This post focuses on the top research-based effective strategies to support all learners in mathematics – no matter what the grade level – with all text and effect size data coming from John Hattie’s Visible Learning and Visible Learning for Teachers books.

**Activating Prior Knowledge & Metacognition**

(Through Student Think-Alouds or Number Talks)

“Students’ prior knowledge, or what students bring to a learning activity/experience, accounts for an effect size of 1.04 (very large). Studies showed that when faced with multistep problems, students frequently attempted to solve the problems by randomly combining numbers instead of implementing a solution strategy step by step. The process of encouraging students to verbalize their thinking—by talking, writing, or drawing the steps they used in solving a problem— was consistently effective. In part, this procedure may be effective because the impulsive approach to solving problems taken by many students with mathematics difficulties was addressed. Results of these students were quite impressive, with an average effect size of 0.98, which is very large.”

Using a graphic organizer such as a KWL/KNL chart can support activating prior knowledge.

The “think-aloud” process is usually introduced in four steps, gradually transferring responsibility to students:

1. The teacher reads a problem and stops as needed to explain her/his thoughts. Students listen. They all solve the problem together.

2. The teacher reads the problem and stops often. Students express their thoughts at each point (and often write them). The whole class, led by the teacher, solves the problem together.

3. The teacher reads the problem, allowing students to signal stopping points as thoughts occur to them. Students solve the problem individually, and then discuss their interpretations of it and solution strategies.

4. Students do this together, in pairs. They work together to solve the problem.

Other strategies to support activating prior knowledge and metacognition (thinking about your thinking) include:

1. **Building vocabulary** (effect size of 0.82 – large); and

2. **Regular, formative feedback** from teacher to student (effect size of 1.13 – very large).

See April 21st Math Monday for ideas to support vocabulary building.

See February 17th Math Monday for math journal ideas, one of many ways to support regular, formative feedback.

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