking
• T2 and students challenge the explanations of peers and teachers
• Students were engaged in the clarification of their own thinking

Other factors:

• Wait time
• Intervening too soon thus simplifying the question for the students

True and False task