Where thinking takes the center stage,
I am reading Building Thinking Classroom in Mathematics by Liljedahl.
Chapter 1 is all about choosing the right tasks.
There are three kinds of tasks
1) Non-curricular tasks (does not address grade level curriculum, but is fastest way to get students thinking)
2) Scripted Curricular tasks (uses prior knowledge and task is presented before any teaching has occurred)
3) As-Is Curricular tasks (uses mimicking thus decreasing thinking)
Good resource for Task 1/Task 2 type questions for Grade 8
At the end of each chapter, are reflective questions.
I will be using this blog to record my thoughts and thinking for next year.
Question 1
What are some of the things in this chapter that immediately feel correct?
At the beginning of each school year, I use non-curricular problems to establish classrooms routines of thinking, sharing, and listening. This chapter validates my decision to do this. My question is, do I need to do non-curricular tasks throughout the year simply to "prime the pump"?
I love the Task 2 approach...using prior knowledge, have students solve a problem before teaching has even happened. I find that I use this approach when I feel like I have the time. Falling back into the Task 3 approach seems to happen when I'm stressed for time to cover a topic.
Question 2
In this chapter you read about the negative consequences of mimicking. Can you think of any positive benefits? If so, do these positive benefits outweigh the negative consequences?
The first thing that jumped to mind was that this is exactly how the MidSchool Math program is designed. The Simulation Trainer is simply mimicking what was learned from the Immersion problem. Is there a way to use this approach to enhance student thinking???
Positive effects of mimicking???? Hmmm.... This is hard, because the jump from the Simulation Trainer to the Practice Printable is always huge. Students struggle because they don't want to think, they don't want to apply the skills in a new context.
Question 3
The introduction mentioned that almost all students who mimic express that they thought this is what they were meant to be doing. This chapter shares that one of the ways in which students come to this conclusion is by having their teachers show them how to do something before asking them to try it on their own. What other ways may we be communicating that mimicking is what we want students to do -- even if that is not what we want?
The one thing that I've been doing that I'm now questioning is the answer-a-question-with-a-question approach. I am taking away the student's ability to think by asking a guiding question. In a way, it is a form of mimicking, because students want to get back on track for solving the problem in the way they believe that I want them to solve it in.
Focusing on my questions to keep them even more open-ended will allow for multiple methods to rise to the surface.
Question 4
You have read in this chapter that curriculum is inherently spiraled and, therefore, there are very few examples where you would introduce a topic for which students have no prior knowledge upon which such a script can be built. Can you think of some examples of such situations in your curriculum? If you can, is there really no prior knowledge that can be drawn on?
Pythagorean's Theorem is a new concept for 8th grade, but prior knowledge would include
- Squaring numbers
- Knowledge of triangles (Triangle Inequality Theorem)
- Areas of squares
Angles is also new, but students come in knowing acute, right, and obtuse angles. Using these prior concepts to find relationships will be helpful
Question 5
In this chapter, it was shown that students perform better on scripted curricular tasks if they have first experiences three to five classes of working on highly engaging non-curricular tasks. How do you feel about giving up this time? What are the barriers for you to do this? What do you stand to gain? What do you stand to lose?
I strongly believe that the non-curricular tasks are very important. I have seen what they can do for thinking and engagement in the math classroom! Finding the right tasks will take time, but getting students comfortable with sharing their thinking and working with others through struggle and failure is biggest gain I can think of. Non-curricular tasks take time, but if done well, can actually buy time in the end.
Question 6
What are some of the challenges you anticipate you will experience in implementing the strategies suggested in this chapter? What are some of the ways to overcome these?
Challenges
- finding the "perfect" task
- constructing questions to move thinking --> Can use the Question Wheel and the Rigor/Relevance Framework to help with this
- Allowing time for student sharing so multiple methods can be highlighted
Ways to overcome
- Find a quote to post as a reminder that this is time well spent.
- Review the chapters in Building Thinking Classrooms
