Expected, Inspected, & Respected.
"We do not learn from experience … we learn from reflecting on experience."
-John Dewey |
"We do not learn from experience … we learn from reflecting on experience."
-John Dewey |
As I head into my 3rd straight year of teaching brand new curriculum, I want to make sure I am headed for success, so I'm dusting off the old blog and entering my reflections from my summer learning here.
Yesterday, I enrolled in a 6 module, 12 week workshop called Making Math Moments that Matter with Jon Orr (mrorr-isageek.com) and Kyle Spencer (tapintoteenminds.com). I've listened to their podcast, been to a professional development event with Jon Orr, and used some of their online materials for my Grade 7 math lessons and have enjoyed all of it. The workshop started with Jon and Kyle beating a couple of contestants at this game:
I could definitely see myself offering $5 to someone who could beat me at the game with my Grade 8s next year. That would be memorable start!
Today, one question we were asked was this: What 3 things would we like our students to remember about math class 5 years from now?
I remember getting to use protractors and compasses in Grade 10 or 11 math and really enjoying the puzzles and the satisfaction of drawing perfect shapes with these tools.
See you next time!
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What a terrific book! Todd Rose brilliantly takes us through the history of how the idea of an average person came to be such a dominant and harmful force in education and business, and proposes solutions for how to remake our institutions with the individual in mind. I only remember one time when Rose speaks positively about averages but it seems to be a backhanded compliment at best: "... it is reasonable to sometimes pretend size is one-dimensional if the trade-off is worth it, like when it comes to mass-produced clothing: in return for a lack of great fit for any one person, we get inexpensively manufactured shirts and pants for everyone. But if the stakes are high - if you're altering an expensive wedding gown or designing a safety feature like an automobile airbag, or engineering the cockpit of a jet - then ignoring the multidimensionality of size is never a good compromise." (84) Mostly, Rose gives example after example of how harmful it is when systems are designed for the "average" person. This is because there is no such thing as an average person. In the 1950s, when the US Airforce designed their cockpits for the average pilot, less than 2 percent of pilots measured were average on four or more of 9 dimensions and nobody was average on all of them. Human traits like size, intelligence, character, and talent are jagged and complex, so designs for the average person are often ill-fitting solutions. For example, which one of these gentlemen would you say is bigger? Intelligence is equally problematic. While the following overall IQ scores are identical, at a more granular level, they are wildly divergent. Rose also discusses how traits are a myth. People are not honest or dishonest, aggressive or passive, but behave differently in different contexts. Instead of traits, it is more helpful to think of people as having "if-then signatures". For example, it is not particularly useful to say, "Jack is extroverted", it's more useful to say, "If Jack is in the office, then he is very extroverted. If Jack is in a large group of strangers, then he is mildly extroverted. If Jack is stressed, then he is very introverted" (106). In terms of education, there are a few great takeaways from this book. One is that learning speed has nothing to do with learning ability. A study by Bloom from the University of Chicago showed that in a randomly selected group of students given fixed-pace group instruction, only 20% of the students achieved mastery over the subject material, while 90% of a randomly selected group of self-paced students achieved mastery. This is troubling because most of our instruction is still based on fixed-pace group instruction. Fine grained individualized instruction is not the norm because it would be complex and cost prohibitive to implement. Rose says these problems can be overcome by using technology more effectively through the kind of self-paced learning available on sites such as the Khan Academy. I would add that a flipped classroom where the instruction happens at home and the work takes place in the classroom might be another solution. It has been stressed to us in our university classes that differentiation is the name of the game and Rose concurs: If every student learns at a different pace, and if individual students learn at different paces at different times and for different material, then the idea that we should expect every student to learn at a fixed pace is irredeemably flawed. Think about it: Were you really not good at math or science? Or was the classroom just not aligned to your learning pace? The jaggedness inherent in our abilities, skills, and talents creates a problem when teachers are required to sum up these profiles in a single, one-dimensional grade. Rose quotes Thomas R Guskey from Five Obstacles to Grading Reform: If someone proposed combining measures of height, weight, diet, and exercise into a single number or mark to represent a person's physical condition, we would consider it laughable... Yet every day, teachers combine aspects of students' achievement, attitude, responsibility, effort, and behaviour into a single grade that's recorded on a report card and no one questions it. (174) The focus in The End of Average is on higher education and so the solutions he proposes - granting credentials, not diplomas; replacing grades with competency; and letting students determine their educational pathways - are not quite applicable to the early years teaching that I'm interested in learning how to do but I think it's right on the money. I believe that my own higher education would have been much more enjoyable and effective if it had been designed with those three pillars in mind.
I highly recommend reading this book! I think you'll be glad you did. I've been 6'9" since I was 19 years old and I'm used to people, especially kids, making a big deal about my height. At least, I thought I was used to it. I thought that I would be unfazed by the shocked, amazed, envious, and frightened faces elicited by my arrival in classrooms as a substitute but the volume of these responses I've seen over the past couple of days has been a bit much. I'm starting to feel like I should go live in a swamp with a donkey, or at least charge two bits a gander. I'm sure I'll get used to it, but I also want to make sure I use it to the best possible effect. I know that you have to relate in order to educate, so I try my best to play the part of the Big Friendly Giant, smiling, joking, and discussing whizzpoppers, snozzcumbers, and fizzwhizzers in the interest of making connections with students. However, I wonder if that is the best way to approach students as a substitute. One day is not enough time to build relationships with a roomful of middle-school students, and when they see me smiling, I think some may take it as a sign that I am a softie, leading them to believe that they can get away with shenanigans. I may try some A/B testing to see if the friendly approach or the no-nonsense approach is more effective.
It feels like becoming a teacher has taken a very long time, yet at the same time, it has gone by in a flash. It's funny how time works and how, even after experiencing this phenomenon many times, it's still surprising and strange. My next steps in the profession will be subbing, applying for jobs, interviewing, and continuing to put theory into practice. “Our business in life is not to get ahead of each other, but to get ahead of ourselves.” - E. Joseph Cossman I use the above quote at the end of my emails as a reminder to myself that life and education are about growth and improvement. Carol Dweck, well known for her work on fixed and growth mindsets explains: “In a fixed mindset, people believe their basic qualities, like their intelligence or talent, are simply fixed traits. They spend their time documenting their intelligence or talent instead of developing them. They also believe that talent alone creates success – without effort. They’re wrong. In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work – brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment” (Dweck 381). Dweck’s work resonates with me because I feel that, up until the end of my first degree, I had a fixed mindset; I never pushed myself in school because I was fairly bright, and with minimal effort, my grades were always good enough. Returning to my studies after a 15 years hiatus, I value personal growth more than ever, and I feel this motivation to improve has given rise to more authentic learning. I am convinced that classroom practices that promote a growth mindset are the ones I need to focus on as a teacher, so that my students won’t have to wait until they are in their thirties before they can know the joys of learning. Jo Boaler builds on Carol Dweck’s growth mindset research and applies it to the mathematics classroom in her book, Mathematical Mindsets. As I intend to specialize in mathematics instruction, I am excited to implement the following classroom practices: 1)Everyone can learn math to the highest levels.There is no such thing as a “math person”. This message counteracts the problematic idea that math abilities are fixed from birth. 2) Mistakes are valuable.Growth happens when you struggle and make mistakes. This might be difficult to teach, but Boaler has various methods for doing so: - Share the brain research with students. - Display posters made by students with messages such as, “The biggest mistake you can make is being afraid to make ones.” - Apologize to students if their work is too easy as it robs them of potential learning opportunities. Easy is a waste of time - productive struggle is where the learning happens. - Applaud students who share misconceptions with the class so that everyone can benefit from each other’s mistakes. 3) Questions are really important.Encourage students to ask them. Celebrate good questions by writing them on chart paper and posting them in the room. 4) Math is about creativity and making sense.5) Math is about connections and communicating.6) Depth is much more important than speed.7) Math class is about learning, not performing.Assessment often delivers a fixed mindset message to students and Boaler has some great advice for how to combat this: - Allow students to resubmit any work or test for a higher grade. - Grade and test less. - Share diagnostic feedback with students but not grades. - Give grades not just for getting correct answers but for learning behaviours such as asking questions, explaining work to others, making connections, etc. - Don’t include homework, if given, as any part of grading. (Boaler 269-277) In the spirit of a growth mindset, I sought out opinions that might contradict the growth mindset mania that has swept through academia. Alfie Kohn, an educational thought leader I highly respect, warns of the dangers of a shallow implementation of the growth mindset. In his Salon article, “The Perils of ‘Growth Mindset’ Education: Why we’re trying to fix our kids when we should be fixing the system”, he says, “...books, articles, TED talks, and teacher-training sessions devoted to the wonders of adopting a growth mindset rarely bother to ask whether the curriculum is meaningful, whether the pedagogy is thoughtful, or whether the assessment of students’ learning is authentic (as opposed to defining success merely as higher scores on dreadful standardized tests)” (Kohn). Fortunately, Boaler avoids the pitfalls of a misguided and superficial growth mindset program by filling her book with meaningful mathematic curriculum, thoughtful pedagogy, and authentic assessment techniques. Kohn also criticizes the use of praise to encourage a growth mindset. While Dweck and others commonly recommend praising children’s effort rather than their intelligence, he says that praising children as a pedagogical tool is not a worthwhile practice. It may be true that praising effort is better than praising intelligence, but Kohn posits that when we use rewards to manipulate children into behaving as we would like them to, “kids typically end up less interested in whatever they were rewarded or praised for doing, because now their goal is just to get the reward or praise” (Kohn). He believes that non-judgemental feedback is more conducive to intrinsically motivated learning.
By implementing the core philosophies and practices recommended by Dweck, Boaler, and Kohn in my classroom, I hope that my students will be able to shed their potential fixed mindsets and embrace one of growth. Through an intentional pedagogy where mistakes are valued, praise is non-manipulative, and assessment is used as productive feedback rather than judgement, students will know joyful, authentic learning. I recently finished reading Daniel Pink's When: The Scientific Secrets of Perfect Timing. I've always enjoyed reading these kinds of popular science books but I read them differently now than I used to. Now, I'm always on the lookout for how the research might apply to my teaching. Here are a few of the nuggets I found in When: The first is that having math in the first two periods of the day rather than later in the day increases the math GPA of students. This is because tasks requiring analytical skills are performed better in the mornings when most of us are at our most methodical. Tasks requiring insight, however, are more easily tackled in the afternoons when we have fewer inhibitions. This is because being insightful requires us to be less vigilant about being methodical. Pink uses the following riddle to illustrate what he means by a problem that requires insight: "Ernesto is a dealer in antique coins. One day someone brings him a beautiful bronze coin. The coin has an emperor's head on one side and the date 544 BC stamped on the other. Ernesto examines the coin - but instead of buying it, he calls the police. Why?" Those who attempted this puzzle in the afternoon had a better chance of solving it than those who attempted it in the morning. (The answer is that if the coin had been minted in 544 BC, it couldn't have been stamped with a BC because no one would know about Christ's birth for another 544 years.) According to Pink, the research suggests that because of the human body's natural rhythms during the day, students might perform best in classes like math during their optimal time of day in the mornings and leave subjects such as art and creative writing for the afternoons during their non-optimal time of day. Another interesting thing that relates to education is the idea of chronotype. Pink says you can find your chronotype by answering the following three questions:
Pink states that, "After genetics, the most important factor in one's chronotype is age. As parents know and lament, young children are generally larks. They wake up early, buzz around throughout the day, but don't last very long beyond the early evening. Around puberty, those larks begin morphing into owls... By some estimates, teenagers' midpoint of sleep is 6 a.m. or even 7 a.m., not exactly in synch with most high school start times" (Pink, 29). In fact, "Today, fewer than one in five U.S. middle schools and high schools follow the [American Association of Pediatrics'] recommendation to begin school after 8:30 a.m. The average start time for American adolescents remains 8:03 a.m., which means huge numbers of schools start in the 7 a.m. hour" (Pink, 92). That is nonsense. Along with findings about the timing of the school day, there was some interesting research about the impact of breaks on testing. "Taking a test in the afternoon without a break produces scores that are equivalent to spending 2 weeks less in school each year and having parents with lower incomes and less education. But taking the same test after a twenty- to thirty-minute break leads to scores that are equivalent to students spending three additional weeks in the classroom and having somewhat wealthier and better-educated parents. And the benefits were the greatest for the lowest-performing students" (Pink, 57). The nonsensical part of this is that many school systems cut back on breaks and recess for children so that they can achieve higher test scores, which ends up having the opposite effect. The final tidbit I'll share has to do with how we give good news and bad news. Research shows that when people have the choice of getting the good news or the bad news first, they tend to choose the bad news first. However, when people are responsible for giving good news and bad news, they tend to give the good news first. This suggests that teachers shouldn't give feedback beginning with praise and finishing with criticism. My opinion is that strengths-based feedback should begin and end with good news, as it does in the good old compliment sandwich.
On Wednesday, I led my fellow pre-service teachers in a 10 minute math activity at the University of Winnipeg. I began with a quick slideshow and explanation of how to be a good skeptic:
Then, I invited my classmates to follow these instructions:
If you care to see the raw footage of my presentation, here it is:
And if you care to read my reflection on the presentation, read on.
As a former basketball player, I have long known the value of reviewing game tape. It allows a player to watch their actions with a critical eye, and make adjustments to improve their performance. As an EA, I thought that this common practice in athletics would be very useful if applied to the teaching profession. Simple mistakes such as speaking too quickly or softly, or not waiting long enough before soliciting answers from students could easily be corrected if a teacher was able to see themselves teaching. It surprises me that in the Education After-Degree program, although we have been required to engage in critical self-reflection many times, we have never been required to use video to do so. Without video, all we have to rely on is our own biased and faulty memories of how we believe we performed. As we all have a need to protect our egos, our memories generally paint us in a fairly rosy light. I think it is a missed opportunity to go through a Teacher Certification program without being required to watch oneself teach - especially when most people have smartphones with video recording and playback capability. The barriers to reviewing educational game tape are more psychological than technological. It can be uncomfortable to watch yourself and think, “Is that what I sound like? I didn’t know I said ‘um’ so much. Why did no one tell me I flail my arms like a maniac when I’m telling a story?” However, although the process may be cringeworthy, self-critical reflection should not be shied away from. It should be emphasized and esteemed in Canadian pedagogical practice as a way of showing competence, just as it is in the culture of Japan’s education system. That is why I took the initiative to record myself today. I watched the footage without the rose coloured glasses of memory, viewing my performance under the cold fluorescent lights, warts and all, for a more honest self-reflection.
As I do when assessing my students, I’ll start with what I thought were the positives of my presentation before I move on to the criticisms: I seemed confident and well prepared, my speaking voice was loud and clear, and the quality of the activity was excellent. My classmates seemed to be challenged by it and enjoyed the process of solving the questions and proving it to their partners.
Now for the really valuable part of reviewing the videotape: identifying areas of improvement. Although I seemed well prepared, it bothered me that because of my nerves or my forgetfulness, I forgot to reveal the MATH t-shirt that I had worn specifically for this presentation and didn’t use my daughter’s microphone with the built-in speaker.
It was better that I forgot the gimmicks than the content of the presentation, but I think it definitely would have been funnier. Especially with reverb set to maximum echo.
One key aspect that I would not have noticed without video evidence was how quickly I was speaking. If I could do it again, I would have explained the slideshow more slowly and deliberately. I have several EAL students in my practicum class this Spring and I need to become practiced at slowing down for maximum understanding. At least part of my rushing cadence was due to the nerves that come with presenting to my peers. (There goes my ego trying to protect itself again.) I will have to film myself in front of my practicum class to be sure that I succeed in making that change. Another thing I would change would be my instructions for picking up the two pieces of paper from the front of the room. At first I said that one partner should come and get one of each. That was fine. Then, when someone asked for clarification, I said it should be one sheet per partner, confusing things more than if I had said nothing at all. Whoops. Something that I wonder about is if it would have been better to announce the mathematical goals of the activity at the start of presentation, rather than launching straight into the explanation of how a good skeptic operates. Someone told me after the presentation that they were confused at first because it didn’t seem to have anything to do with math. I feel like I am getting conflicting messages about the efficacy of mystery as a pedagogical tool; some professors say that students should always know exactly what is going on while some say that a mystery can drive curiosity. I can see the logic in both arguments but it’s unclear to me when (or if) deliberate obfuscation can be beneficial. During math class on Jan. 24, my fellow pre-service teachers and I played a game where the goal was practicing turning fractions into decimals. The game was ok, but the really fun part for me was working with my opponent to tweak the game and make it even better. Here are the rules we started with:
Base Game Rules
Jack = 11 Queen = 12 King = 13
My partner and I both quickly realized that it was usually unnecessary to convert the fractions into decimals because we could already see who was going to win the round by comparing the fractions. Here's how we decided to modify the game in order to achieve a deeper level of understanding between fractions and decimals. Modified Rules
I imagine this game has already been invented and ours was simply a re-invention, but it was still kind of thrilling to come up with the ideas and play test them. The actual game was almost as fun as inventing it! There were plenty of times when we immediately knew the decimal because it was 1/2 or 3/3 or 2/10 but it's fine that no points were scored on those rounds because that builds automaticity with fractions and conversions.
Every day during my practicum in December, I read my Grade 8 class a poem. Knowing that they are crazy about memes, on December 11th, I read them two pieces that have been thoroughly memified: This is Just to Say by William Carlos Williams and For Sale: baby shoes, never worn, apocryphally written by Ernest Hemingway. I put together a small compilation of mashups and song parodies from Twitter for their enjoyment. Now, you too, may enjoy.
I had thought that they wouldn't recognize the songs and be familiar with Twitter but I had it the wrong way around: None of them had a Twitter account and they all seemed to recognize the songs. I think I may have enjoyed this poem of the day more than they did, but sometimes it's hard to tell - Grade 8 kids are always trying so hard to be cool.
When preparing for my practicum at General Wolfe in September, I tried to think of a way that I could benefit the school outside of my contributions in the classroom, similar to the LEGO Club I started at Strathcona School last year. I initially proposed launching a lunch-time board games club, but my principal said there was no room in the schedule for any more lunch-time clubs. It didn't take long for a new idea to present itself. Although classes begin at 9:00am, students often get to school much earlier than that and sometimes get themselves into trouble because there isn't much to do except sit around in the hallways. On the first day of my practicum, I had to break up a full-on wrestling match. I noticed that without having an appropriate focus for their energy, some students were behaving poorly. Meanwhile, the gym was locked and dark. I asked if I could supervise in the gym before school and just like that, I'd found my niche. Each day of my practicum, I came to school early to open the gym, take out some equipment, and supervise - occasionally running basketball drills for those who wanted to practice.
There are hundreds of studies telling us that exercise is crucial not only for physical health, but for cognitive function and learning as well. Dylan Wiliam included 20 minutes of morning exercise for students as one of the main pillars of middle school reform in this BBC documentary. There is no doubt that having an open-gym from 8:00-8:45 would be a good thing for those kids who showed up to school early. It would keep them out of trouble as well as give a boost to their learning during the day. The question that remains for me is whether or not I should advertise this open-gym time to the rest of the school. The reason I "wrestle" with making this more broadly known is that I know how absolutely rabid the students at General Wolfe are about basketball. I know that many students who would normally sleep as late as possible, would set an alarm and wake up early to come and play ball. I wouldn't want to be responsible for students losing out on the 8.5 to 9.5 hours of sleep they need. Ideally, the choice between sleep and exercise should not be an either/or question - both are vitally important for good health. But in this case, should I risk student sleep deprivation by making an announcement to the whole school about the opportunity to come to an early open-gym, or should I refrain from encouraging sleep deficits by keeping quiet about it? I'm leaning toward advertising the availability of the open-gym but I'd love to hear what you think. Leave a comment below or get in touch on Facebook or Twitter. |
David Wiebe
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