Monday, March 18, 2019

TRUTH or SNARE: A Math Equivalence Game

TRUTH means equivalent
SNARE means not-equivalent (but really close) 

This game is the reverse of a Number Talk.  In a number talk the teacher gives a problem and students find different ways to come up with the answer.  With TRUTH or SNARE, the teacher gives an answer and the students create potential equivalent possibilities (truths) or non-equivalent possibilities (snares).  The rest of the class has to find ways to determine if the possibilities are a truth or snare.

Let's give an example

Teacher:  Let's play TRUTH or SNARE with the theme being exponents and order of operations.  Remember that SNARES are NOT-EQUIVALENT but are really close to being equivalent and very tricky.  Create at least 2 TRUTHS and 2 SNARES for the following answer:  16      (Teachers resist the urge to give examples.  Don't do it.  Instead, encourage the students to create a problem that has an answer of 16.  Remind the students that it won't matter if their problem is equivalent or non-equivalent...they will not be wrong)

Students:  Work in groups of 2-4 to accomplish the task.  (Teachers  make sure each group has at least one example of either kind)

Teacher:  Pick groups at random to present their possibility.  Students will not be telling the rest of the class if it is a truth or snare yet.   Have the groups put their problem on the board or have the group give them to the teacher to put on the board.

Teacher:  Now take some time in your groups to decide which ones are TRUTHS or which ones are SNARES.  (Allow enough time for all groups to get through at least half of the examples given)

Students:  Work together in your group or with your partner to determine if each problem is a TRUTH or a SNARE.  Be ready to defend your work.

Class Discussion: Take a vote for each example.  Thumbs Up (Truth), Thumbs Down (Snare), and Thumbs Middle (Unsure).  (see my voting thumb pictures below)  Have students walk through the reasoning and or the teacher walk through the reasoning for each example.  Be open about the fact that this activity is meant to push your understanding and that you might make mistakes on what is a TRUTH or SNARE.  These mistakes are helpful for us to recognize equivalencies in the future.

See the example below that we did in class.

Here are a few examples of what the students made.

Group B,C and D are TRUTHS and A and E are SNARES.

The beauty of the game is that students do not fear creating a wrong answer.  Actually, they like to create answers that are SNARES.  Students like to trick their classmates.  

Here are some other examples that we have done.

This is what I have been doing when I have my students voting.

This game is a work in progress.  Do you have any suggestions for me?  What has worked for you?  Please let me know.

Tuesday, July 31, 2018

The Struggle is Real: Devoting 20 Percent of Class Time to Problem Solving

I want my students to struggle--to squirm and to be frustrated.  I often struggle with math questions. It takes me a while to process and sort out my thinking.  Struggling with a math problem gives me confidence for the next one.  In the classroom I love when my students are working on a difficult math question and then someone has an ‘aha’ moment.  It is like someone receiving a clue to the location of a hidden treasure.  It spurs others to continue working and finding other connections. I want them to take ownership and celebrate the journey.  I could sum up my teaching philosophy with the phrase, "I want my students in a productive struggle."  I want my students to struggle, but I want them to be productive in that quest.  If the struggle is too easy or too tough, then I need to help make some adjustments by creating the right environment and finding the right questions to problem solve.  That is why I'm trying 20% Struggle Time.

20% Struggle Time (Problem Solving)
My instructional learning coach  Chris DeWald from BetterLesson recently challenged me.  "Why don't you devote 20% of your class time to (productive struggle) problem solving questions?"  I have accepted the challenge and I've been on this journey since late last year. I'm taking 20% of my class time and devoting it towards problem solving, and not necessarily content-based problem solving either.  As far as actual time in the classroom that means 1 day a week or two half days a week we will be in a productive struggle solving problems.  It has been fun and really rewarding--and frustrating.  It is all about finding the right problems and creating the right atmosphere for learning. 

Easy Problems Do Not Accomplish Much
You know what an easy problem is.... the ones that you don't have to think too much to solve.  If you don't have to think too much to solve something, you probably won't remember too much about your work, nor will you be satisfied with yourself.   I tend to give out too many easy problems.  My lesson will include some kind of formula and the problems use the formula--too easy and too forgettable.  Fawn Nguyen says, “Are they really ‘problems’ if we know how to solve them?”  I firmly believe this.  

Problem Solving creates productive struggle.  I'm not talking about word problems at the end of each section of practice problems.  I'm talking about NON-Content Specific Problem Solving.  The problems students can't just look up in their notes and see one almost exactly like the one given.  A problem that they can solve, but it will take time and maybe more than one class period.  It will take reflection of possible solutions.  It might even take some research, or multiple attempts at the problem, or scaffolding from the teacher or other classmates.

What does 20% Struggle Time look like when Problem Solving?
1.  I have a walk that I take often that leads me under a canopy of oak trees.  Students need to feel like they are in a canopy of oak trees—a safety net.  They need to know that the students around them and especially myself as the teacher are WITH them.   A positive classroom atmosphere creates safety nets in case they don't get it.  Examples of safety nets would be: formative testing without grade impact, retakes on summatives, daily work that explores but does not affect final grades, classmates who are willing to help others, and a teacher who offers multiple avenues for help.

2.  Finding the right problems is important--Inviting and Approachable Problems with Escalating Difficulty (Low Floor High Ceiling).  Everyone has a different threshold of pain.  Some complain wildly because of a small cut, and others would not be fazed by a large gash.  That is just how we are made.  Accordingly, I believe we all have a different threshold of struggle.  For instance, some people might look into a problem with their laptop with bitter frustration and give up quickly, while another might struggle for a long period of time.   It is the same thing with a problem in math class, some students look at the problem and then give up quickly.  Other students look at the problem and start formulating some ideas.  The trick is to find questions that anyone can start and yet most will be challenged at some point in the problem.  Here are some of my 'goto' problems. 

There are actual examples at the bottom of the post

3.  I’m still working out how to approach grading Productive Struggle. Is my 20% struggle time a completion grade?  Do I grade on correctness?  Should there be a rubric?  Maybe I should just build in accountability with group presentations of thinking?  Any thoughts or suggestions on this would be welcome!!

Plumbing and my Father-in-Law
Confidence solving problems is a real world skill.  When we had just bought our first house, my father-in-law and I were looking into the electrical box to see how to stop one of the circuit breakers from going off regularly.  It was a nest of confusing wires.  I asked him how he felt so confident that he could figure this out.  I was ready to give up.  He said, "Whatever mess I get myself into, I’ll just keep trying to figure the problem out by taking a generous amount of time and many setbacks trying to prevail. A last resort solution would be that I could hire someone to fix it." I have used this advice often and have learned that with determination and confidence, I can often see it through.  Like every year when I do my taxes. I can usually figure out most questions (with Turbo Tax).  This is the attitude that I want my students to come out of my class with.  I want them to be confident that they can attempt and find a method of solution with almost anything they encounter and that it will be a productive struggle.  My father-in-law without knowing it, was using the Mathematical Practice Number 1.  I'm hoping that 20% Struggle Time will help my students with this mindset.

Teach Before or After They Need It?
My wife will never let me teach her about any technology until she needs it.  Why?  Because she says she will forget it all and then just have to ask me again when she actually does need it.  We need to give the problem first and then our students will need to use the skills and formulas to get the answer.  That is true problem solving. Sometimes our classrooms are backwards in that we do all this upfront teaching so that they will remember it when they need it.  Which by the way, rarely happens. Needing it might mean that it might be on a quiz that happens a couple days after they learned it so that you can just memorize the steps to get through.  Introducing 20% struggle problems will help exercise the GROWTH MINDSET needed to solve new challenging problems that they have never seen before.

What about the Content?
Some would argue that they don't have enough time to teach the content now, how are they going to introduce more problems?  I get that.  However, I believe math is an attitude not a skill.  We really are teaching our students to have GRIT, to never give up, to exhaust all resources, to struggle, and to fail.  We can teach skills until our students are robots or we can teach them to be real world problem solvers.   

The Struggle is Real, so that is why I'm going on the 20% struggle time journey.  I'll keep you posted.  I welcome any thoughts or advice.

My Best,
A Visual Pattern Task    Here is a collection of a few that I've made

The Toothpick Task

Friday, May 25, 2018

With You

My adult son has had some medical issues recently.  My wife said something to him that really made me think.  She said, "We are 'with you' as you go through this".  It was simple, yet really meaningful. 

Now fast forward to the education world.  I thought to myself, do my students know that I'm WITH THEM?  Do I communicate the idea of "WITH YOU" in everything I do as a teacher?  Do I actually tell them that we are partners in this adventure/struggle?   Every single interaction with each student is important. 

A message to my students:  I'm WITH YOU.   I can feel your struggle.  I hurt when you hurt and am happy when you thrive.   I can't do it for you, but I will be right beside you encouraging you the whole way.  We are partners.  You are not alone.

Saturday, January 6, 2018

I Want My Students to ...

I want my students to ...    (in no particular order)

Have fun in class
Move while learning
Create stuff
Be respectful
Embrace learning from mistakes
Teach someone else something
Think "Whoa, this is cool"
Have an "I can do this" attitude
Give/Take advice freely
Discern what others say mathematically
Notice patterns
Enjoy a challenge
Ask questions
Understand/Believe in many different approaches to a problem.
Transfer learning to new places within the course
Work hard
Listen closely to others
Connect ideas
Feel safe and a part of a collaborative community
Care about others and know that others care

I hope my students....
Love rigor
Transfer ideas to new places outside the course
Say that Math is their favorite subject
Get the grade they want
Are organized
Set personal goals
Ask questions for curiosity sake alone
Are completely ready for next years course

Please help me with this list.  What else?  Please leave a comment with your thoughts on what should be added.

Friday, October 27, 2017

Pass It On! Linear Modeling Activity

Do you want your students to be engaged?  Do you want them to make predictions?  Do you want them to Move and Learn?  Are you working with linear equations?  Try this activity in Algebra 1.

Pass It On Book Passing Activity
Students will be passing 4 textbooks around the room in a established pattern. (see picture)  The number of students that pass the books will be determined and then the length of time will be noted.    (number of students passing the books, time to pass books) = (x,y)    Predictions will be made for the x and y unknowns.

Explain the outline of the activity.
Assign a timer.
Assign a note taker to record the data. (in a google sheet with a common link preferably)
Establish a pattern for passing the books.

Establish a short (approximate 10 second) routine for BEFORE the books are passed.  (jumping jacks, twirls, stacking books one by one, etc. This is to establish some type of y-intercept for the problem) See the video.

Practice passing the books around the path to make before timing the events.

Now time your class doing 3 people, 8 people, 14 people and 21 people.  
Record the data in a Google Sheet.  Here is our data from our class: 
The data is below: these coordinates are in (# of people moving the books, time) = (x,y)
(3 people , 11.17 seconds)
(8 people, 17.4 seconds)
(14 people, 25.4 seconds)
(21 people, 34.67 seconds)

Get your class into groups of three and ask these two questions.  
How long will it take for the books be moved by 30 people?  
(30 people, ? seconds)
If it took 73 seconds to move the books, how many students did the moving? 
(? people, 73 seconds)

I had the groups put their predictions in the google sheet that was created for the data.  
Lastly have your class actually test the predictions by measuring for 30 people and 73 seconds.  It was a lot of fun to find out the actual time for 30 people and the actual amount of people for 73 seconds.  The students were really into it.  

Good questions to ask 
What does the slope mean?
What does the y-intercept mean?
What methods could be used to predict your answers?

Hope you can give this a try.
My Best,

Wednesday, August 2, 2017

Connecting with Colleagues and Learning New Structures

I met with Scott Miller @smiller229 and Dave Elliot @dtelliott today.  Wow that was a treat.  They are amazing educators.  I learned some very cool things.  I always enjoy thinking about some new ways to teach.  I think we should do this often with other educators during our summer time when we can really let the ideas sink in.  I can't wait to try them.

Have your students in groups.  Have half of the students facing the front and half facing the back.  Now show your students that are looking forward a graph.  Since they are facing forward they can see it plainly and need to describe it to their partner who is facing backward.  The person who is facing backward then needs to draw the graph on paper.  They can dialog back and forth to gain clarity.
I wonder if this could be done with students creating their graphs on their calculators/Chromebooks?

2.  QUIZ, QUIZ, TRADE (Kagan)
Teacher Preparation is to make cards with questions on the front and answers on the back.
Students should be in pairs with all getting a card.  QUIZ: Person A solves the problem while Person B Coaches and Encourages.  QUIZ B:  Then Person B begins their problem with their roles reversed. TRADE:  They then give each other a high five congratulations and then TRADE cards.  Now they stand up and hold up their hand looking for a new partner.  High five the new partner and begin the process QUIZ, QUIZ TRADE over again.
I like this because of the fact that students get done with problems at different times and this structure accounts for that.
Video of Quiz, Quiz, Trade

3.  RALLY COACH (Kagan)
Have your students work in pairs with one being A and the other B.
A problem is posed to the whole class.  Person A solves the problem with Person B coaching and encouraging.  A second problem is posed and the roles are reversed.
Video of Rally Coach 

Put students in groups of 2-4.
Pose a question.  Given:    3x2
Now ask all groups to find an equivalent expression (this works for equations too).  They should be told that they should find more than one because there will be NO REPEATS (voted on by the class if is in violation).  Students will be called on randomly to represent their group.  Do no allow a student to give an answer that has already been given.  Call on a few students until you feel like the students are   Try to give time every once in a while to let students find some new equivalencies.   
5x2 - 2x2

Students are in groups of 4:  A, B, C, D
Work sheets have 4 separate problems on it.  All start in the left corner problem.  When all are finished the paper is passed clockwise.  That person checks the work of the person who gave it to them.  There also might be discussion regarding the question.  Wait until all are done and then start on the problem in the upper left.  Again wait until all are done and then pass it clockwise.  Check and discuss.  Wait. etc. until all problems are done.  You should end up with the page you started with and have all four problems worked out correctly.  

One story that Dave relayed to me was that one of the teachers in his department describes herself as a waitress.  She says that she moves from group to trying to see what they need next to help them.  She sees herself as a servant.  This is beautiful.  I love the idea of students deciding what they need to get to the standards of the class and the teacher being available to serve them in their quest.