{"id":1892,"date":"2023-09-05T10:06:34","date_gmt":"2023-09-05T17:06:34","guid":{"rendered":"https:\/\/theothermath.com\/?p=1892"},"modified":"2024-05-03T07:26:12","modified_gmt":"2024-05-03T14:26:12","slug":"a-formula-for-inquiry-and-direct-instruction","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2023\/09\/05\/a-formula-for-inquiry-and-direct-instruction\/","title":{"rendered":"A formula for inquiry AND direct instruction"},"content":{"rendered":"

In earlier blog posts (this one<\/a><\/span>\u00a0and this one<\/a><\/span>) I’ve talked about two \u2013 seemingly opposing \u2013 views of math instruction: direct instruction and student-centered instruction. <\/span><\/p>\n

There is plenty of evidence<\/a><\/span>\u00a0that students benefit tremendously when given an opportunity to invent\/investigate their own understanding prior to formal instruction by the teacher.<\/span><\/p>\n

There is also plenty of evidence<\/a><\/span>\u00a0that direct instruction supports students to efficiently learn discrete skills and standard algorithms.<\/span><\/p>\n

When thinking about teaching mathematics, you don’t have to pick a side. Rather, think of each instructional strategy as a tool. For some jobs, one tool is better than the other. I recently built a chicken coop\u2026I used a variety of tools depending on the need at the moment. This is exactly what we will do when teaching mathematics.<\/span><\/p>\n

Here are the 8 STEPS of my mental model for a lesson that incorporates moments of both inquiry AND direct instruction in a typical 45-minute math lesson.<\/span><\/p>\n

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STEP 0: Anticipate<\/span><\/strong><\/p>\n

I start with a blank whiteboard and imagine it being cut into eighths. I anticipate what will be written in each of the six regions so as to avoid the need for erasing anything.<\/span><\/p>\n

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STEP 1: Introduce<\/span><\/strong><\/p>\n

I start the lesson by presenting a word problem in the upper left corner of the whiteboard. I often separate the problem stem from the question stem to allow students a moment to think about the “math story” without having to worry about trying to solve anything yet.<\/span><\/p>\n

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Sometimes I introduce the problem to students using the Three-Read Protocol. Other times, I just give students a moment to identify words they can’t read or don’t know before revealing the question stem. Only after unfamiliar words or contexts are discussed do I reveal the question stem.<\/span><\/p>\n

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STEP 2: Explore<\/span><\/strong><\/p>\n

I tell students to represent the problem using any method of their choosing: concrete materials, pictorial representations, or numbers and symbols. I also remind students they are not required to use “the official math” we have been learning in the math unit and that they may use any method to solve the problem.<\/span><\/p>\n

Students grapple with this problem and invent their own understanding of the problem. Students generally work alone and\/or with a partner. During this time, students invariably provide me a tremendous amount of formative assessment data of what they know and don’t know. I will use this information later during direct instruction.<\/span><\/p>\n

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STEP 3: Nudge<\/span><\/strong><\/p>\n

As students are working, I can nudge the entire class in a particular direction by finding a student who is doing something I want ALL students to do. (This is likely something directly from the teacher notes of today’s lesson.). I hold up that student’s work for the class to see and tell the rest of the class to “give it a try”. <\/span><\/p>\n

It might sound something like\u2026 <\/span><\/p>\n