Friday, April 3, 2015

Coding & Probabiltiy


I wanted to spruce things up a little in my grade 11 college math class. My students were working on probability and I was looking to make it more interesting. 

I decided I would have them code games that use probability in Scratch. I choose Scratch because it's easy to use and you don't have to spend a lot of time on syntax. It's also free and web-based, which means it will work on any device that supports Flash. By creating a free account students are able to save their work and they can publish their finished products so that other people can play them.

I started walking students through how to simulate tossing a coin. If you're looking for a tutorial, check out the one made by @brianaspinall here. We spent the better part of a period working on this. The next day I was away, but I left this handout. Students were to 'play' with their coin flipper and make observations about theoretical and experimental probabilities. Once they were finished they had to create a similar program that involved the rolling of a die. They repeated the experiments and then moved on to two dice. The last part of the assignment was for them to create a game using the dice. I was hoping that they would create three games: one that was fair, one that was in the computer's favour and one that was in the user's favour. Upon my return I realized that this was going to take to long. I think next time I will have them choose which type of game to make and to explain what makes it advantageous (or not).

What I liked about the assignment is that students seemed to enjoy themselves. They could be creative. Many of them made some very nice looking dice and backgrounds. They had to do some problem solving when the program didn't work. Best of all, they had a chance to make something with what they learned in math. I would certainly do it again in the future.

Thursday, February 19, 2015

Stacking the Odds in My Favour


I'm currently teaching a grade 10 applied math class. I'm following @MaryBourassa's lead of spiralling the curriculum (Thanks Mary!) and I'm really enjoying it.

Today we had a quiz and a number of my students were quite nervous. Just before class started one girl said to me that she was going to fail the quiz. I reassured her that she was not going to fail. I told her that if she thought about the questions and wrote something down she would do just fine. She didn't buy it. Her response was "No I'm going to fail. I bet I fail. I'll bet you $5 I fail". I smiled at her and told her that I couldn't make that bet because she could easily make things go her way. I was glad to hear her response of "I would never fail on purpose".

As the class worked on their warm-up I thought about how I could guarantee a win on this bet I wasn't going to make. I didn't want to win to get $5 or to say that I was right. I wanted to win to help this student and others who were feeling the same way boost their self confidence. This course is typically comprised of students who don't feel comfortable in math and who don't think they can do math. Today, boosting their self-confidence was my number one priority. As I handed out the quiz I informed them that they would be allowed to use their notebooks. This made many of them feel more at ease and as it turns out, few of them used their notes. I will still get some good information on what they do and do not understand and I will have an opportunity to assess them again at a later date. I'm even toying with the idea of not including a mark on the quiz. I may just provide feedback.

Saturday, February 7, 2015

Sine Law

Last semester I taught the Grade 11 College level math class. I was very disappointed to see that 12 out of 26 of my students had failed the course. Luckily, I get to teach the class again this semester. This means I can make some changes in the hopes of improving my students' understanding. THere is a summary of my first change.

Friday I was teaching the Sine Law. I have in the past created a dynamic geometry sketch. I manipulated it and as a class we noticed how the ratio of the side length to the sine of the corresponding angle was equal for all pairs of angles and corresponding side lengths. For whatever reason, last semester I didn't even show the sketch.

This semester I decided to have the students do the investigating on their own to see what they could come up with. I provided them with a link to the simple worksheet below.



I wanted them to look at the ratios (mentioned above) from a number of different triangles so I had them complete this handout. We completed the first two entries in the table together before I turned them loose. I figured that the table would be fairly straight forward, but I was pretty confident that questions 5 and 6 (where students had to apply what they learned) would be a challenge. Sure enough I had a number of students call me over and say "I don't know what to do here". My response was to have them tell me what they discovered earlier and then tell them to use that information with what was given in the question to set up an equation. That was enough for a number of them to make the connection and do the problems...without any direct teaching. They figured it out on their own. I was blown away.

We had some guests in our class that day. During the activity, one of the guests said to me that this isn't an activity that would be typical in this type of class. I think he is probably right and I think that is part of the reason why the course has such a high failure rate. I challenged my students to learn something on their own and they did it. I think (at least I'm hopeful) that we have established the expectation that students will be active participants in their learning. Now I just need to find a way to maintain that expectation for the remainder of the semester.

The only disadvantage I saw to Friday's class was that many of my students were away. I will summarize the work we did on Friday and give everyone an opportunity to practice. We'll see how it goes.

Monday, January 19, 2015

EQAO Reflection

Our grade nine students wrote their Grade 9 Assessment of Mathematics (EQAO) last week. Often during this time I reflect on the process, because really what else are you going to do for two hours while supervising. This year my thinking wasn't about the pros or cons about the test but rather the way we evaluate it. The test is sent off to be marked provincially but before that happens schools have the option to evaluate it in order to include some or all of the mark as part of the student's final grade. The thinking here is that if it counts for something then perhaps students will take it seriously. At my school we count the test for 10% of a student's final grade. Then about a week later they will write the final exam that counts for 20% of their grade.

The test consists of two booklets that each must be completed in an hour. Each booklet is made up of 7 multiple choice questions, followed by four longer 'open response' questions then finishes with 7 more multiple choice questions. Once the second booklet is completed students are asked to complete a questionnaire.

My observation has been that more often than not students come into the test under prepared and it serves as a bit of a wake up call to them. They then (hopefully) use the remaining classes to prepare for the final exam.

This year I have decided that I am not happy with counting the test for any portion of the students' final marks. In fact, my students did so poorly that after the fact I told them that I was not going to count it at all towards their mark and here's why:


1. Time

Many students did not have time to complete the test. They had an hour to complete each of the two booklets. For the second year in a row my strongest students did not complete the booklets on the first day. These students were very concerned about the impact it was going to have on their overall grade. Rather than providing incentive to do well it caused a great deal of anxiety. As a math teacher my goal is to help students reduce their anxiety towards math not contribute to it. I also try to evaluate what a student knows and does not know. If a question is left blank I have no idea if it was because the student ran out of time or because they did not know how to do it. By removing time from the equation I can make a better judgement of what the student know.


2. Multiple Choice

I have decided that I disagree with the multiple choice questions. They obstruct my view of what the student does or does not know. Some students will get the correct answer by guessing. Others will get the incorrect answer by guessing. In either case, I am unable to see the process that allowed them to arrive at their answer and as a result I am unable make a true judgement of their understanding of the material.


3. Feedback

I don't know much about the official feedback students get so if I'm wrong here let me know. I believe that tests get marked in the summer (the rest of the cohort will write in June) and a mark is returned to the students in the fall. This is far from immediate feedback and is anything but descriptive. Not very useful in my mind. As a teacher I can mark the work, but I'm not allowed to copy anything. This means that I can't show students where they went wrong. I can tell them that they messed up on the bicycle question but unless they can see where, I'm not sure that's useful.


4. Justification

I'd be hard pressed to justify any mark to a student or a parent given that the tests get sent off, never to be seen again. Students should be able to look at their marked work and question my judgement, which is sometimes right and sometimes wrong. In fact, I enjoy when students start questioning my evaluation as it often brings out what they truly meant to write or allows me to better understand their misconceptions.


5. Rationale

When students ask why the test has to count for a portion of their grade I struggle to give a valid reason. I typically say something along the lines of "If you're going to spend two days writing it, we may as well give you some credit for it". It's not an answer I'm comfortable with but it's all I have. One of the reasons I'm not comfortable with it is that the vast majority of my students perform much worse on the test than they do on the final exam. We could probably discuss what that says about my teaching, but let's save that for another post. The real reason that we count the test as a portion of a student's grade is that we believe that this will make them take it more seriously, which means they will perform better, which will make the school look better. Given that twelve out of eighteen students in my colleague's class said on the survey at the end  that they didn't know if the test was going to count (and yes he did let them know on numerous occasions), I'm not sure that counting it is a good motivator. Besides, is this in the best interest of the student or the school?

I'm curious to know whether counting the test as a portion of a student's grade makes them perform better. What does the data say? Do schools that count the test outperform those that don't? Is this information publicly available? Are there any schools that don't count the test?  Or does everyone count the test so that they don't look bad? Is this in the best interest of the students?

What does your school do about EQAO testing in grade nine math?

Tuesday, November 18, 2014

Triangles in Scratch

The video below is a follow up to the one I made here. This one is not that much different. Instead of drawing a square I show how to draw an equilateral triangle. To me the interesting part of the tutorial is having students play around in scratch to see if they can create an isosceles or scalene triangle. I haven't had a chance to do this in a class yet, but I'm hoping that there will be a lot of trial and error and eventually some students will get close enough. Close enough that they will be able to answer the questions "What is the sum of the angles in any triangle?".

The second challenge is to have students draw a regular pentagon, hexagon, etc. In order to do this they will have to determine the sum of the angles in each of these figures. We've done enough visual patterns that I hope this will be easy for them. I'm hoping this will be a fun way to cover some of the geometry in the grade nine math courses.

Give it a try.


Monday, November 17, 2014

Playing With Rectangles



I'm currently teaching my grade 9 students about linear relationships. We create scatter plots, draw lines of best fit, use the information to make predictions and so on. As we came to the end of the unit I felt as though we hadn't done enough. I felt that somehow it would be far more interesting if we could connect this section of the course to another section. The measurement unit seemed like a simple connection.

I gave students 12 straws and asked them to find the rectangle that would give the largest area. They messed around with the straws, made tables and graphs and determined from their graphs what the largest possible area was. Next I gave the 12 linking cubes and asked them to create the rectangle with the smallest perimeter. Again they played, created tables and a graphs but the solution wasn't as obvious.

None of this work is ground breaking or much different from what I have done in the past. The only differences were that I cross pollinated (some might say spiralled) the units. I think this helps show students that mathematics is interconnected, that it's possible for units to have a common thread. The other difference was that I physically gave them objects to manipulate, which is different from how I taught this before. In the past I would have them draw out rectangles. I think something gets lost here. It was very obvious to students what was going on when they were manipulating the physical objects.

Although neither of the graphs were linear it was useful to create them and to discuss what type of correlations there were and read information off the graph. We will revisit this concept again in the measurement unit. I look forward to seeing how well they retain the information.

As a side note, the graph of the maximum area was a parabola as expected. Without thinking too much about it, I expected the perimeter to do the same. As I saw students' graphs I wondered why they were the shape they were. I did the algebra and recalled that the resulting function was a rational function. Looks like a good problem for the grade 12 students. Tomorrow: Determine the function that minimizes the perimeter of a rectangle.

Saturday, November 15, 2014

Let's Start Coding

The second week in December is Computer Science Education Week (CSEd Week). I get really excited about this because more teachers start talking about coding. The trouble with this event is that it often seems to be a one off event. Teachers give up an hour of their curriculum time to participate and once the hour is done they tend to move on. It's great that they participate but it could easily become part of any teacher's curriculum. I realize that it's "one more thing" to do but it can be very engaging for students and I believe that it really helps develop skills that are useful in many disciplines both in and out of the class.

Why are teachers not extending coding into their regular routines? I think for many of them it's about comfort. The Hour of Code tutorials are great. They are well laid out and could be coordinated by anyone. If you're going to start building coding into your classes, however,  you need to understand the tools a bit and you also have to find a way to weave in some curriculum expectations. No small task.

Brian Aspinall is a teacher who has not only embraced coding in his class but has taken it upon himself to help other teachers see how their students can code and meet curriculum expectations at the same time. He uses Scratch, which is really easy to use. You can find his videos here.

Brian's work had inspired me to play around more with Scratch and to find more ways to work it into the curriculum. I've decided to create videos that introduce some coding ideas but also create a challenge for teachers (or students) to work through. Hopefully, some teachers out there will decide to follow up on the challenges. If not, at the very least I will have thought more about how coding can be woven into my courses.

If you're interested in integrating computer science into your curriculum check out the #CSk8 hashtag.

Here's my first video.