Helping a friend with Math

Today as I sat for my pedicure (forgive me, I was supposed to be doing my homework! Report cards are due soon) my manicurist's son was upset. His mother thought that math was just facts and that to do "math homework" it should be worksheets with drill and kill questions. Martin tried to explain to his mom that math was much more than that. (He is in grade 5). He explained to her that the thinking games on a math site that look like computer games, is in fact practicing math. I pulled out my iPad and had him work on the app Dragon Box (ok, I've said it before, I love this game!)When I told Martin to play it, He was adament that it was NOT a video game (as he was grounded)! She agreed when I explained the algebraic connection of isolating the variable -- the box alone on one side and he played and got to the third chapter before I was finished! I told her that I would help her explore more math and science "games" on the web for the summer! Does anyone have any other suggestions? Thanks!

Math and Music

After reading some of these blogs, I like the idea of connecting math to the arts. Let's be honest, math is not everyone's favourite subject! As a teacher, being able to connect math to different subjects is key for students (for whom math is not their favourite subject) in order to relate to the math world and understand why we need math.

For myself, this was not always an easy task. This website is great for connecting math beyond school.

http://mathcentral.uregina.ca/beyond/articles/Music/music1.html

This link will take you to the part of the site that specifically connects math to music (something that I find is not done that often). It connects music to things like fractions (a more obvious connection) and the Fibonacci sequence ( a less obvious one).

You can search in the "math beyond school" section anything that would like to relate math to. This would be a good activity to do with students during class time OR integrate this website into a project.

Enjoy!

How to Marry the Right Girl: A Mathematical Solution

I found this when looking through a website; the title seems humourous, but it actually explores the method of optimal stopping, or considering the "Secretary Problem".  When faced with many choices, a person should go through the first 36.8% of their sample, and not choose anyone in that first batch.  After the first 36.8%, you should stop at the one that you like.  Either offer the job (or propose or whatever) to the first one that you are satisfied with and forget the rest.  This is more strategic and likely to bring about happiness more than random chance, thus, mathematically makes sense.

The problem is explained in a book by Alex Bellos, The Grapes of Math, and discusses Johannes Kepler's problem in finding a wife.
Short but interesting read.  Something that might be a good high interest activity in a math class; read the article, and have students make up their own "Secretary Problem".

Link to article:
http://www.npr.org/blogs/krulwich/2014/05/15/312537965/how-to-marry-the-right-girl-a-mathematical-solution

What do Survivor, An Executive Superintendant, and the Mathematical Processes Have in Common?

There is more than one way. As I was watching Survivor with mom last week, which is her favourite show, I made a connection with math in the way that the contestants were going about the challenge to win immunity. If you have the time to watch the challenge, you will see what I mean.

At about the 1:50 mark, the commentator notes how Spencer is "struggling" and Tony is off to a fast start. Tony it should be noted, uses more of a trial and error method using his athleticism and speed, while Spencer does everything more methodically, trying to think his way through each part of the challenge without making a mistake. And at 4:30, the commentator again notes just how far ahead Tony is.  As much as I want to tell you about how it ends, I'm going to leave you in suspense hoping that you'll watch the video!

The point is that even though these two particular contestants used very different strategies, both strategies worked better than the other at different points.  It should also be noted that if Spencer used Tony's method and vice versa, each might have struggled rather than have any success at all.  What does this have to do with an executive superintendant and the mathematical processes?

In a May 16, 2014 CBC article, Hamilton-Wentworth District School Board executive superintendant Manny Figueiredo said, "We need to understand that there's more than one way to teach math. Some students might learn using concepts like borrowing and carrying over, while some might learn better using pictures and language."

If we take Figeiredo's quote and what we see in the Survivor video, and connect it to the mathematical processes, I think we should get a good idea about how we need to be teaching math. Here are some selected quotes from the curriculum:

"Teachers...  help students to develop and extend a repertoire of strategies... when solving various kinds of problems."

"Good problem solvers...  recognize when the technique they are using is not fruitful, and to make a conscious decision to switch to a different strategy, rethink the problem."

"Students need to develop the ability to select the appropriate electronic tools...and computational strategies to perform particular mathematical tasks."


 "Developing the ability to perform mental computation and to estimate is consequently an important aspect of student learning in mathematics."

It really isn't enough to simply teach the equation of a line, how to find the middle of a line segment, or how to solve for a variable.  According to Survivor, Figueiredo, and the curriculum, we should be taking a wholistic approach.  We shouldn't just do this to reach more learners, but also to teach our students to think on their feet and adapt to the situation. That would be to create a critical thinker. Do you think that if Tony or Spencer had changed their approach at some point that the race might not have been as close as it was? It's food for thought.

Constructive Feedback

             In math, I think it is common, when marking, to have the attitude "its right or its wrong". Consequently, this results in either a check mark or and "x". It is important for teachers be constructive with their feedback. What has been done well? What needs some work? What are the next steps the student needs to take? I first saw the following exercise during my undergraduate degree in a course called "Mentorship and Learning". I have also used it with my own students during placement to help them to understand the importance of constructive feedback during peer assessment. It is not enough to say: "good job! awesome!". We need to be specific in our language. I hope you will find the following exercise as helpful as I found it.

             During this exercise you select 4 volunteers and have them leave the room. With the remainder of the class you give one person a tennis ball and have them put it in their desk. Each of the volunteers will come back into the room one at a time and be told to ask 3 people of their choice 3 yes or no questions to help them find who has the tennis ball. Before each volunteer comes in, the class is given instructions on how to answer the question. In between each question the volunteers will be told to move on to the next question quickly.

             The first volunteer comes in and asks their questions. The class remains silent and does not answer any of the questions.

             The second volunteer comes in and asks their questions. The class responds positively, but is not helpful. For example: Question: Is the person who has the tennis ball female? Answer: Thats a great question!! Question: Does the person who has the tennis ball have brown hair? Answer: I like the way you worded that!

             The third volunteer comes in and asks their questions. The class responds negatively. For example: Question: Is the person who has the tennis ball male? Answer: That is not a good question! Question: Does the person who has the tennis ball have brown hair? Answer: Why would you ask that?

             The fourth volunteer comes in and asks their questions. The class responds positive and CONSTRUCTIVELY by helping to lead them to the next question so they can find the tennis ball. For example: Question: Is the person who has the tennis ball female? Answer: Yes. That is a really good question. Her hair is very long. You should ask what colour is it. Question: Does she have brown hair? Answer: No she has blond hair and she is wearing a t-shirt.

             By the end of the exercise, the fourth volunteer will be the closest to finding the tennis ball. Each volunteer is given the opportunity to share their feelings about the feedback they received and if it was helpful. The teacher then compares the first volunteer to receiving feedback that consists of check marks and x's. This lets the student know whether they were correct or incorrect, but gives them no information on how to improve. The second volunteer is compared to positive feedback that doesn’t give students a next step. There is always room for improvement and it is important for students to know what they can do to improve their work (being more specific, organizing their work more neatly, including a "therefore" statement, showing all of their work, etc.). The third volunteer is compared to negative feedback where students are only informed that they were incorrect and not given any feedback on what they could do to improve, where they went wrong, etc. The fourth volunteer is compared to constructive feedback where students are given specific details for what their strengths were, what they need to improve on and how. 

             This exercise is very effective in illustrating the importance of constructive feedback for both teachers and students. This is something that would be great for a professional development workshop, as well as for a classroom before student are going to go through peer review, a gallery walk, or some type of peer assessment. I think that it is also beneficial in providing students with ideas for what questions they can ask after receiving feedback. What should I have done differently? How can I improve? Where did I go wrong?

Flipped Classroom in a Math Class

When I came home from school Friday afternoon, my new copy of Professionally Speaking was waiting for me. At our house this can be confusing because my daughter is also a teacher and her copy was there too! When I read the cover, as I was taking it upstairs to get ready for a night of Report Card writing, an article caught my attention. "On the Flip Side" by John Hoffman was about a topic that we talked about in my 7/8 Math course this year. When I first heard about flipped classrooms, I thought what was different from when I went to school and we were required to do a reading about a subject to be prepared to talk about it the next day. ("READ CHAPTER 7 for tomorrow-- there may be a quiz" was the battle cry of my youth.) Today, instead of assigning chapters or concepts to read about, students are required to watch short videos about a lesson (or the entire lesson) and work on applying the learning in the class the next day with the teacher. This concept would hold the students accountable for their own learning. It also states that it is more work for the student but is it? The student is still required to listen to mini-lessons. The student is still required to do practice work on the concept taught. The student is still able to ask questions and receive clarification and descriptive feedback in a timely (and some say more) timely fashion. The student is required to take quizzes and other assessment pieces. To me this holds the student accountable with the same amount of work! How can I incorporate this in my math teaching? I can go back and assign students to create minds on activities about concepts that are going to be taught. I can then tape the students teaching this for the class and have them downloaded to a private youtube channel where students will be responsible for watching and responding to their classmates. This could be the start of something that can be expanded on as we see the benefits of such activities.

JUMP Math

This program is currently being used in Canada for classes 1-8 and uses a balanced approach called “guided discovery”.  Essentially, students explore on their own (with guidance), and go through a series of challenges increasing in difficulty, receiving immediate feedback.  This program allows students to work at their own pace and breaks down lessons into manageable chunks.  This helps everyone learn better, because they move at the speed they feel comfortable and never get overwhelmed with information.  This means LD kids can learn the material just as well as academic students.  Each small concept is immediately practiced and assessed.  This keeps students more engaged.  By learning a small concept, immediately practicing it, then immediately getting feedback, it resembles more of a video game format of a reward system – immediate feedback for accomplishing a task.  Even students with short attention spans can get through the challenges and learn effectively.  In addition, this format of learning ensures that no child gets left behind and greatly reduces the chances of students developing gaps.  Kids get a more solid foundation on which to build in the future.  The JUMP program also provides training and resources for teachers to make implementing the program easier.  For more information, visit jumpmath.org.