Creating sequences of curricular tasks help students to think more
And ultimately cover large amounts of content in a short amount of time.
"If we are thinking, we will be engaged."
"If we are engaged, we are thinking."
Goal is to keep students in the flow
By finding the task that meets them where they are at.
Not too challenging.
Not too easy.
Timing matters as to when we increase the challenge.
To do this,
CREATE SEQUENCES of problems.
Teacher: If I add three to my number, the answer is 12. Thumbs up if you know my number.
Calls on student when enough thumbs are up for the answer.
Teacher: If I double it and add three my answer is 15. Thumbs up if you know my number.
Calls on student when enough thumbs are up for the answer.
Teacher: Before I give you the next one, we have to learn how to write what I just said.
x + 2 + 3 = 15
Teacher: And before I give you the next one, there are three rules for this task.
1. You can use a calculator.
2. If you use a calculator, you must write down on the whiteboard what you are typing in.
3. You have to check your answer by putting it back into the calculator.
Here's your next one
x + 3.014 = 7.22
Randomizes groups and send them off to work.
Rest of the sequence
x - 15.1 = 7.88
x * 4.25 = 24.8
x / 1.356 = 4.02
x * 2.5 + 3.67 = 18.3
Variation can only be seen against a backdrop of non-variation.
The increase in challenge from one task to the next is incrementally small.
Just pushing the envelope a little bit in each step, which helps keep the students in flow.
Changing engagement can also maintain flow.
If a group has answered wrong, or even if they are right,
Simply ask them if they would bet $100 on their answer...and then walk away.
They just went from DOING to JUSTIFYING.
When they call me back to EXPLAIN, they are required to articulate their thoughts for an outside audience.
To further increase the challenge, I may point them to a group to TEACH them something.
And finally, at the pinnacle, having them create a new task for a group.
REMINDER! To avoid falling into stop-thinking questions, use these instead.
1. Why did you do that?
2. Can you tell me what you are doing here?
Question 1
What are some of the things in this chapter that immediately feel correct?
I love the subtle variations to build confidence in students' ability to solve curricular problems! My mind was already making plans to create these sequences this summer so I have something to rely on when the school year starts. And then I saw Question 2 and 3. Don't worry, I will have several sequences ready to rock and roll.
Question 2
Pick a topic that you have just finished teaching, and try to build a sequence of incrementally more challenging tasks that cuts through a part, or all, of the topic.
Created sequences for solving one- and two-step equations for rational numbers (decimals), rational numbers (fractions), and rational numbers (integers). This will be very helpful as students struggle with all of these concepts.
Question 3
Now do the same thing for the next topic you will be teaching.
My next focus will be
- Pythagorean's Theorem
Question 4
Think about a topic that you believe is brand new to students. What is the minimum set of instructions that you need to give in order to prepare students to be able to think their way through the first task you would ask them to do? What can students learn from this first task?
Pythagorean's Theorem. I would do the Discovery activity where students find out what the theorem actually is. From there, I would give them problems for finding the missing side lengths.
Question 5
Do you think your students have developed the autonomy they need to allow them to help themselves to stay in flow? If not, reread Chapter 8, and think about how you can continue to further their growth in this area. This does not mean you can't start to play with creating and maintaining flow. Flow is a great context in chich to keep working on mobilizing knowledge to building students' autonomy.
We shall see. You can bet I will be reviewing these notes and the chapters in the book as I implement these new ideas!
Question 6
Have you seen instances where your groups exhibit tremendous perseverance or patience while working in a thinking classroom setting? If so, could they have done this at the beginning of the school year?
I have seen this. Students will make comments of "I feel so accomplished" or they won't want to leave to go to their next class. I have used non-curricular tasks to establish class norms in the past years, but I love how these non-curricular tasks have a purpose to create more thinking opportunities, which also has been my ultimate goal. Now I will have the tools to make it happen!
Question 7
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?
Creating sequences that go step-by-step.
Creating the atmosphere for students to "steal" the next problems.
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