Teachers demonstrated procedures, students silently practiced with worksheets and workbooks, and answers were quickly assessed as right or wrong. In contrast, today's vision of mathematical proficiency blends computational fluency, conceptual understanding, and application, moving math beyond memorization and computations into reasoning and problem solving. As we work to adjust our teaching practice to align with our goal of developing mathematical thinkers, we recognize the importance of talk and writing. Through math talk, our students are able to process their ideas, hear others' thinking, and ultimately revise and refine their own understanding.
Can you group these Can you see a pattern? How can this pattern help you find an answer? What do think comes next? Is there a way to record what you've found that might help us see more patterns? What would happen if? Assessment questions Questions such as these ask children to explain what they are doing or how they arrived at a solution.
They allow the teacher to see how the children are thinking, what they understand and what level they are operating at. Obviously they are best asked after the children have had time to make progress with the problem, to record some findings and perhaps achieved at least one solution.
How did you find that out? Why do you think that? What made you decide to do it that way? Final discussion questions These questions draw together the efforts of the class and prompt sharing and comparison of strategies and solutions.
This is a vital phase in the mathematical thinking processes. It provides further opportunity for reflection and realisation of mathematical ideas and relationships. It encourages children to evaluate their work.
Who has a different solution? Are everybody's results the same? Have we found all the possibilities? How do we know? Have you thought of another way this could be done? Do you think we have found the best solution? Levels of Mathematical Thinking Another way to categorise questions is according to the level of thinking they are likely to stimulate, using a hierarchy such as Bloom's taxonomy Bloom, Bloom classified thinking into six levels: Memory the least rigorousComprehension, Application, Analysis, Synthesis and Evaluation requiring the highest level of thinking.
Sanders separated the Comprehension level into two categories, Translation and Interpretation, to create a seven level taxonomy which is quite useful in mathematics.
As you will see as you read through the summary below, this hierarchy is compatible with the four categories of questions already discussed. The student recalls or memorises information 2. The student changes information into a different symbolic form or language 3.
The student discovers relationships among facts, generalisations, definitions, values and skills 4. The student solves a life-like problem that requires identification of the issue and selection and use of appropriate generalisations and skills 5.about a topic by looking for evidence of their thinking.
• The focus is not on grammar, punctuation, and/or mechanics but on the What is the question? Talking and Writing During Math? “Math Talk” to Math . whether they are engaging in effective critical thinking when speaking, writing, or studying. Each of the critical thinking skills is defined in terms of a corresponding mental action and is followed by a trio of sample questions designed to promote that particular form of thinking and.
Carol Dorf is the poetry editor at Talking Writing. In addition to being a widely published poet, she is a high school math teacher. In addition to being a widely published poet, she is a high school math teacher.
Sometimes people use the phrase “going meta” when talking about metacognition, referring to the process of difficulty directing their thinking about how to solve a mathematical word problem.
Young children build their their thinking before writing an essay. Ms. Good questioning techniques have long being regarded as a fundamental tool of effective teachers. This article for teachers looks at different categories of questions that can promote mathematical thinking.
These questions can be used be the teacher to guide the children through investigations while stimulating their mathematical thinking and gathering information about their knowledge and strategies.