Building Thinking Classrooms: Ch 1 - Types of Tasks

So in an effort to transform my classroom next year

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

http://www.aliciaburdess.com/problems-worth-solving-in-a-thinking-classroom.html

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

Practice is a MUST!!!

Today 8th graders got a first hand glimpse at the importance of math practice.

Math practice allows students for mistakes to be made BEFORE the quiz.
Mistakes are necessary for learning.

But when math practice is not completed,
Mistakes can't be made,
And learning is at a standstill.

Today we reflected on our first quiz we took on Friday.
It was eye-opening to see the impact that practice actually makes on a quiz grade.
The average score for students completing all their practice before the quiz was a 74.5%
The average score for students NOT completing all their practice before the quiz was almost 20 points lower...55%!

74.5%...basically a C grade.
Compared to 55%...an F.

Practice is needed.
Practice does make a difference!
Practice helps us all learn math!!

That's Not Your Ordinary Golf Hole!

Enjoy our showcase of creativity with some of the golf hole models created in math class last week.

A Positive Angle to Frustrations

Math can be challenging.
No doubt.
But that doesn't mean it's not doable.

On Thursday, students walked into 8th grade math to find their frustrations from the day before listed on the board.

The lesson that followed, addressed each frustration, allowing students to move their thinking so they could continue to work towards a successful hole-in-one.

Powertools were needed to create the framework for the golf hole simulation.

Ms. Weimer and Mrs. McCabe practicing the night before to see how the lesson would play out.

Using a golf ball dipped in neon paint, students "putted" the ball against the framework to see the angles of incidence and reflection created right before their eyes.

Real life angles in action!
Where was the angle of incidence?  The angle of reflection?
How do I use a protractor in real life when the angles aren't just given to me on an assignment?
Were the angles of incidence and reflection equal in real life? Or were other variables involved?

Back to work!  

Working hard.

Total concentration

This is what perseverance looks like!  Mistakes are NECESSARY in moving our thinking!!

Extension: Can a hole-in-one be found by bouncing it off more than one wall?

The Math Behind a Hole in One

And so it begins...
Math.
So far we have been busy with looking at the math behind the solar eclipse and setting up our classroom expectations, ISNs, and notebooks.

But today, we were able to get our minds on math,
And our hands as we worked on figuring out how to get a hole-in-one.

Precise use of protractors is a must.
Understanding that the angle of incidence must equal the angle of reflection is critical.
But where do we have to hit the "ball" to get a hole-in-one???

World Famous

In Seattle, Washington John Yokoyama took a failing fish business and made it world famous by simply changing how he thought and implementing four simple steps.

So in 8th Grade math class, our goal is to become "world famous".
When things get challenging, or we are failing at understanding a concept,
following these four steps will at least point us in the right direction.

Students brainstormed how these four simple steps would look like in a math classroom.

With thoughts like these, I'm excited to see these students take on 8th grade math!

Welcome to 8th Grade Math!

Dear 8th Grade Parents,

Welcome to 8th grade math!  I am really excited about what this year will hold as far as math content and our classroom is concerned.  For those parents that I got to meet last night, this might be a little redundant...or it might be refreshing to read it at your own speed instead of listening to me try to cram it all into 7 minutes!  :)

Our math classroom is based on real-world problems where math conversations and discovery are the focus.  We value multiple methods when solving a problem so we can make broader mathematical connections.  Mistakes are avenues to learning and are expected in my classroom. 

Our first unit will be working with angles...measuring them, identifying angle types, and using angle relationships to find missing angle measures.  Your student may come home with stories of getting a hole-in-one on their miniature golf hole or how a railroad yard is just chalk full of angles!

We do not have a textbook, but instead are building TWO of our own as we go.  A 3-ring binder will be used for all of our handouts, practice, and activities.  The students will also keep an ISN (Interactive Student Notebook) in the classroom where specific notes will be organized in a glossary-type book. I ask that these books stay in the classroom so they can always be used as a reference when learning, but students are more than welcome to take pictures of their notes (or we can make a copy) before or after school so they have something to study from at home. 

In the attached brochure, you can read about my grading policy and how quiz retakes will be handled. Below, you will find the parent letter from Ms. Weimer, my student teacher this first 10 weeks of the semester so you can get to know her a little better.  

If you should ever have a question or concern about your student in math, please feel free to email me.  I am a strong believer that when we work together, we can ensure the best path for your student's success!

Dear parents,

I wanted to introduce myself to you all, since I will be student teaching with Mrs.
McCabe for the first 10 weeks this semester! My name is Jenna Weimer and I am a
senior in Sterling College’s math education program. I grew up in Fresno, in the
Central Valley of California, but came to Sterling three years ago to continue my
softball career as a collegiate pitcher/outfielder and to learn a thing or two (or maybe
a bit more) about teaching.

I grew up in a family full of teachers and loved almost everything about it (except
maybe the paperwork), so for most of my life I’ve known this is what I want to do!
Math looked to be a pretty fun concentration, and I have not regretted that choice
once!

To many people, math simply means an algorithm of meaningless computations
aimed at a single solution with no real relevance to life and career, and I do not want
that to be the experience of any student I ever work with. It is my goal this semester
to join Mrs. McCabe in bringing math to life for every student we teach. During my
time here, I hope to help deepen our understanding of the field of mathematics,
discover the many ways a problem can be tackled and why these ways work, make
real-world connections to the concepts we are learning, and push each other toward
excellence through a variety of collaborative, hands-on activities.
I am extremely excited to be working with your students at Reno Valley and look
forward to getting to know and invest in each and every one of them! I would so love
to meet you while I am here, so please come say hello! If you have any questions,
feel free to shoot me an email at jweimer@sterling.edu, and I will happily chat with
you!

Thanks so much!
Ms. Weimer