Vision Statement (Part 1 of 7?) – Authentic Problems and Inquiry-Based Instruction

28 Sep

I am hoping to use this blog to talk about the teacher that I aspire to be and not the teacher I am now. I have gotten so much from the blogs of other Math teachers and I want to be a contributing member of that community.

This is going to be part I of my Vision Statement. Teach for America is pushing its corps members to articulate their visions for their classrooms. I feel like I have many ideas and goals and not enough of this actually happening in my classroom right now. Since this is my second year it feels like I should have my shit together, but transitioning to a new school, a new age group, and new content has been hard. This Vision Statement is in no particular order. I am just going to post throughout the week when I have time.

Why I want to use authentic problems and inquiry-based instruction in my Math class:

(Many thanks to Dan Meyer, Shawn Cornally, and the many other bloggers in my feed reader for these ideas.)

Too often, problems in Math class are given without context or with “pseudo-context” that tries to pass itself off as a real-world application.

Audrey and Sara are making jewelry. Audrey buys 2 bags of beads and 1 package of clasps for a total of $13. Sara buys 5 bags of beads and 2 packages of clasps for a total of $27.50.

Do you see where this is going? Audrey and Sara know how much money they spent in total and how many of each item they bought, but somehow they don’t know how much each individual item cost and they need us to graph some equations to figure it out for them. Funny, they must have lost their receipt. This problem sends the message that math only applies to contrived situations and has nothing to do with real life. Not only is this problem a poor example of the real world applicability of systems of equations, but it is also extremely boring. Who cares how much beads and clasps cost? I don’t and I can hardly expect my students to, especially students who are struggling with Math. Maybe some of my students do know how much beads cost. Maybe they make jewelry just like Audrey and Sara. If they use that background knowledge to answer this problem, they will almost definitely get it wrong. We teach our students that their background knowledge isn’t worth much in Math class. Math is this separate world that they just visit for an hour at a time in class.

I want to use problems and examples in class that either place Math in a legitimate real world context or, at the very least, provide contrived problems that students actually want to know the answer to. There are great examples of both types of problems all over the web. Once they are curious about the problem, they are hooked. I know that I am not going to be able to do this on a large scale everyday, but I want to integrate elements of this into my class on a daily basis.

I shouldn’t be giving students formulas, we should be discovering them together. I want them to see for themselves that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. This hasn’t been the kind of teacher that I am now, but it is the kind of teacher that I desperately want and need to be for my students. They deserve to be challenged like that everyday. I don’t want to sacrifice understanding of how to manipulate numbers and equations, but when conceptual understanding is not there, that knowledge is tenuous and fleeting anyway.

Some teachers that I have talked to worry that doing an inquiry-based activity in class isn’t the best use of time and the objective for the day could be accomplished more efficiently using traditional methods of teaching Math (direct instruction). I think based solely on achievement data from students in my charter network, a different approach is needed to boost student achievement.

I will leave you with some concerns I have about my ability to pull this off in my classroom…

  • I won’t do a good enough job connecting authentic problem or inquiry activity back to the Math involved.
  • My classroom management will limit the types or activities I can do.
  • Conceptual understanding won’t translate back to achievement on assessments.
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