Coherence is the idea that all big mathematical ideas are connected to each other. When topics are introduced so students see connections between what is being taught now and what they've learned before, they are more likely to do well.
Mathematics should be taught in a logical progression so if they learn to multiply a whole number by a fraction in fourth grade, they have a proper foundation for multiplying a fraction by a fraction in fifth. Coherence allows students to understand the topics to a much deeper degree while they are better able to grasp the more complex topics.
If students have not learned a previous skill, there are opportunities available to sneak it in so students get the chance to learn it. For instance, use the missing skill in a warm-up that connects to prior learning. Another possibility is to build prerequisite instruction into a grade level lesson, or actually teaching a lesson on the previous skill before teaching the actual grade level lesson.
Take time to monitor the progressions across grade levels so you know what skills they should have learned in the past, in what order. With this information, one can look at the skills you might have to include in your instruction so students will be successful.
Then begin the class with an activity that builds on a previous skill that relates to the topic for the current lesson. This helps students be successful and it highlights how what they know already, relates to what they are learning today. When teaching a lesson, allow students the opportunity to explore the current topic to see how it relates to what they've learned previously, by using rich tasks that have multiple entry points. In addition, check for student understanding of the current lesson before providing the opportunity to practice and experience differentiation via reteaching, reinforcement, or enrichment.
Next blog entry on Monday, I'll look at representation and structure. Let me know what you think, I'd love to hear. Have a great day.
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