Category Archives: Math

School IS a Student’s Real World

runningI like to think I live in the real world even though I am an educator and for years my students thought I lived, slept and ate in the school. Students would stare at me when I was in public and for the longest time I would check for the roll of toilet paper stuck to the bottom of my shoe, or look in the mirror to see if I still had a milk mustache (or something worse), or was I in one of those dreams where I forgot to get dressed and was still in my pyjamas? And then it dawned on me that they were used to seeing me in their world at school and the world at Wal Mart was a seemingly different place. Many people say that in school we need to present real world problems for students to solve and I for a long time I went along with it. But then I heard Tom Hierck at SELU say that “school is a student’s real world”.

In education I hear people say that school does not reflect the real world and with the latest spotlight on assessment, I really hear the complaints that our current practices do not reflect the real world nor prepare children for the real world. And that makes me think about the real world I live in.

I enjoy running. Most of the time. Sometimes I simply enjoy the scenery, the weather, or I feel grateful that I am able to run where I want, when I want. That I am capable of running. And sometimes I think. What I like the most about running is allowing my thoughts to run wild as I just try to put one foot in front of the other even if it is at a turtle’s pace.

One day this summer I was thinking about running while I was running. I was preparing for a run in Banff. Each time I went out for a run I would set a new mini goal or challenge. Sometimes the goal was to run a certain distance, sometimes my goal was to run at a certain pace, sometimes my goal was to run hills and sometimes my goal was simply to get out there and move.

All of these mini goals or challenges could be measured in different ways. This made me think about education. Each year we set broad goals for students and challenges are created to test and prepare for those goals along the way.

I measure my running progress in different ways and there are different benefits to achieving my goals. I set smaller goals just as a teacher may scaffold learning. Some days I can easily accomplish my challenges when my body is rested and sometimes I am unable to achieve my challenges when the weather is windy or too hot or the goal I have set is beyond my zone of proximal development. When I achieve a goal I feel good about myself and I am ready to continue to challenge myself. When I feel good about myself I feel like I can conquer anything I set my mind to. I think about our students who achieve and feel confident to continue to challenge themselves. When I run I am more cognizant of my habits and I drink more water and eat healthier foods. Why would I work so hard exercising and ruin the benefits by eating junk food? When our students experience success and achievement in one area, they are more apt to be ready to learn in other areas. When I don’t feel successful I try something else or try what I was doing a different way and to be honest, sometimes I quit. I purchased an app which was supposed to improve my pace. The voice told me to run faster. I couldn’t run faster; I didn’t know how to run faster so I quit for awhile because I didn’t know how to improve and I felt like a failure. Then I downloaded an app that tracks my data; the app tracks the time I run, the distance, the elevation, the number of work-outs per week, it allows me to set goals and tracks those goals and every once in awhile I get an e-mail certificate notifying me an accomplishment.

In terms of measuring my progress, there are many ways I can determine my progress. One of my goals for running is weight loss so of course; I can set goals and measure my progress with the scale. But that is not the only way I can measure my progress. I can also self-assess by asking myself how I feel (health/unhealthy), seeing how my clothes fit (tight, loose, just right), taking measurements and collecting data on my speed and distance when I run. Triangulation of data – the same reason we don’t simply use one piece of assessment evidence to determine student learning, I can’t only use the scale to determine my progress.

Although I am an adult and in more control of my life than many of our students, it is still up to me to get myself off the couch and out running. I don’t get a 0 or feel like a failure if I miss a run. If I miss some runs I may not progress as quickly as I might like. If I miss a lot of runs, I won’t be ready for the road race and I will feel foolish. I know this because I have been unprepared for races and I have learned that I need to train and prepare for road races. There will always be people around me that will run faster and farther regardless of how much I train and that is why I have to set goals for myself. There are people that will challenge me and whom I will provide a challenge. A couple of years ago my friends and I were running in Banff and we all agreed to wear our Rider jerseys. Shortly after the start line we split up to run at our own paces. Near the finish line a man ran up beside me and said he had been trying to catch up all race because he didn’t want a Rider fan to beat him. I had no idea I was providing a challenge for this man and I had no idea I would be trying to beat a stranger to the finish line but a little healthy competition provided me an opportunity to push myself further than I thought I could. (And yes, I did beat him across the finish line!)

Running is a part of my real world. I set goals for myself, I assess my progress of those goals regularly and I respond to the data to continue to make improvements. In a classroom, we have outcomes as broad goals for students. We chunk or break down those goals into smaller achievable pieces and provide opportunities and experiences for student learning, understanding and growth. Sometimes students are unable to meet those goals and we need to respond to those needs by possibly changing our instructional strategies, teaching the material in a different way or using different tools. We find different ways to measure the goals of our students and use various pieces of evidence to determine student learning in relation to the goals that have been set. We know that when we provide meaningful feedback to kids that they can see what they have to do to improve and when we don’t provide feedback students disengage in their own learning and progress. When students achieve a goal, we need to celebrate and that celebration can simply be the internal feeling of accomplishing that goal (I climbed that 5km mountain in Banff and finished the 10k run) or having someone share in that celebration (a teacher commenting on a job well done) and sometimes that extrinsic certificate along the way gives some required prompting to continue along the journey to achieving a personal goal.

math is real lifeWhat do you think? Do you live in the real world? What kinds of goals do you set for yourself? How do you measure your goals? How do you respond to your successes and failures?

Is school a real world?

October 9, 2014Permalink Leave a comment

Summing It Up

By Kim Cottini

It is difficult to determine and define when you truly learn something new.  Sometimes the “new ideas” have been presented before but for whatever reason, we only hear what we need to hear when we are ready to hear it.  I have been interested in learning how to infuse aboriginal content in Math as well as working on student collaboration and student “talk” in classrooms. At the beginning of May I attended the SUM Conference in Saskatoon. Who knew that these ideas could be fused together from different sources at one conference in new ways?

Prior to the conference, Dr. Lisa Lunney Borden offered a session about her experiences as a teacher with Mi’kmaw students in Nova Scotia. She is currently an Education Professor at St. Francis Xavier University. Although cultural differences are evident, I found many similarities in her stories to my experiences as a teacher in Saskatchewan. She consulted elders from her community regularly and they fed her thirst for knowledge. She asked how to say various words in their language and found that some things simply cannot be translated. For instance, when she asked the names for numbers, the response was a word meaning enough or not enough. Which makes sense. As traditional people, when they needed to hunt and fish, they wouldn’t bring back ten fish, they would bring back enough fish to feed the people. It also depends on what you are counting in Mi’kaw – numbers are verbs in their language and need to be conjugated to the situation. Which I then started to understand what she was talking about when she said that the word Mathematics is not an English word but a borrowed word.  Math is not a verb and yet we do Math.   Aboriginal languages are verb-based languages and yet in English, we make processes things in Math. The ways we think are embedded in our language. As an English speaker, it is as difficult for me to wrap my brain around thinking of Math in a different way as it is for students to wrap their brains around thinking of Math in my way in my language. Dr. Lunney Borden also shared an interesting thought; it is a false assumption that because someone speaks English, that they think English. She had 3 key pieces of advice – know your kids, know your community and know your kids can learn. She expressed the importance of learning from her students and listening to her students to understand their thinking.

The SUM keynote was Steve Leinwand and his message echoed the message of Dr. Lunney Borden but from a different context. Steve Leinwand is a Principal Research Analyst at the American Institute for Research in Washington, D.C. His articulate and passionate keynote focused on kids and learning. It’s about finding the best way to help kids learn. It’s about looking at test scores and talking about the issues. We need to ask ourselves: what are we teaching? How well are we teaching? How well are we doing – what does the data tell us? How do we use data to change what we are doing? He doesn’t claim this to be easy, but it is necessary. If what you are doing as a teacher isn’t working, you have got to change. He suggested working with colleagues and going into each other’s classrooms to learn from each other. Find something in my lesson that you will try in your next lesson and when I observe you, I will be looking for something I can try in my classroom. You have got to know your students and you have got to know your students can learn (hmmm…sounds familiar). He encourages kids to collaborate, he wants to hear how kids learn by asking kids to explain their thinking. His message – “tell me how you know” – “convince me of your thinking” – was repeated throughout his sessions. These are powerful statements in a classroom and provide insight to how kids learn.

When I prepare a workshop or lesson, my intent is to provide an opportunity for growth. I want people to walk away with a new thought or idea. And in reality, sometimes these thoughts stay in our minds and are not acted upon immediately. So what does all of this mean to me? I learned from Dr. Lunney Borden that aboriginal content does not mean counting buffalo but being culturally aware by listening to our students and learning about how they think.  Understanding how our students think is so much more than determining whether or not a student found the right answer. Sometimes the answer is irrelevant; the answer may not reveal the learning but the way a student convinces us of the answer can reveal the learning.  We are often so busy in our day to day lives and the busy-ness of a classroom that sometimes it is difficult to really truly be in the moment to listen and hear what a student says. So it is important to carve those moments into the lesson plan.  Mr. Leinwand reminded me to take time to listen to students. Make time to take those pieces of information that students give us and respond accordingly. What can I learn from the students in front of me in the moment and how can I respond in the best way to meet their needs? And maybe as I ask kids to convince me of what they know, I can convince students of the importance of the current lesson in addition to the importance of life long learning.

June 3, 2014Permalink

Use it or Lose it

When I was in high school, I was a lifeguard.  I took many training courses to be hired at the local pool and after I was hired I was required to attend weekly inservices.  During the inservice time we practiced life saving skills in the water, first aid, and we maintained a certain level of physical fitness.  As a group we also attended a number of lifeguard competitions which helped to improve our skills, reasoning, decision making and teamwork.  If a person were to collapse in front of me now, many years after my days as a lifeguard, I could probably perform some type of CPR but I would be rusty and without that kick of adrenaline, I would really have to think through and consider the necessary steps.  If this person were to collapse, I’m not sure that I would automatically think of the ABCs – I might jump straight to CPR when perhaps they were choking.  Thankfully I haven’t been involved in such a life threatening situation to test my skills.  But it makes me wonder, if I don’t use it (or practice), do I lose the skills and knowledge that I could easily recall at one time?

The first year I taught grade 7 Math, I followed the text book and read ahead of the students to be ready for my lessons and although I understood the Math, I didn’t always know or see where it was going or why I was teaching certain lessons.  During my second year of teaching the same course, I knew what was coming, I understood the importance of building upon student understanding and teaching Math was clearer and made more sense to me.  By my third and fourth years of teaching grade 7 Math, I felt like I was a pro but it made me wonder about my students’ experiences.  Here I was, an adult, with University Math classes to support my understanding, struggling at times with how to teach my students and yet they were expected to remember everything they learned in grade 6, apply that knowledge to new understandings, and hopefully become proficient with that skill in the three to six weeks I took to teach it.  Once a chapter was taught, I didn’t refer back to it again unless it was necessary for another concept coming up.  Yet I expected that my students would remember what I taught them when they went to grade 8.

We expect our students to remember everything we teach them.  It sure would be nice if they did but in reality, do we remember everything we learn?  Do we always remember the things we are interested in?  I find the differences between toads and frogs interesting but every time I wonder about the differences, I have to look it up to remind myself.  Imagine the things I don’t find interesting!  In Math we have a possible advantage in that once we teach an outcome, we can assess our students and move on.  But I think we have to remember to constantly review and remind our students about the skills and understandings they have learned as they continue to learn new information.

I had the advantage of teaching the same group of students for three years in a row.  I remember on more than one occasion when I referred to the fact that I had taught them something the previous year.  I remember being surprised that my students didn’t remember that valuable lesson I had taught the previous year, a year later, with approximately three weeks to practice the skill.  And yet, I did expect that my students would remember amongst the Science lessons, Social Studies lessons, Health lessons, reading strategies, etc. as well as other important pieces of information from their lives such as their home phone number, Mom’s work number, Dad’s work number, Grandma’s home phone number, Mom’s cel number and Dad’s cel number in case anyone needed to be contacted in an emergency.

There are many things our students must remember.  There are many things our students must learn and apply.  There are many things we must teach.  I think we must also remember, however, to provide time for practice and review so that once our students learn it, they can use it, so they don’t lose it.

March 3, 2014Permalink