Count Down – Part Trois

A few months ago I wrote about a book I read called “Count Down” which related the story of a group of mathematics students and their journey to the Mathematics Olympiad. Today I had my own experience as our students from St Michaels University School went to the Math Challengers competition at Camosun College.

While there are many events that happened today I could focus on in this post I want to highlight two students who took a chance and went to the competition. These two students were reluctant to come. They are actually enrolled in the grade 7 class at school but went to this completion because they have an aptitude for mathematics. It could be said that it is their age that made them reluctant but I can not say this for sure. It could also be that attending a completion at a post secondary institution when you are in middle school is intimidating. To be honest the reason really does not matter. What matters is the look of excitement and joy that was on their faces after the first round. What matters is that they found a new aspect of mathematics they had not found before in quite the same way … the joy of solving a tough problem that they had not seen before.

To all the teachers and students who students who have not been to a math completion before but have a chance to go I encourage you to give it a try. What do you have to loose.

PS. To the students who came today, well done. To Mr. Williams, thanks for all of the hard work. To the people at Camosun who hosted the event you have my gratitude and that of the students.

Is it personal or professional?

I remember a few months ago attending a session where the talk was centred on encouraging people to use Web 2.0 tools. I always like to try new things so I was more than happy to jump in. Indeed I thought this may be answer to many of my problems. I am a busy person in both my professional and personal life. Like many other people I work all day and then go home to volunteer for a couple more things just to round out the day. I don’t mind doing this. I would even go so far as to say it is these volunteer organizations that help me fill in some of the gaps in my person and professional life.

The real trick in maintaining balance is … communication. I need to know what is happening and get the word out to the people in my various circles. Sure social media, email and texting make it easier but it can result in information overload and an identity crisis. How do we separate … personal and professional in a web 2.0, web 3.0 or web 4.0 world? Is there a worry that what we think is “right” today is wrong tomorrow? What impact does this have on our personal life? What about our professional life?

I have chosen to error on the side of caution. I have seen friends delete Facebook accounts after taking a personal path that has changed or impacted their professional lives. How do you separate personal and professional in a world where information is readily available and we all still want our privacy?

Rubrics to Marks

It has been a busy couple of months getting settled into a new position as a middle school teacher. This past two weeks has been especially busy as the second set of report cards for the year is being prepared to be sent out. The first set of reports did not seem nearly as hard to construct as they were interim reports and designed more to highlight potential issues and strengths in student learning. This set of reports has a different flavour to them. Why? This time marks must be included.

What is it about marks? All of the students in my class want to know what they “got.” The main question they ask is “did I get an A?” I think I would ask the same thing if I were in their position. Indeed I think I did every time I took a course. I am not so sure that this is the question to ask however.

It seems to me the real question is “do I understand the mathematics?”. After all unless the only goal is to complete the course there is a rather high probability that the topic covered will come up in successive mathematics courses or (heaven forbid) in a situation outside of school.

This brings me to assessment and report cards. In one section of the report students are identified as “not yet meeting, approaching, meeting or exceeding expectations” based on the learning outcomes. This is consistent with the learning happening in my classroom as I have been using rubrics to do most assessments for the year. Students are given the rubric when the task is assigned and are explained the expectations both verbally and in print. I have moved away from a mark based on either a percent or letter grade. I have instead talked about student performance based on the learning outcomes.

Yet each student must also be assigned a grade as per the Student Progress Report Order (This Ministerial order guides reporting within British Columbia). The question I have been grappling with is how these two are liked. Don’t get me wrong I do think there is a correlation between the two but I am not sure it is as easy as saying you are meeting all of the expectations so you get an “X” on your report card. I believe that a student should meet all/most of learning outcomes to be a “B” student. Likewise I think a student should meet/exceed all of the learning outcomes to be an “A” student. So where does a student who has achieved a meeting expectations on all of the learning outcomes fit? Is s/he an “A” or a “B” student? Is there a consistent way to determine this? Is there a need for letter grades when the focus is on student learning? Are others struggling with this question?

Cartesian Plane

I don’t know about others but I find it hard to believe that Canadian Thanksgiving is here already. It seems like only a few days ago school started. I guess the old saying “time flies when you are having fun” holds true.

This past week the middle school teachers at school were starting to investigate transformations on the Cartesian plane. We decided that a good place to start was with a scavenger hunt. Using Google Earth (Satellite view in other programs also works) we obtained a satellite view of the school. Gimp then provided the rest of the imaging that we needed to complete the task as a grid was superimposed on the satellite image.

Students in the 5 grade 7 classes then had to make some decisions:

• What is the best scale to use?
• Does it matter which scale is used?
• Is there a need for consistency?
• Where is the origin?
• Does it matter where the origin is located?
• Do people actually have to make these decisions in “real life?

All of these questions were great ones. I felt some real connections were made up to this point. The mapping aspect afforded an opportunity to discuss conventions and the need for consistency. Just like any other language it is important to have these conversations so we would all be talking about the same thing when we got out side.

Once the “Cartesian plane” was standardized questions were generated for the scavenger hunt. For example, “(10, -5) How many windows are on the south side of the building?” Since classes are less than an hour teachers agreed that we should limit the number of questions to eight. This would allow for 2 questions in each of the 4 quadrants. We had hoped that students would plot the coordinates and then proceed on their quest. This did not happen. As a result a few groups were unable to complete the quest in the time allotted.

This activity was great for examining the Cartesian plane, however, what were the other lessons:

• Planning a problem solving strategy can be beneficial (those who plotted points first saved themselves a lot of running around).
• The Cartesian plane (or any coordinate system) can be used to define a location in space.
• Connections were made between a map and real objects in 3-D space.
• Students ventured into areas of the school they had not seen since arriving at middle school.
• Students can quickly determine if they have read coordinates correctly as well as a need to standardize the format for discussing coordinates.
• Holding the map in the proper orientation and being able to orient the map based on physical characteristics in 3-D space is important in map reading.
• Read instructions and questions carefully.
• Working in a group (students were in groups of 3).
• Communication skills.
• Exercise

The grade 7 teachers hope to use this activity as part of the transformations unit in the near future. More on that in a separate post.

If you give this activity a try, please let me know how you improved on it. If you have tried it in the past … what worked for you?

3 Question Strategy

This week I tried a teaching strategy to promote more collaboration and independence from the teacher.  I have not tried this strategy since I was teaching in the arctic and I was not sure what would happen and how the students would react. I call it the 3 question strategy and while not revolutionary it has had interesting results with more to follow.

The premise of the 3 question strategy is simple. Provide students with an assignment, instructions for doing the assignment and plenty of time to complete it. Once all 3 of these conditions are in place  the class is only allowed to ask the teacher three questions related to the assignment. What can the 3 questions be? Anything that relates to the assignment. For example, “Do I need to write my name on the assignment?” would count as one of the 3 questions. Is this a good question to ask? Probably not in my opinion as it borders on the obvious. Is it one a teacher would get asked? Yes! Should I really have to answer this question? Not in my opinion. I think the students in my class are very smart. I think the students in most classrooms are very smart. In fact I think the combined brain power in anyone of my classes (or almost any other classroom) is much smarter I am. The goal is to tap into this brain power and have it would as a cohesive unit when needed. So far I am finding, as I did in the past, that this strategy helps to move closer to this goal.

As we move through the 21st Century it is important to promote group work and collaboration therefore, I think it is important to promote activities like this so students get used to talking to each other, asking each other questions, solidifying their understanding by explaining solutions to each other. In this particular assignment I made it even more open by providing time for students to draw upon sources outside of school such as parents, the internet and anything else they could think of. In this respect, the 3 question strategy works for me in developing these skills. Is this not how we all work everyday? Calling on colleagues for the majority of our work and only going to the “boss” when absolutely needed.  (I don’t like using the word boss in a blog about education but it seems to be appropriate in this context no matter the reader)

So what are some of the pitfalls?

• I have found that students spend almost as much time figuring out which 3 questions to ask as they spend trying to finish the assignment. I think this can  be turned into a positive as well if you redirect as it provides a good way to talk about time management and first things first.
• Students WILL consider this cheating if they have not done it before. This is the point when a good “real life” story about hoe mathematicians work is very helpful.
• It can be scary … some of the students are nervous that they will not hit the target for the assignment. I don’t consider this a big issue as those who collaborate will create a better assignment by talking it over with peers. Those who don’t collaborate will not do any worse than they would have in the past working alone.
• The right type of assignment is needed. I have chosen geometric constructions for my first one and since the work must be original the opportunities to “copy” are minimal at best.

If anyone else gives this a try I would appreciate knowing how they make out. I look forward to the results on Monday.

Working Smart

I had a great class today on geometry and I would like to say it was all on purpose but it wasn’t. The students made it a great class by one simple question. I am sure that every teacher out there has encountered this question or some form of it. It is not a tough question to ask but it can be a tough one to answer. I know the curriculum is full and there are lots of outcomes to cover but taking the time to answer this question, at least sometimes, can more than make up for time later. Can you really pass up the time to develop thinking skills?

By now I am sure you are wondering what this question is … quite simply the question that the student asked was … “what happens if …?”

In the context of today’s lesson we were looking at geometric constructions of parallel and perpendicular lines with a compass and straight edge.

We have been working on this for a few days and the students are pretty good at it. I have modeled the constructions on the SmartBoard and often ask students to come up and perform the constructions.

Today one of the students asked “what happens if the lines are not horizontal?” It had not even dawned on me that all of the constructions they had done were all horizontal. I decided that I would ask a few students to help me figure out what happens if the lines are not horizontal and the implications on the constructions.

While some students worked on an assignment due next week some of the students who were further along explored this on the SmartBoard. The advantage of this was that I could pause those working on their assignment to see the implications of doing constructions when the lines are not horizontal.

So what was the key thing I learned today … using the SmartBoard as a digital recorder to explore the “what happens if” questions is definitely a way to work Smart.

Basic Facts – Cards

I expect that the day I retire there will still be as much talk about basic facts as there is today. It seems to always crop up as part of a conversation about mathematics.

I wanted to mention one strategy I have found particularly effective. I have to admit this was not my idea and like many other strategies I use it was borrowed from my wife, Darlene. Cards can be an effective tool for working with number.

When students arrive in class I have them break into teams of two. In some cases I create the teams and in other cases I have them choose the team. It really depends on the day. I have found that creating teams can  be an effective and non threatening way of not having some students sit by others later in the class.

There are many games that can be played but the premise it pretty much the same for all of them. The cards are divided evenly among the students. The value of each card is set prior to starting (aces can be a 1 or 11, face cards are 10, jokers are worth 0).

Each student flips over one card. The desired operation (multiplication, division, addition, subtraction) is completed based on the cards showing and the student who get the correct result wins the cards. In the case of a tie the cards stay on the table and the student who wins next gets all of the cards.

There are of course some twists that can be used to make things interesting such as making red cards are negative and black cards are positive or using three cards.

We have been doing this for the first 5 minutes of class and so far it has resulted in:

• students coming to class quicker
• a non threatening ice breaker which starts class with a bang
• time for me to play with students to see how well they know their basic facts
• lots of laughs

If anyone has other ideas which work I would love to hear them.

This post was inspired by a recent tweet about an article posted by William Emeny

Tessellations and the iPhone

I am very proud of my son. This summer he started his own little business cutting lawns in the neighbourhood

with the intention of saving some money to buy a computer. After a lot of work and a lot of debate he decided to get an iPhone. I was happy with this decision although it will cost me for his monthly plan (a different post on that later).

This weekend we went to the Lower Mainland for a British Columbia Association of Mathematics Teachers executive meeting. On the way we stopped at IKEA. I had told my son that we were going to be working on tessellations and he offered to take some pictures to use in my classes.

I have posted a few of the pictures within this post but what I can not post is the conversations that he and I had about which patterns were, and were not, tessellations. It was a great activity to see how well he understood the concepts and as a result it is one that I think I will be using in my class as we start to move into tessellations in the coming weeks.

I must provide a bit of a disclaimer … my son is in grade 6 and tessellations is not in the BC curriculum until grade 8.I think this low stress fun way of doing a scavenger hunt was a great way for him to pass the time in IKEA and made the trip enjoyable for him. Much better than sitting in a chair and playing games or continuously asking when we are leaving. Mathematics is everywhere … you just need to look.

Math Happens

It was a great week for me at school this week. Sure it was the first full week and it was busy but I felt charged. Great students, great parents and great people to work with. The math team at the school is second to none and always welcome to help out. The other staff members are equally welcoming and always welcome my “newbie” questions with a welcoming smile and all the help you could hope for. I am tired but I am also charged.

Today was a particularly good day. It was a day when “math happens.” Earlier in the week math teachers dressed in togas and went outside to talk about how mathematics would have been discussed in the time of Pythagoras. The students enjoyed using the sidewalk chalk and sand to bisect angles and create perpendicular bisectors. I really enjoyed the comment from one person who asked what the “alien language was in the parking lot was for.” Although it was in jest it was nice to raise the profile of math.

This afternoon went equally as well. I started the afternoon hoping to have students draw some circle and start to talk about circle properties, how to use a compass and some of the advantages of this tool. I still managed to do this but not quite the way I planned. It was a day when …. math happens.

As the class walked outside staring us in the face was a great opportunity to do some practical math and have some fun. There was nothing less than several basketball hoops with no “key” (free throw lane) painted on the pavement. As a result, student started with some string and sidewalk chalk and were tasked to create a basketball “key” (free throw lane) where one did not exist. The task involved students:

• creating a plan and defining the task
• working collaboratively in groups
• determining the main characteristics of parallel lines and circles
•  developing a strategy to create parallel lines using string
• developing a strategy to determine the centre point for the circle between two parallel lines
• using a referent (height of a student in one case and height of the hoop in another) to add the foul line at a reasonable distance
• solving and correcting errors (yes there were a few and that was some of the best learning)

I think in the end the students enjoyed the lesson and the problem solving involved.  Best of all students got to shoot some free throws at the end of the class.

Score one for mathematics!!!!

WOW

After 12 years in curriculum development at 3 different Ministries of Education I had my first day with a classroom of students. It has been 12 years since I was in a classroom and I was a little nervous but that has passed. So what were my impressions coming back after so long … the only think I can say is WOW! What a difference!!!

The energy in the room was contagious. Students desire to learn new things and pass on what they know to new students was electrifying. The students could not only be heard but felt as activities throughout the school shook the building. The place was alive.

This week has been filled with meetings, getting to know the new school and it’s procedures which has been great. People told me all week that they could not wait for the students to come. Now I see why.

So what more can I say but WOW. It is going to be a great year.