Thursday, August 1, 2019

Changing the SCRIPT: A Student Perspective

A student stayed after school this past spring to talk with me.  I figured it was something about a grade or some help he needed.  He actually wanted to talk with me about the math class SCRIPT.  Here is what he said about math classes in general...

...everyday we had a note sheet, some set examples, a target written out with what we were learning, and then there were blanks so you would wait for the teacher to put it up on the board so you could then fill in the blanks.  Then you just followed all the examples.  It is like a script.  I guess it was really efficient in teaching you exactly what you needed to know, but there was no thinking in it.  The teacher wants you to follow exactly how they tell can't deviate at all...I couldn't do it another way or skip this step.
As a math teacher, you know the script:  review homework, present any tools/formulas you need for the lesson, then show how to do problems step by step using those tools/formulas and then give alone/group time to practice all of that.  I know the routine very well because I learned math using this script when I was in school K-12.  Once I become a math teacher, I modeled this script for many years.  And it works!  The script is efficient and mistakes are minimal.  If the students do the work, they will be prepared for the test.  I as the teacher gave the most efficient method to the students to solve a problem and then they practice.  Many students like the script because it works for them.  Students know what is expected and respond to it.  If students practice enough, they can reproduce the work on tests/exams.  If you look at the last few things that my student said:  follow exactly how they tell you, don't deviate, don't do it another way.  This is worth looking at because I don't always follow the script in my class anymore.

My student went on to say a few things about my class in particular.

...when I first took your class, and you suddenly threw us into this place where we have to do it and think ourselves, I was like...crap I'm not going to do good in this class.  

Whoa.   As you can see, it was not pretty in my class the first part of the year.  I often have many students that are completely frozen with fear in my class because they have never had to do a problem without first being confident on how to solve it.  I'm working on how to calm this fear, but in reality, this is a mathematical mindset that is important for all students to confront.   I often ask my students to look and engage with a problem BEFORE they are given any kind of formulas.  Here is the reason I do this...“Trying to solve a problem before being taught the solution leads to better learning, even when errors are made in the attempt.” ― Peter C. Brown, Make It Stick   Furthermore, students tend to be more engaged with the problem and own it after they have tried it themselves.  So when you give the problems to the students (in varied ways) before you have shown them how to solve it, they remember it better and they are more engaged and empowered.  This is typically how I run my class.

And my student says a little more about my class.

...I got the hang of it, and then I started to realize ...Oh, I'm doing this automatically in other classes now.   

What?  What did he get the hang of?  I explored this a little more with him and he said this...

...for example when I first started physics it was just really hard because I wasn't able to think freely.  I wasn't able to think abstract or imagine things.  Now I can think on my own and decide which way is the right approach. 

He is evaluating his own work and practice.  He is actually empowered by thinking on his own instead of just following a script.

I have been thinking about this all summer long.  There are things in this conversation that are really important to note.  One, he felt awful at the beginning of my class.   This is important for me to help smooth out.   Second, he felt liberated by going outside the script.   And thirdly, he uses this technique in other classes.  Since there are pros to the SCRIPT and there are pros to being off the SCRIPT, it is important to remember that students, parents, and other teachers are not always on board when you deviate from the traditional math class SCRIPT.

Benefits of the math class SCRIPT
Do the work, and you are prepared for the test
Mistakes are minimal
All the expectations are given in a concise manner
Many students like the script because it works for them
All are on the same pace

Benefits of being outside the math class SCRIPT
Lack of direction creates a mathematical need
There are MANY ways to solve a problem.
Making mistakes and learning from them is OK and needed
Many students love being in charge of their own learning

I would say that I am using the SCRIPT less and less as time goes along.  I'm forever tweaking my teaching to get better.

I encourage you to try a different approach.  Make sure you tell your students what you are doing and why.  Then give it a go.  Give the students a problem before you have explained all that is needed to solve it.  Give them time to work alone and then with others to solve it.  ENGAGE.  Lastly, discuss what math is needed to solve the problem and work through how students can get that information.

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,