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.

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
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?  

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)




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






DAY 1 TOPIC: Multiplication

DAY 2 TOPIC: Subtraction
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

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

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
25% of $200

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