Tuesday, May 23, 2017

Blue Tape Math

What is Blue Tape Math?  

Simply put, it is having your students use blue masking tape to represent math on the wall, floor desk or windows.  


Why use Blue Tape in Math?

MATH:  Students are using ratios, scale models, fractions, decimals and graphs ALL THE TIME.  Blue masking tape also 'slows' the math down a little bit so all can jump in and be engaged.
MOVEMENT:  Students are moving while learning which helps our kinesthetic learners.
MEASURING:  Students are using rulers, protractors, tape measures.
AND NO MESS with painters masking tape.  It comes right off of walls, glass, desks and floors.


Math Skills

Ratios
Scale Models
Measuring an angle
Measuring a side length
Fractions (While measuring distances)
Graphing
Areas


Where can students create their shapes?

Walls, Windows, Floors or on the Desks.

Ideas for when to use blue tape

Create a figure with a specified area.
Create a regular hexagon or pentagon.
Create parallel lines, or parallel lines by using a traversal
Create a parabola from a quadratic function.
Create a kite.
Create a triangle with Blue Tape.  Find the area of this triangle in multiple ways.
Create a shape (triangle, quadrilateral, etc. ) .  Create a different shape with the same area or perimeter.
Create a circle using blue tape.  Now guess how many diameters will be needed to make the circle?  Test your guess by creating diameters to go all the way around the circle.
Quadratic expressions and equations.  Click to get to the activity we did in class.

This project students created their own non-right triangle and then found the area of it using 3 different formulas.  #precalculus 

This group had a "random triangle that turned out to be an equilateral triangle.  They called the PERFECT triangle.  They were proud.



In this project students are making shapes to understand quadratics. This was in Algebra 1.  A colleague @rachelfruin and I wrote this  if you are interested, here is the progression.   


Try Blue Tape Math with your colleagues in the office.  We did.  It was a great experience.  @rachelfruin  @smiller229 and @mthor_  all have been working on blue tape math together.  The best way to describe what happens when you are using blue tape to get at a solution is that the process is 'slowed down'.  It helps everyone collaborate together at the same pace.  Try it in your office, and then try it in your classroom.  

Take the Blue Tape Math Challenge 

Find one or two colleagues that are up for an adventure, and create a regular pentagon with only a ruler, protractor, and some blue masking tape.  You can create the regular pentagon on the floor, desk or wall.  At the end of your creation reflect on the things you needed to accomplish the task.  Then discuss how you might use blue tape math in your class.  If you have time, let us know what you think @rachelfruin  @smiller229 and @mthor_ @dsladkey


A Word of Caution.  

Your lesson is going to take a lot longer.  This was something that was frustrating at first, but I realized that sometimes when a problem takes longer, the students understand it more thoroughly.   Another word of caution is that I always measure the figure on the INSIDE.  It has much crisper lines.  Also, I have my students use 1/4  inch blue tape.  See below.



#bluetapemath  







Wednesday, April 5, 2017

The Ups and Downs of Blended Learning

I feel like a first year teacher again.  Do you remember that?  The roller coaster you were on emotionally?  Well welcome to my world this semester.  I have taken the Blended Learning Plunge. See my first post about blended learning here.   I have my students for "In Class" days 3 times a week.  Then for two days a week they have "Independent Days".  These are days in which they do not have to attend class unless they have a grade below a 70%.

The Ups
The independent days have been spectacular.  There has been some "ah hah" moments for my students that could never have happened in a traditional setting.  Let me share a story.  I gave a visual pattern assignment to my class on an "Independent Day".  (this is where only a few of students are in my class)   So I only had a handful of students doing this problem in class.


We actually followed Michael Fenton's steps through this visual pattern with a piece of typing paper.  Click here to check that out.  So a student and I were working on a problem together.  Although she is very slow at processing arithmetic, she is very good at seeing patterns and growth of patterns.  For this problem we progressed by giving steps 1, 2 and 3.  (see picture)
Then she was asked to draw step 4.  No problem.
Then she was asked to draw step 10 with relative ease.
Then I asked her to tell me about step x.  (This was the key moment I had been waiting for.)
She said do you mean step 11.
I said no, step x.
She said I don't know what you mean by step x.
This girl has taken 8th grade algebra, Intro to Algebra and now Algebra 1.   Now she was finally able to ask  about what x means.  It was a breakthrough. We continued to work together.   She put together the expression that represented the xth step.  Yes it took a while, but that was an amazing day of teaching.  I felt like it was a day that I live for when a student "gets" it.  A student finally figuring out what x is in an algebra class. Thank you Fawn Nguyen for visual patterns and Micheal Fenton for a format to teach visual patterns.

Here is another girl explaining the problem.  She did her work OUT of class on her own.  This is amazing work on Independent Day.




The Downs
So not all things can work perfectly.  That is certainly the case for me.  I had two students email me this past week with frustrations about the Blended Learning process.  They don't feel like they are getting enough practice.  These are strong students too.  I need to listen to them and try to improve the way that we are doing things.    
Planning:  Am I giving the students enough resources?  Am I providing the structure for the students working outside of class?  I'm not very confident right now.
Getting Enough Math?  I continue to struggle with the idea that the students are not getting enough math.  I don't see it happening (because they are not in my sight two days a week) so it is not as easy for me.  The balance is trying to give enough resources for students who are out of class and also make them appropriate for where their learning is.  If it is too tough, they can't complete it.  If it is too easy, then they tend not to do it.  We must keep our ideas and our routines fluid to see if we can improve them.  I certainly do. 

Refining
Since we are always learning we must always refine our teaching.  That is certainly what I'm doing now.  I am trying to provide the right balance of digital resources and practice.   I'm now working on a document for the chapter that we are working on.  I wouldn't call my document a Hyper-Doc.  However it is similar.  Below is the document I'm working on right now for the chapter we are in. Note:  this document  Always learning.



Tuesday, February 28, 2017

Feedback with a WORD

Feedback is important.  Here is an idea to try to get some more feedback to our students.  Give them a WORD that represents them.  Give them a WORD for them.  No other student in the class has that word.  That means no repeats in that particular class.  (I have 4 classes so I used some words repeatedly in different classes)




Students like this kind of feedback is that it is personal.   It is a way that they stand out to me and most students like that feeling of being special.  The second reason that students like this kind of feedback is that it is concise.  It is easy to remember a word.

I was scared to try this at first.  I wondered if the students would not care or think it was silly.  However, I have received a lot of feedback from students saying they really liked hearing something directly about them from me.  It is funny that I'm getting feedback on the feedback I gave.




All the words that I'm handing out are Growth Mindset words or phrases.  Here is a list   http://tinyurl.com/growthmindsetwords They are also at the bottom of this post.

Give your students a gift today.  Give them a WORD!

What do you think?  Do you have any Words or Phrases to add to the list?






Saturday, December 31, 2016

Half and Half: Managing Technology Use During Math Assessments


I'm just saying....this is new for me.  I have tried it once and would love some feedback on this idea.  

Splitting up the time a student is able to use technology on an assessment is not new.  You have seen it before where you give the first part of the assessment as "No-Technology" or "No Calculator" and the second part of the assessment as "Technology Allowed".   So this idea of giving the whole assessment at once and then splitting up the time half and half for "No Technology" and "Technology Allowed" is new for me.  It accomplished a few goals that I had for it.  Let me tell you how I worked it and then you can give me some feedback on what you think.

1.  Give the whole assessment to the students at the beginning of the class.  (You are not giving a part of the test to be no-technology and part of the test to be technology allowed)  
2.  Do not allow technology for the first half of the assessment.  
3.  Then allow the students to take out their technology to finish their assessment.  

Here are the positives.
1.  Students are usually looking at a problem twice.  
2.  Students are making predictions about the problems without technology and then confirming their predictions with technology.
3.  It affirms the use of mental math.
4.  It forced students to make a plan instead of just guessing with technology.

Negatives
1.  It takes away a really useful mathematical tool for part of the assessment.
2.  Students are a fearful to be without their technology
3.  The traditional problem solving approach is thwarted by not having all the math tools available.

Please give your thoughts and ideas in the comment section.

Wednesday, November 9, 2016

Starting the BLENDED LEARNING Journey


Our school district is piloting Blended Learning starting second semester of the 2016-2017 school year.  I am going to teach my Algebra 1 students in a Blended Learning environment.  I'm really excited.  Let me tell you about a few things as I prepare.




1.  Blended Learning is combining the best of In Class learning with the best of Independent (out of class) learning to create the most effective teaching environment for all our students.
2.  We will have approximately three IN-CLASS DAYs per week and two INDEPENDENT DAYs per week .
3.  Independent Day means that students do their work outside of the classroom.  They can go to the cafeteria, library, or a nook in the hallway to work.  They do not have to work on my class at that particular time.    They could also get extra help in the classroom.  The teacher will always be at the classroom on Independent Days.
3.  In Class Day means students will all need to be present for the whole period in the assigned classroom.
5.  Students with a grade of an A, B or C are eligible to use the Independent Day in the way that they choose.  Students who have D's or F's must come to the class everyday.
6.  Google Calendar will help to communicate which days are blended and which days are engaged classroom days.  Our learning management system (LMS) is Canvas which will be where the digital course is hosted.  
7.  Many topics in Algebra are two day lessons.  This is ideal for Blended Learning.  The first day will be our exploration day in the classroom during our In Class Day.  The second day will be the Independent Day in which students will work outside of class to work on a task, video, assignment, discussion, or homework assignment.
8.  During Independent Days students will be have a special ID marker that will allow them to travel freely to and from the classroom during that class period.
9.  I know there is a lot of adjustments ahead.  I think of this process as FLUID and always changing.  ALWAYS LEARNING.



I'm excited about....
I'm excited about the chance to work with some of my students on a one-on-one level.
I'm excited to give more responsibility to my students.  They usually rise to the occasion.


I'm nervous about...
I'm nervous about the amount of preparation it will take to prepare for Blended Learning
I'm nervous about finding a good digital math platform to share ideas and solutions.


Please let me know if you have started Blended Learning.  I would love to hear from you.

Follow our district hashtag on Blended Learning on Twitter #blendedlearning203  




Monday, October 31, 2016

6 Reasons Why I'm Not Giving Worked Out Answer Keys to My Math Students Anymore

                               

I have been giving out worked out answer keys to my math students for years.  These are handwritten PDF keys that I have made showing how I would do the problem.  Homework assignments and review assignments all had a worked out answer key online.  At the end of last year, I started having second thoughts about my answer keys.   And this year, I have completely abandoned them.  Why?  Mostly, I felt like I have been robbing my students of the typical thought process that should happen with any good math problem.  You know, problem solving stuff like creating patterns, accessing prior knowledge, discovery, conjecture, failure and so on.   So here is my list of 6 reasons why I have stopped making worked out answer keys.  Also, at the end of this post, I have a couple of things that I'm now doing to replace the worked out answer keys.


1.  Worked Out Answer Keys Eliminate "The Struggle"
What is "The Struggle"?  I think of it as the tension of which path to take while solving a problem.  This is a good thing.  It is a natural thing.  We all have "The Struggle" with math.  It is the "uncomfortable" part of math.  I love the fact that Brene Brown tells her students that they SHOULD BE UNCOMFORTABLE in her class.  Why?  Because learning is stretching, growing, and being vulnerable to say I don't know.   If we eliminate this "Struggle", we will be taking away the "Joy" of mastering the problem.  And yes, there is "Joy" in a high school math class.  However, with no struggle, there is no joy.  And the typical high school math class nowadays is just that... BORING.
2. Worked Out Answer Keys Reduce Collaboration
Students often use each other to collaborate.  When students have the worked out answer key in front of them, they don't need to work with anyone else to get at the solution.  As a matter of fact, students don't even want to talk to another student for fear that it will mess up their thinking with incorrect advice.  I think it is good for a student to listen to another students advice and be able to discern what is correct and what is not correct.  It is a life skill.  

3.  Worked Out Answer Keys Create the Fear of Being Wrong
Another problem is that when we create a key, we are telling the students that you must do it MY WAY.  Whether we intend that or not, we are sending a message.  Do the problem my way or you will be wrong.  Students get this right away and will not proceed until they know they are on the right track.  They become afraid to try.  Have you ever had a math student say they don't know what to do or where to start?  I think this is a classic "I'm afraid to try something and be wrong".


4.  Worked Out Answer Keys Stifle Creativity and Promote Memorization
I'm coming to the realization that creativity comes from the need to be creative.  If we never give our students the opportunity to be creative, they won't do it.  My own most creative moments have arisen because I had thought long and hard about some problem and couldn't get anywhere.  Then, I would usually be doing something else, or exercising and think...VIOLA, I need to do it this way.  The worked out answer key never gives our students the a chance to think long and hard on a question.  It gives them the answer. It really never gives them the chance to be creative.
One thing I have been trying to avoid is having my students just remember the steps of how to do a problem.  When students are memorizing the process, they are not really understanding the math.  Typically this type of math memorization does not last too long either.  Students might be able to repeat it for the test the next day, but is not in their math "tool box".  When students see answer keys, they try to remember the steps of a problem instead of actually thinking through how to do it.
5.  Worked Out Answer Keys Encourage Short Cuts
Can you imagine if someone EXPLAINED the solution to Towers of Hanoi to you before you actually tried it?  That is not the idea of a puzzle.  The idea of worked out answer keys is so that students will work out the problem on their own, and then check with the worked out answer key to see if they are correct.  This doesn't usually happen.  What end's up happening is the students will have the problem and the answer SIDE BY SIDE.  So when the student gets even the least bit anxious about not knowing what to do, they look at the worked out answer key.  Go ahead and try the puzzle below.  Towers of Hanoi  I almost can guarantee that after you tried Towers of Hanoi the first time you realized right away there is a better way.  You worked at it.  You figured it out. And you tried something different.  This is called LEARNING!  Giving worked out answers is like explaining the solution to Towers of Hanoi to someone BEFORE they try it.

6.  Worked Out Answer Keys Decrease Questions.
I have found that when students have the worked out answer key, they don't need to ask questions. Worked out answer keys make it easier for us, but not so good for students in the long run.  Questions are the essence of learning.  We want our students to ask questions.



Two Alternative Ideas to Worked Out Answer Keys
1.  ANSWER POOLS
Answer pools are the answers to the problems in RANDOM order.  First of all, the answer is not worked out.  Secondly, they know that if their answer is not in the pool, they have made a mistake.  Then the students will keep trying.  Click here for an example of an answer pool.  Many times I put too many answers in the answer pool.



2.  Public Posting of Student Answers
Students answers are different than the teachers answers.  That is because the student is not sure if another students answer is correct.  It gives our students the analysis skills.  They look at another students work and glean anything that they can from it.   Sometimes the student might consider different approaches to problems depending on the solution given.    Example of a Padlet with student answers posted.  I like Padlet to post answers.  However you can use any discussion thread to accomplish the same thing.


What are your thoughts?

Friday, September 30, 2016

Ask Me a Question

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?