## Friday, September 30, 2016

The next time you open your class for questions, do not use the phrase "Do you have any questions?" Change it to "Ask me a question."  It has been a really fun ride for me this year.  Let me explain where I got this idea and how I've used it so far.

## This was My Daughters Idea

I have been seeing the statistics going around twitter regarding the amount of questions that a teacher asks compared to the amount of question a student asks.  It concerned me.  Soon after this I told my daughter and my wife about the statistic that I was seeing:  Teachers ask 200 questions per week and the average student asks 2 questions per week.  I continued to tell them that my students had not asked very many questions that very day.   My daughter listened and then suggested I should require my students to ask a question.  I thought that was brilliant.  I decided to use it the next day when a colleague Rachel Fruin @rachelfruin suggested I use the phrase ASK ME A QUESTION.  So there it began.

## My First Experience

I immediately used this technique in class the next day.
My students were working independently on a few problems when I set the Ground Rules.  I told my students that I was going to require them to "Ask a Question" when I was walking around to each person.  I also said that if they did not have a math question, that they could ask any other (appropriate)  question that they liked.  One way or another, they would have to ask me a question.
It was amazing.  I had really good questions for the most part.  Most of the questions were math related.
• I gained a whole new appreciation for some of my students who usually are silent.
• I could tell that this was freeing to some students who were embarrassed to ask a question previously.
• It was really fun to dialog with the students.
• I actually had a conversation with most of my students that day.  Which was unusual.
• Some questions were related to math but not necessarily about a concept.  IE Why does the slope formula start with the second point?  That was a cool question.
• Many of the non-math questions were superficial.  Some were complex and not easy to answer.  One of my students asked if I would take 3 trillion lions or the Sun in a fight?  Where do they think up this stuff?

## My Second Experience

The next time I used this technique was within a whole class experience.  I presented a topic that was complicated.  I asked for questions and no one had any.  (They probably had some but were a little nervous to ask)   Then I told them that they had to talk to their partner about a possible question they would like to ask.  Then I said "Ask me a Question."  Then I called on students at random. Here is what I found.

• The questions were vague at first
• Other peoples questions helped refine the new questions.
• I didn't answer all of the questions.
• When I didn't know the answer, I told them so.
• Some students said they didn't have any questions.  I just came back to them after someone else asked a question.
• The same questions were being asked in different ways.  This told me that A) They weren't listening when someone else was asking a question or B) They really don't understand what is going on.  This helps me to know where the class stands on their understanding level.
• The class really did have a lot of questions but needed the structure to ask questions freely.

Overall, I would really encourage you to try "Ask me a Question" sometime soon.  What do you think?  What have your experiences been with this?

## Monday, August 29, 2016

### 10 Days of Number Talks for High Schoolers

This summer I read a book called "Making Number Talks Matter" by Cathy Humphreys and Ruth Parker.  It was outstanding.  It really called me to action.  I highly recommend it.

Also, I read a great blog post regarding Number Talks by Sara VanDerWerf @saravdwerf called "Secondary Number Talks"  Sara challenged me to give Number Talks 30 times in a year and also for 10 days in a row (I'm trying it for the first 10 days of school)

Number Talks are short mental math problems given to students to work out individually and then discuss as a whole group.  They are fascinating and fun.  Mostly it reverses the typical way a math class is run.  You give the problem with no introduction and no explanation and no hints.  Then you discuss the many different ways students solved the problem.  It is amazing the different thought processes that happen in with this method.  The students are set  free from the boundaries of whether they did it the same way as the teacher.  They relish in the coolest and fastest way.  They oooh and aaahh at the different methods.  The most amazing part is that the students start to see the connections in math that we have been trying to beat over their head for so long.

Typically this is how the Number Talks have gone.

1. You will be given a problem and time to work out the problem mentally.
2. You will be given some time to share your idea with someone near you and get feedback.
3. As a whole class we will share out potential solutions.
4. Then as a whole class we will share out methods for those solutions.
5. Depending on time, we will use one or more methods on a new problem.

Here are my Ground Rules

Everyone's voice matters.  Be respectful when someone is giving their opinion.
Everyone will be asked to take risks and be uncomfortable. Being uncomfortable is OK.  It is a part of growth and learning.
If you find one way to figure out the problem, then see if you can find a different way.
Try to think of a visual method of solving and explaining your solution.

Here is the one I gave DAY 1 (I got this problem from @joboaler ICTM 2015 keynote)

Simplify

POSSIBLE DISCUSSIONS and SOLUTIONS

Here is another thing that I think would be great to start doing on day 1.  EQUATIONS

5(18)=90
5(10+8)=90

5(18)=90
5(20-2)=90

5(18)=90
5(2)(9)=90

5(18)=90
2(5)(18)=2(90)

5(18)=90
18(2+2+1)=90

10 DAYS OF NUMBER TALKS
DAY 1 TOPIC: Multiplication
Simplify

DAY 2 TOPIC: Subtraction
Simplify
DAY 3 TOPIC: Visual Pattern
How is this growing?
What does step four look like?  How many small squares are in step four?
What does step 43 look like?  How many small squares are in it?
What does the xth step look like?  What is the equation for it?

DAY 4  TOPIC: Fractions
Simplify

DAY 5 TOPIC: Visual Pattern
What does step 10 look like and how many mini squares are in it?  What does the xth step look like?  What is the equation for it?

DAY 6  TOPIC: Division

DAY 7 TOPIC: Visual Pattern
What does step 43 look like and how many squares are in it?  What does the xth step look like?  What is the equation for it?

DAY 8  TOPIC: Multiplication
Simplify

DAY 9 TOPIC: Visual Pattern
What does step 43 look like and how many squares are in it?  What does the xth step look like?  What is the equation for it?

DAY 10 TOPIC: Percents
Simplify
25% of \$200

Here is what I give to the students
Day Topic URL (to copy to your drive)

## Friday, July 22, 2016

### Visual Patterns: Concrete Results

I would encourage you to use visual patterns in your class as soon as possible.  There is an excellent website to get yourself started at http://www.visualpatterns.org/
I gave this problem to my students in the middle of the quadratics unit for Algebra 1.  Any student has a chance at this.  That is what makes this so wonderful.  The playing field is leveled.  This particular problem is very cool because there are so many ways to view it.  So the beauty of visual patterns is that each student can look at the problem differently and still get the same answer.  The key is having them JUSTIFY their work.  You might want to try it yourself before looking below.
Here is my original problem
Some things that I try to do when using this kind of problem.
1.  Have students work on their own first.  Then after some alone time, give time for collaboration.
2.  Have students try to work multiple solutions if they finish with one.
3.  Push students to visualize the problem in some way.  (manipulatives or drawing or sketch or computer based image...)
4.  Push students to give some meaning to the problem with algebraic symbols.
5.  I try to remember that this problem might take 20 or more minutes to work out.

Here are a few examples of what my students created with this problem.

This one saw the perfect squares involved and then just subtracted the two missing pieces off at the end.

This group saw the smaller perfect square in the pattern.  Then dealt with the rest in a linear way.

I love this one because it incorporated a graph to make sure of their answer

This one is detailed.  The recognized the perfect square in the middle and then dealt with the other stuff as linear.
I made these visualizations for the problem.  However, many of the students had these types of things on their papers before they wrote up the equations.  You can also see by the video below how the students were visualizing this problem.  Also, next year I'm planning on having the students do this type of visualization with a spreadsheet that @alicekeeler made.  http://alicekeeler.com/pixelart I found it in her blog post:  http://alicekeeler.com/2016/07/17/modeling-division-brownies-joboaler/

(x+2)(x+2)-2

(x+1)(x+1)+2x+1

(x)(x)+4x+2

More questions were asked for this problem.
Are the algebraic results all the same?
How do we know that the algebraic results are all the same?
Can we use DESMOS to see if they are the same?
Can we simplify to see if the algebraic results are the same?

Can you imagine your students wanting to know these questions?  It was so much fun.

Here is the reward of the day.  One student who has trouble with the algebraic concepts and who almost never wants to talk about it got up and did this....magical.

Lastly, I'm thinking about taking the @saravwerf Number Talks challenge.  See her blog post at https://saravanderwerf.com/2016/06/27/secondary-number-talks-ill-convince-you-with-ducks/