Can We Just Take Notes?

Frustration by Sybren Stüvel

The first week of school is drawing to a close. After seven months off it's good to get back into the swing of things. I was greeted warmly by students (some I have taught, others I have not) and staff upon my return. My goal for the first week was to make it fun, or at least somewhat enjoyable. So many students hate math...or so they say. I wanted to destroy this notion during the first week.  I figure if I can tilt a student's perception of math in the positive direction at the beginning of the semester at least we'd be off on the right foot.

I wanted to minimize the amount of talking I did and maximize the amount of talking my students did. I had them working in groups, often up at the board. I was more interested in working on the mathematical processes and setting the tone for a collaborative environment than covering specific curriculum expectations.

We did some estimating, some visual patterns, some problem solving, some data collection and played a game. It was great for me to be able to spend most of my time circulating and listening to the conversations that were taking place and asking questions. I was enjoying it and it seemed as though most of my students were as well. Some of them would get frustrated at the problems we did. Many were able to overcome that frustration and feel the pride that comes from conquering tough problems.

Today I received mixed, unsolicited feedback from every class about how things were going. How did they know I wanted feedback? A couple of students from my grade nine class and one from my grade eleven class all said something along the lines of "You make math fun. Last year I hated math. Now I like it". On the flip side one of my grade nine students asked if we were going to be taking notes in the class. She looked relieved when I told her that we would eventually. Finally, from a number of grade twelve students today: "Can we just take notes? I don't want to do this group work and problem solving". As it turns out I was going to summarize some of the work we had done with a note towards the end of the class. I was dreading it. It was a boring note as the two people who fell asleep would probably attest to. Why would anyone want to do this rather than being an active participant?

The grade twelve comment is the one that had me thinking the most today. I kept wondering what we have done in our school system to make students want to sit around passively, hopefully, soaking up information. I couldn't help but think that we have trained these students to sit quietly at a desk, listen to a recipe and then follow the recipe a bunch to practice it. They would rather do this than think independently or solve interesting problems. It seems that some of my students don't want to experience productive struggle and the sense of accomplishments that comes with coming out the other side of that struggle.

Don't get me wrong. My students are great and I think this is going to be an excellent semester. I believe that many students are very accustomed to (and good at) 'playing the game'. You know the game I mean: show me what you want me to do, help me figure it out when I get stuck, test me on it and give me a good mark when I give you what you want. They know the game well and many of them are very good at it. When we as teachers change the rules of the game the students who are good at it (often the high achievers) get very nervous. They are still going to do well, but they're not as confident about it.

My grade twelve students are likely the students who will experience the most varied teaching methods when they go off to university next year. They will have lectures, labs, group project (formal and informal), open ended projects, etc. I really feel that they have the most to gain by experiencing different teaching methods and yet they seem to be the most reluctant.

One thing is certain. There will be more problem solving and group work throughout the semester! I can't wait.

A Shift in Formative Assessment

Up until this year I have struggled with formative assessment. I get the idea behind it. I know that it's designed to inform both the student and teacher of where students are in their learning. As a teacher I can then adjust my teaching based on what students do and do not understand and hopefully students can focus on what they don't understand. 

In theory it all sounds good but I felt that there was always a huge hurdle to overcome. How could I get students to take formative assessments seriously if it wasn't going to count? We've all heard it before: "Does this count for marks?". To me this question translates into "How much effort do I need to put into this?". I didn't see much point in using valuable class time on an assessment if students we're willing to give it their best shot.

This year I have decided to change my perspective on formative assessment. I realized that formative assessment isn't for me at all. I know how students are doing on certain topics based on my observation and their conversations. I don't need a mark to justify this. The purpose of formative assessment is not to give me feedback, it's to give my students feedback about how they're doing. It should provide them with the tools they need to take the next steps in planning their learning. Following the assessment a student should be able to say "This is what I need to do in order to be successful".

A couple of weeks ago I decided to give my students a formative quiz. I let them know that the quiz didn't count for anything. I also let them know that the purpose of the quiz wasn't to inform my practice, it was to let them know how they were doing. The big difference this time is that I informed my students that there would be no marks on their quizzes. I decided that marks were a distraction from the learning. The purpose of formative assessment had to shift from grades to learning. Instead I provided only feedback. I circled things, underlined stuff, drew arrows and asked questions to help guide their thinking.

Learn by GotCredit

The result is that when the quiz was handed back students didn't just look at their marks and file the quizzes away (either in their binders or the recycling box). There were no marks to look at. If they wanted to see how they did they needed to look at the questions and read the feedback. Reading the feedback led to them asking questions amongst themselves and if needed asking for my assistance. Some of them were upset about making silly mistakes, others were trying to make sense of the topics that they didn't really understand. Not only were they learning, they were learning from each other. This slight shift in focus for formative assessments has made them far more valuable in my class.

Group Test

Last semester I taught the Grade 12 Advanced Functions course. It seemed that every time a test approached a student would ask if they could write the test as a class. We all had a good laugh then inevitably someone would ask if they could write in groups instead. Needless to say the entire class thought this would be a good idea. I dismissed the idea on a number of occasions explaining how it would be difficult to have a good sense of who knew what in a group. My students, however, were very persistent and would ask every time a test was nearing. 

On the second last test of the year (just before the Christmas holidays) a student asked if they could write their test as a group. I jokingly said "Sure" and a student immediately replied "Really?". When I told my students I was just kidding they provided a lot of reasons why such a test would be a good idea, in the hopes of getting me to change my mind. I let them know that I would think about it for a bit and get back to them; possibly a strategy for delivering a delayed "No".

As I thought about it I had a lot of questions about logistics for this possible test. They included:

1. What would such a test look like? Surely it couldn't be a regular test that students worked on in a group.

2. How will the groups be determined? Self-assigned? Teacher assigned?

3. How many students should be in a group?

4. What happens if some group members aren't pulling their weight?

5. Do students hand in one test each or one test as a group? Do they get the same mark or different marks?

6. Is this a bad way to prepare students for University?

Some of these questions and their possible solutions occupied my thoughts for several days before I had the courage to go ahead with it. I figured that if things didn't work out I could always call it a test review and give a traditional test afterwards.

Here are the answers that I came up with to the above questions.

1. The test should be less knowledge based (although there were still some knowledge questions) and should be more heavily focused on thinking and problem solving. The knowledge would show up as part of the problem solving.

2. I decided to let students choose their own groups and as it turns out students tended to group themselves by ability level, which is probably how I would have grouped them.

3. I went with three students in a group. I felt that this would allow for some good discussions while not allowing anyone to sit back and do nothing.

4. This is not that different from any other type of group work (assignment, presentation, etc.). The difference is that here I was able to watch to see who contributed what. It would have been possible for me to assign different marks based on the participation, which I didn't do.

5. Students handed in one test and received the same mark.

6. Perhaps, but it was only one test. Besides, is my goal to prepare students for university or for life beyond university? I would guess that once out of school most of these students will do far more collaborative work than they will test writing. Shouldn't I be preparing them for that as well?

Here are some things that I observed:

• There was no anxiety as students entered the class.
• There were some great discussions happening the entire time
• There was some learning going on during the test. Students who didn't understand didn't just let their group do the work, they were trying to understand it.
• There were no questions that were left blank.
• Students seemed to be enjoying the test.
• Students reported that the time just flew by.
• We had a modified schedule the day of the test. Our class was shorter than normal but I told the class that they were welcome to stay into lunch if they wanted to. Most stayed for the period and most of lunch. I was amazed that nobody just wanted to leave.

Here are a few comments that I heard during the test:

• After some discussion with the group..."I think I understand this now"
• S1:"That works!" S2: "Yeah it does." S3: "We've got it!"
• "YES! That's it."
• "I love this test. It's great to communicate."
• A student to me: "Can you tell me...?" Me: S:"Maybe I'll ask my group."

The test was a big hit among students. They said afterwards that they felt less stressed, they really enjoyed bouncing ideas off one another and wished that all tests could be done in the same way. From my point of view it was a great experience as well. Students were totally immersed in the work, there were lots of great discussions and the atmosphere in the class was very pleasant. It almost felt like a coffee shop, a productive coffee shop.

How did the students do? I would say that they performed at about the same level they normally would despite the test being more challenging than a typical test I would give. My hope is that by the end of the test they came away knowing more than had they written a regular test. I didn't measure this but I suppose a regular test after the fact might have provided some insight.

This is certainly something that I will try again. 

Great Start (So Far)

We have just completed the second day of the semester and I'm having a blast.
I've changed my routine a little(see my previous post) and I have managed to make some changes that are hopefully for the better.

My students are sitting in groups and we've started to develop a collaborative environment that will hopefully continue to grow. Students are not only sharing their work with their groups but with the entire class.

We've looked at some low floor/high ceiling problems and we've spent much longer on those problems than I had anticipated. Longer because students were generally interested in the work they were doing and I felt bad pressing one. My students seem to enjoy the work we've been doing and they seem curious about the problems we've looked at.

I haven't covered any curriculum yet but I'm hoping the time we've spent on developing a good classroom environment will pay dividends in the long run. I know that it has only been two days but I'm hoping for more great classes.

Here are some highlights from today:

•  Had five student stay at lunch to share how they solved a problem I gave towards the end of the period
  
• Heard "I feel so smart"
  
• Heard "I love finding patterns"
  
• Heard "Can't we just take notes and memorize them?"

Hoping to Suck a Little Less

Creative Commons Licensed photo by Flickr user benjamin_scott_florin

After five months off I'm getting ready to start teaching again. Over the course of the past five months I've thought, read and learned a lot about teaching math. I've read a lot of blog posts by amazing math teacher. I took Jo Boaler's How to Teach Math course. The one thing that I kept noticing is that there are a ton of great teachers doing amazing things in their classrooms. Which led me to the questions: why am I not doing these great things? Why is my teaching sub-par? Although I didn't have any answers for these questions I've decided to step it up a little this year. I don't claim that I'm going to be amazing this year but if I can suck a little less that's a move in the right direction.

What do I want for my students?

Comfort: I want my classroom to be a place where students are comfortable making conjectures, thinking outloud and sharing their ideas, even especially if they are wrong. Learning from our mistakes will be very important

Number Sense: I want students to develop better number sense so that they can make sense of the world around them and check to see if their solutions make sense. I'm hoping to working on number sense by using estimation180.com and visualpatterns.org on a regular, if not daily basis.

Collaboration: I want my students to share their thinking and reasoning. I want them to help one another and to learn from each other.

Enjoy Math: My hope is that by doing the above students will enjoy math a little more, be actively involved and hopefully seek out mathematics in the world around them.

To all the great math teachers out their doing great thing: thanks for the inspiration.

Connecting Elementary & Secondary Teachers

CC licensed photo shared by hanspoldoja

A few weeks ago I had a chance to meet with some grade nine math teachers from my school, grade eight teachers from our feeder schools, a guidance counsellor and a vice-principal. As I sat in the meeting I realized the in my 11 years of teaching at the same school, I had never actually met with elementary teachers. This struck me as being quite odd.

The meeting was coordinated by one of our guidance counsellors in an effort to improve our students' transitions from grade eight to grade nine in the area of math. As secondary teachers we shared some information about the content of the courses, but really focused on highlighting the differences in the streams (locally developed, applied and academic) and the pathways students could take based on their choices in grade nine.  We talked about alternate pathways and how there were a number of ways a student could move from one stream to another. The elementary teachers seemed very receptive and asked a lot of great questions. By the end of the meeting I had the sense that many of the teachers felt more comfortable and had more information to present to their students about recommendations for high school. I can't believe that we hadn't done this before.

For me the best part of the meeting happened once the official meeting was over. After the meeting there were lots of informal conversations about "What's the best way to teach X?" or "How do you teach Y?" and the like. It was great to see teachers connecting and discussing math. I think conversations like these give us a window into other teachers' classrooms. They allow us to share best practices, bounce ideas off one another and hopefully improve the way we do business. I think somehow we need to find more time to informally discuss how we teach math.

What does your school or district do to promote discussion between subject area teacher or to promote discussion between elementary and secondary teachers? What more can we do more to ease the transition from elementary school to secondary school?