Tag Archive | Mathematics

Change is Bad

Change is really hard to take, especially in education. Change is usually uncomfortable, and at times a nuisance. If it ain’t broke, why fix it?

Well, in a field as broad as education “broke” is not black and white. It’s not simply working or broken; sometimes, things can be bettered by an uncomfortable change.

Here is one of my many frames of reference: students like predictability. They like things they’ve done before. They like things to stay the same, and they seem quite complacent with the hierarchy of the class — the weak stay weak, and the strong shall remain strong. A change in teaching styles could shake up the hierarchy or at least make them uncomfortable. The students who tend to protest most about change are those who are at or near the top.

Photo credit to Sara Thibeault. (CC) 2013.

Photo credit to Sara Thibeault. (CC) 2013.

For instance, in one of my math classes, we will be starting a math circuit. I haven’t worked out the finer details of exactly whose doing what, where, when, and why, but I’ve got the basic concept down pat. I’ve decided to split my class into seven groups, loosely based on ability, but also on compatible workers. I created seven stations for my students to work at — Thibeault Time (3 on 1 instruction/help with me), Mad Minute (drill and practice on basic math skills), Math Mysteries (a few problems or related games to play), Practice (work time on an assignment, which they will visit twice), Literacy Time (reading at-level math history or math-related articles that I found), and Skill Check (a short quiz that students will take after they are ready to show mastery of a specific math process, or more practice time if they aren’t ready). I plan on working through 5 ten-minute rotations each day. I have a 62-minute class, and I’m allotting 5 minutes for Oh Canada/attendance/setup, as well as 5 one-minute breaks for rotation time, and two minutes for clean up. All of this will flow under the guidance of their individual learning contracts. This hopefully will minimize chaos and maximize awesome learning time. It’s going to be hectic and crazy, but I’m ready for the challenge.

Here’s the catch: I didn’t tell them about it. Why? I wanted to flip a unit with them (the polynomials one above, actually, with a few improvements) and they complained bitterly for days leading up to it. They were uncertainly about it for the first few days, and by the end they enjoyed it. A few students complained afterward too, and it was enough to rattle my confidence. So I went back to teaching on the board (not even the SmartBoard) and powered through the next unit.

The biggest complainers involved in this whole ordeal were the students, barring a few, who were at the top of the class. Maybe they were nervous that they weren’t going to be #1 anymore? Maybe they were nervous that it wasn’t going to work for them? Maybe they knew that they could coast and not have to do a ton of work with traditional teaching, so weren’t prepared to step u their game? I don’t know. I’ve seen it in a few of my other classes as well, and I’m a little disheartened by it. Just not enough to make me scrap my plans or kill my enthusiasm.

So this is where I stand — I have big plans for change in my classroom and students who are hesitant because it will be different and maybe even a bit awkward. Any advice for keeping them calm and getting them on-board? Also, has anyone else tried math stations in their classroom successfully (or unsuccessfully)?


Crappy Teacher

I guess I’m trying to make up for lost time. I’ve been meaning to blog about this for a while now, but I just haven’t had the chance. I’m glad to be procrastinating doing my laundry and blogging instead.

I figured out why one my classes seemed to be getting progressively more poorly behaved. I’ll keep you in suspense while I explain.

One of my classes had a class list that made other teachers cringe. In my wonderful student profile survey, they all explained that they hate math. Joy. They also solely are taking math to get out of high school. Double joy.

As the days progressed, my classroom management got worse. I started out the year as the nice teacher with really strict rules. Then I morphed into the really strict teacher, who was grouchy all the time, and had so many tough rules that I couldn’t possibly enforce them all. I tried detention. Kids didn’t show up, so I doubled it. I had a student who racked up four hours. We had a “Bathroom Board” so that I knew how long my students were gone for washroom and/or drink breaks. Forty minutes is excessive, don’t you think? I don’t really want to go on, but let’s just say that there may or may not have been laser pointers.

I had an epiphany while I was at a conference. I’m not sure where it hit me, or why it did, but it occurred about 10:21 a.m. The more poorly my students behaved, the more worse of a teacher I became. I’d threatened my student with boring notes, and I’d followed through. My classes were getting progressively crappier, as was my students’ behaviour. No wonder. I didn’t enjoy teaching the class, and I’m CERTAIN they didn’t enjoy being there either.

So I decided to change things. I took about a week and sunk the majority of my time into revamping my entire upcoming unit plan. I created a “flip-flopped” classroom (for an overview, see my previous post).

I can honestly say I was terrified. I had admin support though, so I gave it a shot. And it kind of worked.

I won’t say my management problems are gone, but they are certainly much better and improving as we speak (or write/read as the case may be. Except that it is Saturday, so my students aren’t in my class, but you get my point).

I guess what I’m trying to say is that I learned that teacher-student relationships go both ways. I need to be a good teacher to have good students. I can’t “crappy-teach” them to be good students.

Just Smile and No One Will Ever Know

I was talking with friends today and I wanted to share this story. We all laughed, but it bothered a lot, especially when I was driving home afterward. I’ll tell the story as if I am the friend who shared it. She’s in her early seventies, but regularly works with youth.

My niece lived with me for a while during her elementary and high school years. She was never good at fractions. In grade five, my son was tutoring her to give her a hand with this somewhat challenging topic for her. One day, he turned to me and said, “Mom, I think it’s hopeless.”

I loved baking with my mom as a child, but I can imagine that not understanding fractions could have changed my opinion of it rather quickly. Flickr Photo Credit to CaroleChapman.

I knew from that point that she wasn’t all that bright, but we kept up with school. Never once was she held back due to her grades. She got into grade nine and we were baking a cake one day. I used the one-cup measure to pour some milk, but she needed to measure out a cup of sugar. Naturally, I grabbed the nearest measuring cup, which happened to be a one-third of a cup measuring cup,and said, “Here. Just use this.” She turned to me angrily and asking, “What am I supposed to use this for?”

The next day, I went straight to the principle. We talked to her math teacher and, sure enough, she had received 2% on some assignment or test. She was still struggling with her fractions. According to the math teacher, she sat in the back and just smiled every day, so he had no concern as to her learning.

The discussion that followed this story talked about how easy it is to “fake it” in school. I can’t say that I’ve often times just smiled and nodded in school, but I can imagine it happens a lot. That’s a scary thought. We talked about how it would be really hard to ask a question when you feel like you are so far behind that you don’t even know what to ask. Again, I guess this is true. I have been so blessed to not be in that situation, but I can imagine it’s a pretty scary place. What startled me the most is that this is what my friends (age range: 20 to early-seventies) considered a normal for a math class. It seemed like the teacher was completely off the hook for not showing any concern over 2% on an assessment (granted it was likely more of an evaluation, based on the limited facts I have). Where were the teachers in grades 6 – 8? Should they have not made a fuss over the fact that she didn’t understand fractions?

I stayed pretty quiet during this discussion, since I know that I can get pretty passionate about education, and it was pretty lighthearted, but it’s been bugging me for the last couple of hours. I know more than anything that I desperately need to set my classroom up so that I can truly assess each student to give me an idea of where he/she is at all times. I don’t have the answer for this, but I certainly don’t want to have any students “faking it” with a pasted on grin and a few bobs of their head every time I explain something.

Should I flip my class? That would probably be the first step, but even then, I can’t stop there. Diagnostics? Well, they are pretty exam-like, but they do give a pretty good survey of knowledge, provided I design it so that I find out what I want to know. More parent-teacher communication? Absolutely. More manipulatives, inquiry, technology, etc.? I’m sure the list can go on. What do you suggest? Have you had kids “fake it?”

So How Did I Do? My ECMP Self-Evaluation

One of the hardest things I’ve been asked to do all semester is self-evaluate. For my Technology in the Classroom class, we were given the freedom entirely self-evaluate ourselves. Initially, this seemed like a pretty sweet deal. What could be better, right? Wrong.

If you’ve never visited my blog before, I’ll give you a quick heads up — I’ve been doing a lot of rethinking this semester. I haven’t really come to terms with grading and evaluating. I’m all for assessment. I love assessment, but numerically evaluating someone’s work just doesn’t quite sit right with me. This is compacted by self-evaluation. We’ve all been there — the stress of marking one’s self. You know how it goes… the students who put in a ton of work are really tough on themselves, while the students who put in the bare minimum give themselves outstanding marks.

I suppose part of my anxiety of this whole thing is that I know what grade I want. That’s the part of me that is so marks-driven. The other part of me worked to my advantage though too. That part of me saw an opportunity to learn, and, free from rubrics/grades/scary stuff, I learned for the sake of learning. I can honestly say that if I was being graded on my blog, it wouldn’t be half of what it is today. Why? I’m not entirely sure, but I guess it has a lot to do with me doing this for me, not for anyone else.

My mission today: honestly and fairly grade the last four months of my progress.

I’ve been sort of keeping track of my learning from this class on an excel spreadsheet, just to keep myself on track. Dean gave us a list of assignments that we needed to complete this semester. Each assignment is to be weighted no less than15%. How we distribute the marks after that is up to us. To make the math simpler, I gave myself a mark out of whatever percentage I had each category weighted at. He also asked that we justify each mark. Since I’ve become a reflecting maniac, that’s no problem at all.

Assignment: Weekly Blog

Grade: 29 / 30

Justification: Our blog was intended to hold weekly updates with reflections about our class, as well as its presenters. Over the last four months, my blog has grown into a regularly updated (usually a couple of times per week) blog. It has stuff not just from this class, but from other classes, as well as anything education that pops into my head. It’s become a platform for me to think about ideas, gain insight from others, and network. I’ve used to do reflect for the sake of learning (not just because a class told me to), publish projects, write a mini-blog series about WestCAST, post my philosophy of education, and so much more. I do regret not commenting on my classmates blogs nearly as much as I would’ve liked to. However, I did develop the confidence to start commenting on other blogs of the professionals I look up to. It also opened the door for me to have conversations via twitter with many teachers world-wide.

Assignment: Teach Us Something

Grade: 14 / 15

Justification: This was interesting. I decided to present about the flipped classroom unit that I was working on for this class, as well as my Math Ed (then Moral Ed for the assessment). I really wanted to talk about the website Sophia, but part of that meant explaining a flipped classroom. I figured that to really talk about a flipped classroom, I needed to flip my presentation. I couldn’t exactly do that, since I wasn’t able to get the Sophia Tutorial (as recorded on Jing) done in time for the class before. Instead, explained what a flipped classroom was, showed the tutorial video, then talked about how I was using Sophia for my flipped classroom. Aside from how chaotic it was to use Jing to record a tutorial about Sophia in order to talk about flipped classrooms within a 10-minute time frame, I thought it went fairly well. I did find it kind of bizarre to be presenting to a class, but have no indication of whether or not they are listening, engaged, or even in the room. It was certainly more nerve-wracking than I thought it might be. I did have some technical difficulties while using Elluminate at the beginning, but once things got going, I powered through. Overall, I’m really proud of my Teach Us Something presentation.

Assignment: Virtual Internship

Grade: 9 / 15

Justification: I have to say, I really dropped the ball on this one. I was in contact with one of my mentors and ended up being involved in her classroom for their celebration of the 100th day of school. It was very cool. Being a secondary math major, seeing how math looks in a grade 1/2 classroom was eye-opening. I couldn’t get over how capable the students were! They were so inquisitive. I did plan on doing lesson with her class again, but the end of the semester caught up with me and I wasn’t able to. Being one to keep my promises, once my semester calms down, I would like to reconnect and teach a lesson! No reason for learning to stop just because I’m not paying tuition! While that mentorship went well, I can’t say the same for the other. Between me not understanding time zones, getting overwhelmed with homework, and procrastinating, I only skyped with my other mentor once. She taught philosophy in a private high school. While it sounds like a fantastic class, it really wasn’t my cup of tea. I had all the good intentions of the world of getting involved, but I wasn’t as motivated to do so as I thought I would be. I’m really disappointed with myself for this one. I know I’m not that type of person, but I seriously dropped the ball.

Assignment: Create Your Own Assignment

Grade: 24 / 25

Justification: This assignment that I “created” flowed really nicely from my Teach Us Something assignment, my Math Ed project, and my Moral Ed project. I decided that if I’m really going to dig deep into something, I may as well dig as deep as I possibly can. I decided to completely flip the polynomials unit in the Math 9 Curriculum. How I justify putting that project in this course is that I know I put in the effort for more than three courses worth of work (if that makes sense). I specifically justify it in that I used technology for everything for this project. I learned how to use Sophia. I learned how to make a good screencast/tutorial. I learned how to reach out to my twitter network (and build a bigger twitter network) to aid my research. I primarily used blogs for my research (I didn’t use on theoretical, scholarly journal article, since I wanted my research to be grounded in field-tested, real-life classrooms). I used my blog as a platform for publishing my project, reflecting, and networking with other teachers. Lastly, and most frustratingly, I learned how to negotiate Movie Maker when it doesn’t want to cooperate. I spent nearly 14 hours trying unsuccessfully to get it publish my video reflection for the Moral Ed portion of this assignment, so I tried to play it on full-screen mode with a screen recorder. Eleven different software programs later, and still no luck. Magically, it began working again, so my project saved. I then learned how to compress a wmv file down to a mp4 file, then adjust the compression settings to keep it under 500 MB. Needless to say, I feel pretty tech-savvy right now. All in all, I am beyond happy with how this project turned out. It really pushed me to re-establish my beliefs, it’s changed the way I feel about education, and it’s changed the way I want to teach. Because I didn’t have a grade looming over my head with this project, I had the freedom to take it as far as I could, and I certainly did. This project will forever evolve and it will never be complete, which is the beauty of publishing it on a blog. All I can say is, “Stay tuned, folks!”

Assignment: Final “Exam”

Grade: 14 / 15

Justification: Little did I know, but I was learning about my learning while I created my video reflection. It went a lot more smooth than my Moral Ed video did, but it was still a learning experience. I am not a short-winded person (my word count right now is at 1390… oops), so summarizing an entire semester of learning in 5 – 7 minutes was like pulling teeth! I had so much to say and so little time to say it. I can honestly say that I did stay within the time requirements. That in and of itself was a victory. I decided to combine video, audio, and visuals to enhance my reflection. I spoke somewhat candidly to the camera for part of my reflection, but for other parts, I recorded myself in Audacity to make a kind of a podcast that I added visuals to (screenshots and photos from flickr). For ambiance, and to make it seem more professional, I went on a hunt for some soothing music for the background. I initially searched through FreePlayMusic, but I couldn’t quite find what I was looking for. I tweeted out my conundrum and got a few responses of different websites. That’s where I found “6-26-11,” as song by “Easy Listening Section” on Sound Cloud. I messaged him, and he was quite flattered to receive the message asking for his music. It was so cool to get in contact with a complete stranger all for this project. I am so in awe of what I’ve learned to do. Never would I have guessed that I would experience that. My only regret is that it wasn’t done the night before. I finished editing it and publishing it only a few hours before class, so many of my classmates didn’t have a chance to watch it prior to class.

Overall, I have been pushed, challenged, and amazed throughout this entire course. I don’t know what I would do without Google Reader, my Twitter feed, or my blog. It’s really helped to change the way I look at education.

FINAL TOTAL: 90 / 100

How do you think I’ve done? Leave some comments for me — I’m always up for some input.

Flipped Classroom – EMTH Reflection

*Please be advised: this is not a new post. It is the reflection that used to be on the “Flipped Classroom – Math 9 Polynomials Unit” Page. I just needed to reorganize a bit.

For my final project in EMTH 450 with Rick, I had free range to do anything I liked that pertained to education and math. The possibilities were endless. I changed my mind about 1,000,000 times. I finally settled on what I figured to be a manageable project of creating a set of videos to “flip” a unit in the Math 9 Curriculum. During my internship, I had the opportunity to teach Math 9 for the full 4 months, and I loved every minute of it. While for the most part, I liked what the textbook had to offer, I was not particularly impressed with how it delivered Polynomials. They came packaged in two clunky, non-consecutive chapters. I knew that I needed to avoid using the textbook, so I went hunting for some resources and made up my own work-package for the students, as independently from the textbook as possible.

Since Rick gave me free range to do whatever I fancied (within reason), I decided that I wanted to revamp the way I taught polynomials. Little did I know, that this project actually helped revamp the way that I want to teach in general. I’ll say it one thousand times over — my internship was great. Now, I think I can be more than that. I can see it, so I decided to push myself with this project.

This unit is entirely flipped. There are eleven video lessons, eleven worksheets, a “What Can You Do With This?,” and a project. The assessment is an outcome/indicator-based assessment guided by a learning contract. There is no unit exam. There are no formal quizzes. The closest thing to a quiz is a “skill check.”

I struggled with having this flipped classroom avoid direct instruction. Part of flipping for me was to avoid direct instruction. It seemed that it was inevitable, so I decided that if I can’t fix it, I might as well embrace it in a weird sort of way. Instead of making long and boring videos, I decided to keep them short and simple. I did my darnedest to ensure that my worksheets were inquiry-based. My theory behind this was to give a bit of instruction, just to send the students in the right direction, then let them work in-class on exploring each concept thoroughly. Answers will all be posted on the wall (answer keys coming soon). Students are invited to collaborate with one another.

Part of me thinks I may have had a mental back-lash during this project too. During my internship, I found that students felt bombarded with problems, and there was not nearly enough drill and practice. Both have their place, but I felt that problem solving was interfering with the students understanding the concepts concretely. I decided to not include the “token problems” at the end of each worksheet. Instead, I designed each worksheet to act as a set of notes, since the students wouldn’t be taking any anyhow. Each sheet contains what I think are the essential questions/big ideas (i.e. Explain in your own words how to divide a monomial by a monomial), as well as several examples. Because the answers are posted and students have no set “time limits” for each assignment (which was a big pull for me to the learning contract), every student will get every single question right. They have access to their peers and to me, so finding the correct answers is only a matter of effort.

To “address” word problems, I decided to have a unit project. This satisfied the old-school innate need deep down inside to have a unit assessment. “At least it’s not an exam,” is what I told myself. I’m not one to undermine or under-appreciate a good word problem, but at least a unit project ties together all the concepts and involves a “real world” situation. It’s a little bit less contrived. I decided to go with an area-based project, which lead me to think about the areas in floor plans. About ten minutes after staring at my computer hoping it would finish my project for me, it dawned on me. I should do a WCYDWT with a floor plan, and then ask the students to work in reverse by creating a floor plan and designing the dimensions on their own. All of a sudden, the “contrived” unit problem sat a lot better with me (and it squeaked in another teaching strategy beyond direct instruction).

My last word about this project, I promise: I am so glad I opted to work with a learning contract. It enabled me to build an outcome/indicator-based assessment and evaluation system that was free of rigid timelines and stress-(and/or vomit-) inducing exams. One of my initial concerns beyond the direct instruction bit was that flipped classrooms somehow guarantee only 20 minutes of homework per night. What about the student who doesn’t finish the in-class work? Does he/she have extra homework? So much for the nice guarantee. If we stick to the guarantee, then what good does it do for that student? Conversely, what about the student who finishes in fifteen minutes? They now have to “kill” 45 minutes. Yes, I could load them with extra work, but I’m going to challenge them anyway. Why not let every student work at his or her own pace? A learning contract does just that. To keep things reasonable, I will set a time-guideline and a conservative completion due date. Aside from that, every student can be working on what he or she needs to be working on.

As always, I welcome, encourage, appreciate, and pray for your comments to pour in. The more feedback I get, the better I’ll become.

Special Thanks to the following: Dan Meyer, Joe BowerSophia (They have fantastic Twitter Support), Kyle WebbRick SeamanEvolving Classroom, and Andy Schwen

This is my utopia right now. I can’t wait to put it into practice.

Math Sucks?

I’ve heard that many students think math sucks. These students grow up. Some become lawyers, some become doctors, some become electricians, some become executives, and some become teachers. Firstly, that’s okay. Not everyone needs to like everything. My biggest concern is not that people don’t share my inexplicable love of math, but they don’t like it and believe they can’t do it. Chicken and egg conundrum — which came first? Disliking math or having trouble with math?

At WestCAST, I saw Dr. Jerome Cranston (@dr_j_cranston) present on his research about pre-service teachers entering university. All data was collected prior to the students took even one education class. A few things really stuck out for me. According to Dr. Cranston’s research, only 46% of females stated that they had average or above average math skills. That means that over half of the large data poll thought that they were below average (or worse) in their math skills. That’s kind of scary.

Similarly, only 69.3% of males participating in the survey thought they had average or above average math skills. That’s a little more promising, but the lack of confidence is still astounding.

The scariest fact that he presented was that only 47% of middle years teachers felt they had average or above average math skills. Over half did not believe that they were at least average. Yikes. Based on the Saskatchewan Curriculum, middle years is where math starts to get abstract (think algebra, variables, etc.). Confidence in math skills goes a long way to helping students learn these skills. Instilling self-trust in math is imperative.

While many teachers don’t like math and are fantastic at pretending they do, it still can come through in subtle ways. Think back to your education — if a teacher didn’t like doing something, could you tell? Did you like it even though they didn’t? Scary stuff.

So what can we do about it? We need to break the cycle. We need to build math confidence in our students. I don’t know exactly what this might look like, but somehow it needs to happen. What are your thoughts? How can we help our students like math or, at the very least, feel confident in their own math skills?

Is Reading a Textbook a Necessary Skill?

Using a single textbook as a resource is frustrating. Flickr photo credit to casalewebnet2.

I’ve been following the #flipclass chats, as well as doing quite a bit of research on flipped classrooms lately. I noticed a somewhat uncomfortable shift in the change of thinking and the pedagogy, all of which comes with being “new.” There is a growing concern about students loosing out on the “skill” of using a textbook. I can appreciate the value of being able to navigate a textbook, since I have $4000 of textbooks sitting on a bookshelf that I’ve needed to navigate to varying degrees in the last four years. Understanding how to interpret Academia in print isn’t always the easiest task to accomplish. I agree that learning how to do this is, in fact, as very useful tool for the students who are going onto any sort of post-secondary. I could also argue that most people will encounter professional or academic writing at some point in their careers regardless of whether or not they attend post-secondary, whether it be in the the form of a management report, highly involved news article, or a contract.

However, who is to say that a single textbook is the best way to teach this skill? I would like to argue that a variety of resources would teach this skill better. For example, looking at math since that is my background, most school divisions pick a specific publisher or series of math texts to use within their classroom. One one hand, that is fantastic for continuity. On the other hand, students are only exposed to one specific type of writing, style of problem solving, one particular format/layout.

One common fallacy that is easy to slip into — I did during my internship at times — is that the textbook is “perfect.” Once I made up my mind that the textbook wasn’t the bible for my math class, I instantly became a better teacher. I could feel it, I saw it in my students, and my students saw it in me. It was necessary to experiment with teaching from the textbook, but I’m glad I deviated.

As for the continuity argument, the curriculum is designed to encourage continuity. Part of a teacher’s job is to encourage retrieval of prior knowledge when students are learning concepts. Finding out what students do/don’t know through KWL charts, diagnostics, just asking them, etc., can help with continuity, and perhaps even inspire teachers to find other resources to help with continuity far beyond that of the standard textbook.

So here is where I stand now: the textbook is a powerful resource. Why not combine these powerful resources? Blend the use of several textbooks, online resources, self-created resources, resources from other teachers, and student-generated resources. I will admit that this will be a TON of work. I know that teachers are already bogged down with so much work and so little prep time, but why not give it a shot? This will give students multiple perspectives, different samples of academic (and non-academic writing), and a welcome change from their “boring” textbook (let’s face it — how many high school math textbooks do you read just for fun?). This, to me, puts to rest the need to learn how to use a textbook, since they’ll be better at it.

Am I way off base on this?