Building Thinking Classrooms: Planning for Winter 2024

 I am hosting a professional learning community for my state-level organization (SBCTC) and am sharing some thoughts on how I am planning my next term, using the Building Thinking Classrooms (BTC) framework. Below is the post I made on December 20th 2023 to our internal discussion forum.

If you have thoughts, questions, or ideas about the BTC framework, post it below!

------------------------------ 

I am teaching MATH 104 Finite Mathematics with Support next term, and want to weave thinking questions throughout the course . This corequisite support course allows students can enter the course with below college level placement, and earn college credit in one term instead of two. These students are majoring in business, accounting, or other programs, eventually need to take MATH&148 Business Calculus. The course covers linear equations, systems of linear equations, linear programming, the Simplex method, functions (polynomial, rational, exponential, logarithmic), financial math, and annuities.

Having tried thinking questions in MATH&146 Introduction to Statistics, I'll be focusing on specific computational skills that students usually have difficulty with. The example on factoring from page 27 of Building Thinking Classrooms in Mathematics (BTC) is a good model to start with for curriculum-aligned tasks; ask a question about prior knowledge, extend it, then "ask students to do something without telling them how" (BTC pg. 35). For most topics I feel like I have ideas of how I might go about this (famous last words!) but the non-curricular tasks are a bit of a puzzle. What question(s) will capture student's attention and get them thinking?

I've taught this and the 'standard' version of this course (MATH 105 Finite Mathematics) before, and one area that all of these students have a deep interest in is money. How to earn it, how to spend it, how to lose it, scams on getting more, they are interested in every opportunity to exchange currency for goods and services. Unfortunately we don't cover much of that material until the end of the term, and with a recent change in textbooks I am not setup to move topics around, yet. One of the questions I ask at the end of the annuities section is "How are you going to retire?" It requires estimating how much money students will need on a monthly basis in retirement, calculating the present value of those regular payments over time (an annuity), and then much money they will need to put into a retirement account in terms of a future value annuity. If a student can do this then I am fairly confident that they understand annuities. Most students are very interested in answering this question, and will change variables to test out other assumptions and see what has a bigger impact; interest rates, time, or payments.

So why not start there? Here's my plan for the first day;

• Brief introductions: course name, me, who the course is for.
• Pose the question: How much money will you need to retire? Chapter 9 of BTC has some specific recommendations about hints, but for the start I'll pose the question and see how they respond. I'm planning on letting them think through their answers for 20 minutes, and have groups report for another 20 minutes. I am hoping some students might assign variables for unknowns, and use them in their answer. Here are a few hints I'll share based on where they have trouble. 
  • How much money do you think you'll need a month?
  • When do you anticipate retiring?
  • How long do you think you will be in retirement?
  • In mathematics, if you don't know a quantity, how do we give it a 'name'?
• POGIL activities: one on how to work in groups, and the other about the syllabus.

I am very tempted to provide guidance, variables, and other 'hints'. At the same time my framing of the thinking question will be something like "I want to see what you can do, AND I want you to see what you can do." Providing additional supports would kind of defeat that goal.

For the rest of the week I'll share some other thoughts and planning using the BTC framework, specifically some thoughts on grading, testing out some curriculum-aligned questions, and other thoughts.