In this TEDx video, Jo Boaler explains that with the right teaching and messages we can all be good at math.
What is Flexible Thinking?
Flexible use of strategies and representations is a cognitive variability, encouraging students to solve problems quickly but also with accuracy (Heinze et al., 2009). When students are given the opportunity to engage their flexible thinking, they are encouraged to use a variety of strategies to solve one question rather than being told that they need to learn one standard method for solving problems. The idea of supporting multiple ways of solving problems has become more prevalent in education in recent years. It has become a popular idea that the ability to use different strategies for solving questions and being able to switch between representations - including pictorial, verbal and written - is a key component for solving mathematical problems. (Heinze et al., 2009).
Strategy Flexibility is defined as using a variety of solution strategies (Verschaffel et al., 2007)
Students who struggle with flexible thinking may show the following behaviours at home or at school (Understood.org, n.d.).
Strategy Flexibility is defined as using a variety of solution strategies (Verschaffel et al., 2007)
Students who struggle with flexible thinking may show the following behaviours at home or at school (Understood.org, n.d.).
- not accepting other's ideas
- arguing the same point repeatedly
- being easily frustrated when small things go wrong
- not following new schedules
- becoming anxious when plans change
- struggling to take on new tasks
- difficulty switching from one task to another
- being upset when others don't follow the rules
Strategic Competence
Strategic Competence can be thought of as knowing how to use your language to communicate effectively. In math this is the ability to create, represent and solve math problems.
Lemaire and Siegler (1995) explain 4 dimensions of strategic competence:
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Strategic Competence is one of the key strands of mathematical proficiency - areas that are deemed necessary for anyone to learn math successfully. The five strands of mathematical proficiency are conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition.
How to use flexible thinking
.Verschaffel et al. (2007) suggests implementing an instructional approach that encourages the students the develop their own preferences for solving questions based on a variety of factors, including the task, subject and context. Doing math is not only about the end result and answer, there should be an emphasis on how the final result was achieved. Flexible thinking in math should focus on multiple ways to solve a problem
"Once multiple ideas are brainstormed, flexible thinking looks for connections between ideas and helps students go beyond the obvious to devise alternative situations or solutions (Sitorus & Masrayti, 2016)"
Jeannie Curtis (2016) explains that students need regular opportunities to build flexibility in problem solving, she suggests three ideas for building problem solving-flexibility:
"Once multiple ideas are brainstormed, flexible thinking looks for connections between ideas and helps students go beyond the obvious to devise alternative situations or solutions (Sitorus & Masrayti, 2016)"
Jeannie Curtis (2016) explains that students need regular opportunities to build flexibility in problem solving, she suggests three ideas for building problem solving-flexibility:
- Encourage students to use various solutions when solving their math problems - allow the class to share their strategy with others so that they can see other ways of solving problems
- Build a culture of sharing
- Show different strategies of solving problems (concrete, representational, abstract)
Courtney Dickinson (n.d.) explains five ways to spark flexible Thinking and Courage in Math Class... and Beyond:
- Create an atmosphere of growth
- Encourage flexible thinking - allow students to use multiple means to solve problems
- Make it relevant to the real world
- Have an individual learning plan for every child; ideally, math groups are ability based
- Recognize courage
References
Curtis,J. (July 6, 2016). How To Help Students Develop Flexibility In Math. Elementary math Consultant. http://www.elementarymathconsultant.com/help-students-develop-flexibility/
Dickinson, C. (n.d.). Five Ways to Spark Flexible Thinking and Courage in Math Class...and Beyond. Acera School. https://www.aceraschool.org/five-ways-spark-flexible-thinking-courage-math-class-beyond/
Heinze, A., Star, J.R. & Verschaffel, L. Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education 41, 535–540 (2009). https://doi.org/10.1007/s11858-009-0214-4
National Research Council (2001). Adding It Up, Helping Children Learn Mathematics. The National Academies of Sciences Engineering Medicine. https://www.nap.edu/read/9822/chapter/6#128
TEDx Talks. (May 22, 2016). How you can be good at math, and other surprising facts about learning | Jo Boaler | TEDxStanford [image]. Youtube. https://www.youtube.com/watch?v=3icoSeGqQtY&t=89s
The Understood Team. (n.d.). Trouble With Flexible Thinking: Why Some Kids Only See Things One Way. Understood. https://www.understood.org/en/learning-thinking-differences/child-learning-disabilities/executive-functioning-issues/flexible-thinking-what-you-need-to-know
Verschaffel, L., Torbeyns, J., De Smedt, B., Luwel, K., Van Dooren, W. (2007). Strategy flexibility in children with low achievement in mathematics. Educational & Child Psychology, 24(2), 16-27.
Images
Happyaprilboy. (unknown). Colorful slinky on Blue [image]. FreePik. https://www.freepik.com/premium-photo/colorful-slinky-blue_5270291.htm#page=1&query=flexible%20thinking&position=45
The Counselling Teacher (unknown). How to Teach Flexible Thinking for Student Success [image]. https://thecounselingteacher.com/2021/01/how-to-teach-flexible-thinking-for-student-success.html
Unknown. (n.d.). [image]. Pinterest. https://www.pinterest.com/pin/534098837041912924/
Curtis,J. (July 6, 2016). How To Help Students Develop Flexibility In Math. Elementary math Consultant. http://www.elementarymathconsultant.com/help-students-develop-flexibility/
Dickinson, C. (n.d.). Five Ways to Spark Flexible Thinking and Courage in Math Class...and Beyond. Acera School. https://www.aceraschool.org/five-ways-spark-flexible-thinking-courage-math-class-beyond/
Heinze, A., Star, J.R. & Verschaffel, L. Flexible and adaptive use of strategies and representations in mathematics education. ZDM Mathematics Education 41, 535–540 (2009). https://doi.org/10.1007/s11858-009-0214-4
National Research Council (2001). Adding It Up, Helping Children Learn Mathematics. The National Academies of Sciences Engineering Medicine. https://www.nap.edu/read/9822/chapter/6#128
TEDx Talks. (May 22, 2016). How you can be good at math, and other surprising facts about learning | Jo Boaler | TEDxStanford [image]. Youtube. https://www.youtube.com/watch?v=3icoSeGqQtY&t=89s
The Understood Team. (n.d.). Trouble With Flexible Thinking: Why Some Kids Only See Things One Way. Understood. https://www.understood.org/en/learning-thinking-differences/child-learning-disabilities/executive-functioning-issues/flexible-thinking-what-you-need-to-know
Verschaffel, L., Torbeyns, J., De Smedt, B., Luwel, K., Van Dooren, W. (2007). Strategy flexibility in children with low achievement in mathematics. Educational & Child Psychology, 24(2), 16-27.
Images
Happyaprilboy. (unknown). Colorful slinky on Blue [image]. FreePik. https://www.freepik.com/premium-photo/colorful-slinky-blue_5270291.htm#page=1&query=flexible%20thinking&position=45
The Counselling Teacher (unknown). How to Teach Flexible Thinking for Student Success [image]. https://thecounselingteacher.com/2021/01/how-to-teach-flexible-thinking-for-student-success.html
Unknown. (n.d.). [image]. Pinterest. https://www.pinterest.com/pin/534098837041912924/