What is critical and creative thinking, and why is it so important in mathematics and numeracy education?
Numeracy is often defined as the ability to apply mathematics in the context of day to day life. However, the term ‘critical numeracy’ implies much more. One of the most basic reasons for learning mathematics is to be able to apply mathematical skills and knowledge to solve both simple and complex problems, and, more than just allowing us to navigate our lives through a mathematical lens, being numerate allows us to make our world a better place.
The mathematics curriculum in Australia provides teachers with the perfect opportunity to teach mathematics through critical and creative thinking. In fact, it’s mandated. Consider the core processes of the curriculum. The Australian Curriculum (ACARA, 2017), requires teachers to address four proficiencies: Problem Solving, Reasoning, Fluency, and Understanding. Problem solving and reasoning require critical and creative thinking (). This requirement is emphasised more heavily in New South wales, through the graphical representation of the mathematics syllabus content , which strategically places Working Mathematically (the proficiencies in NSW) and problem solving, at its core. Alongside the mathematics curriculum, we also have the General Capabilities, one of which is Critical and Creative Thinking – there’s no excuse!
Critical and creative thinking need to be embedded in every mathematics lesson. Why? When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.
How and when do we embed critical and creative thinking?
There are many tools and many methods of promoting thinking. Using a range of problem solving activities is a good place to start, but you might want to also use some shorter activities and some extended activities. Open-ended tasks are easy to implement, allow all learners the opportunity to achieve success, and allow for critical thinking and creativity. Tools such as Bloom’s Taxonomy and Thinkers Keys are also very worthwhile tasks. For good mathematical problems go to the nrich website. For more extended mathematical investigations and a wonderful array of rich tasks, my favourite resource is Maths300 (this is subscription based, but well worth the money). All of the above activities can be used in class and/or for homework, as lesson starters or within the body of a lesson.
Will critical and creative thinking take time away from teaching basic concepts?
No, we need to teach mathematics in a way that has meaning and relevance, rather than through isolated topics. Therefore, teaching through problem-solving rather than for problem-solving. A classroom that promotes and critical and creative thinking provides opportunities for:
- higher-level thinking within authentic and meaningful contexts;
- complex problem solving;
- open-ended responses; and
- substantive dialogue and interaction.
Who should be engaging in critical and creative thinking?
Is it just for students? No! There are lots of reasons that teachers should be engaged with critical and creative thinking. First, it’s important that we model this type of thinking for our students. Often students see mathematics as black or white, right or wrong. They need to learn to question, to be critical, and to be creative. They need to feel they have permission to engage in exploration and investigation. They need to move from consumers to producers of mathematics.
Secondly, teachers need to think critically and creatively about their practice as teachers of mathematics. We need to be reflective practitioners who constantly evaluate our work, questioning curriculum and practice, including assessment, student grouping, the use of technology, and our beliefs of how children best learn mathematics.
Critical and creative thinking is something we cannot ignore if we want our students to be prepared for a workforce and world that is constantly changing. Not only does it equip then for the future, it promotes higher levels of student engagement, and makes mathematics more relevant and meaningful.
How will you and your students engage in critical and creative thinking?
The sites listed below provide lesson plans and resources for promoting problem solving, creativity, and critical thinking. Click on a topic from the site index below to find what you need or go to my Gifted and Talented page.
Site Index: problem solving lesson plans,problem solving resources,creativity lesson plans,creativity resources,critical thinking lesson plans,critical thinking resources
Problem Solving Lesson Plans
Problem Solving Lesson Plan Index
Fourteen lessons for a variety of subjects and grade levels.
Teaching Critical Thinking and Problem Solving
Lesson ideas from Pinterest. Membership is required to view them all, but it's free to join.
No Quick Fix? Developing Problem-Solving Skills
A lesson plan from the NY Times.
A lesson plan in which students learn a 6-step process for solving problems.
Discover the Roots of a Polynomial Function
A high school lesson in shi9ch students are introduced to the four-step problem-solving plan.
Problem Solving Using Tables
From BrainPOP. See also Word Problems.
A high school lesson plan in which students apply technological problem solving to everyday problems.
Practical Problem-Solving Lesson Plan
This lesson from a nutrition unit requires students to use problem-solving skills to deal with "perennial problems."
Classic Middle-Grades Problems for the Classroom
Students work in groups to solve two classic problems (Mangoes Problem and Sailors and Coconuts) that can be represented and solved in several different ways
Problem Solving: Math, Episode 2
An elementary lesson plan requiring students to explore different ways to find solutions to problems or situations. See also Problem Solving: Math Episode 1.
Working with Environmental Issues
A learning module from the Peace Corps' World Wise Schools. in which students use problem-solving skills to address a real-world problem. It is intended for elementary and middle grade students.
Goldilocks and the Three Bears
A creative problem-solving lesson plan for grades K-3.
Problem Solving Resources
Puzzles and Mental Activities. See their Teacher's Resources.
Improve Problem-Solving Skills by Teaching Chess
Adaptable to many grades/
Problem Solving: Definition, Terminology, and Patterns
A concise, informative essay. See also What is Problem Solving.
Big 6 Model
Information and online resources for using this strategy.
The Problem Site
Educational Games - Free math problems, puzzles, word games, brainteasers, and mystery hunts.
A lesson plan for grades 2-3 requiring flexible and creative thinking.
Pourquoi Stories: Creating Tales to Tell Why
A lesson plan for grades 3-5 dealing with stories or folk tales that explain how or why something exists (usually in nature).
Creative Writing through Wordless Picture Books
A lesson plan for grades 6-8.
Create a New Ammendment
A middle grade or high school lesson plan from Education World in which students demonstrate critical thinking and creative thinking skills in developing a new amendment to the Constitution.
Writing Up a Spanish Storm: Using Creative Thinking for Creative Writing
Ideas for an advanced high school Spanish unit. The site also contains quite a bit of background information on creative thinking.
Creative Science Activities
Many lesson plans. Not all involve creativity.
Clasroom art projects that allow students to express their creativity.
Creative Ideas for Science Projects
The Adventures of a Cardboard Box
A lesson plan involving divergent thinking based on a film by the above title.
Puzzle Solving 101: Lesson 9: Lateral Thinking
A lesson plan that helps students "think out of the box."
Creativity is Great
A lesson plan from Great Britain.
Creative Drama Lesson Plans
Many lesson plans sorted by age level.
An art lesson plan for grades 6-7.
Crayola Creativity Central
A searchable directory of lesson plans using Crayola products.
Lesson Plans for a Creative Writing Course
Lesson plans for a thirteen-week course!
Ideas for exploring fluency, flexibility, elaboration, redefinition, and originality.
The Creative Teaching Web Site
An excellent site with articles, ideas, and information for developing more creative teachers.
How to Promote Creative Thinking
22 Simple Ideas for Promoting Creativity in the Elementary Classroom
From Edutopia. See also 40 Ways to Add Creativity to Your Lesson Plans.
Torrance Framework for Creative Thinking
An explanation of this framework for creative thinking processes.
Creativity and Innovation Rubric
For grades 6-12. See also Creativity and Innovation Rubric (Grades 3-5).
What is Creativity
Many definitions fro California State University, Northridge.
Creativity for Kids
Arts and crafts products.
Links to "handouts" with concise information on definitions, characteristics, traits, etc.
Critical Thinking Lesson Plans
Remodeled Lesson Plans from the Center for Critical Thinking
See their selection of "remodeled" lesson plans organized by grade level toward the bottom of the left-hand index. For information on the Center's approach to critical thinking, see Our Concept of Critical Thinking.
Critical Thinking Lesson Plans
More than 20 lesson plans from the Leonore Annenberg Institute for Civics.
Critical Thinking Lesson Plans
Many lesson plans for a variety of subjects from Learn NC.
Critical Thinking Lesson Plans
Many lesson plans for a variety of grade levels from Kimberly Kludt.
The latest activities from Teachable Moment, many of which foster critical thinking on current issues.
From the NY Times Learning Network.
Rock or Feather? A Critical-Thinking Activity
From Education World.
Book Sorting: Using Observation and Comprehension to Categorize Books
A primary-grade lesson plan that addresses critical-thinking skills, observation and categorization processes, as well as reading comprehension and writing skills, while at the same time providing teachers with a vast array of diagnostics through observation of student interaction and conversation.
An Exploration of Simple Machines
An elementary lesson plan designed to promote the use of critical thinking and problem solving skills to help students understand how simple machines work.
Several lesson plans, ideas, and online mysteries to teach critical thinking and reading comprehension.
Critical Thinking with Fables New and Old
A lesson plan from Education World adaptable for grades 3-12.
Detective Fiction: Focus on Critical Thinking
A unit for grade 6.
Draft Letters: Improving Student Writing through Critical Thinking
A high school lesson plan from Read-Write-Think in which students write reflective letters to the teacher, identifying theirown thoughts on the piece that the teacher is about to read. See also Developing Students' Critical Thinking Skills Through Whole-Class Dialogue,Analyzing Character Development in Three Short Stories about Women and Lights, Camera, Action . . . Music: Critiquing Films Using Sight and Soundfor other high school critical thinking lesson plans from Read-Write-Think.
Critical Thinking Resources
Critical Thinking Value Rubric
See also Higher-Order Thinking Rubric.
Resources and Downloads for Teaching Critical Thinking
Tools, rubrics and lesson plans from Edutopia.
The Critical Thinking Community
Much information and many resources.
Critical Thinking: A Streamlined Conception
Concise article written by Robert H. Ennis.
Glossary of Critical Thinking Terms
"An Educator's Guide to Critical Thinking Terms and Concepts."
What is critical thinking?