But it's baking in my classroom facing the hot, hot sun, and I'm tired! So, for today's blog post, I will let the pictures do the talking...
If I were a good teacher, I'd have co-constructed criteria with them, and had them play their games and then measure the success of their games against said criteria. Or, I could have tied in my persuasive literacy unit and had them write advertisements trying to convince others to play their games. Or I could have assessed their rules for the game and used it as a mark for procedural writing.
But it's baking in my classroom facing the hot, hot sun, and I'm tired! So, for today's blog post, I will let the pictures do the talking...
Today I rec'd a comment from a reader asking about the assessment template for an oral interview in Geometry which I had blogged about a few weeks ago. She wondered if I could share a copy to use as a base from which to build her own template.
Here it is below (on the left). I've also included another, more generic, class list for math (on the right) -- this one happens to be for the Measurement strand.
I should mention that I am not in favour of reporting on discrete strands in math, because over the year I have come more and more to believe that the skills developed in one strand of math are interconnected with other strands. A good, rich problem may require the use of tools and skills from a variety of strands. However, our current reporting reality in Ontario predicates reporting a mark in each isolated strand of math, so I offer this template below (on the right) as one possible option: Three spots per student are included for "marked" or graded assignments; in addition, there is space for anecdotal comments to be made over the course of a unit. Once the overall data is considered, and a "final" mark for the unit is arrived at, it can be recorded in the space to the left of each student's name. These marks can then be quickly entered into report cards
Students wrote their questions and concerns on index cards, which I collected and grouped for tomorrow's math class. Based on this self-assessment, my support teacher and I will work with small groups and individuals to do a bit of specific remediation on the topics which student self-identified as still tricky. In some cases, students will be partnered with other students who indicated their comfort with and willingness to tutor a specific concept.
I am also planning to dig up an extension activity for the 4 students in my class who are very confident overall in math; I had them share what they wanted to learn more about, and will follow up with that later this week for those students.
Once EQAO is done, students will work with a partner or in a small group to create a "math game", addressing at least two strands of math, to teach Grade 2 students for next year.
Something that came up at the OAME conference we recently attended was the idea of learning goals: Should they be clearly stated at the beginning of a lesson for students, or not?
Dale blogged about this very topic recently, after reading John Hattie's "Visible Learning for Teachers". The research seems to indicate that when students know where they're going, they are more likely to get there. It kind of makes sense: The video games our children so often play always begin with a goal or a "mission", so why not our math lessons?
On the other hand, the goals of a lesson can be manifold: A recent lesson on probability I taught to my grade 3 students focused on the vocabulary of the new concepts we were learning: certain, possible, impossible, likely, unlikely, equal chance and so on... So, one goal was to learn and correctly use these new words. But another goal was communication. I wanted students to communicate their solutions effectively, using a sentence to share their "answer" to a problem I had presented, and to include some sort of explanation (diagram or illustration, math term, or more words) to tell how they arrived at said answer. A third goal was reasoning. We've been working on asking ourselves, before we present solutions to a problem, "is this a reasonable answer? How do I know?" Finally, since students were working with a partner to discuss this particular problem, we were focusing on collaboration for learning skills; I was observing how well they listened and shared with one another during the work period, so that I could collect some data for report cards.
Am I to share ALL of these goals with my students? And if so, when?
After fiddling around with some different models, I have found it effective to highlight the mathematical goals of a lesson or unit early in the lesson, right after the "minds on", and before presenting the actual problem that students will work on. An addition, I will often draw students' attention to the criteria which we co-constructed earlier in the year, about how to best communicate thinking, which are permanently posted in the room for handy reference. I do this as they are working, but before they share their solutions.
At the beginning of May, Dale and I were lucky enough to attend OAME, an enormous, annual conference for mathematics educators across Ontario. We had submitted a proposal to present a double session at the conference, sharing our own work, and this allowed us to attend the rest of conference free of charge. (Release time was provided by the TLLP and our Board’s Program Dept.)
We both attended the keynote on the first day, as well as an “advanced bansho” session on Day 2. In addition, each of us attended one other session, and spoke with a number of attendees on both days. Our own session, entitled simply “Smart Bansho”, had about 30 attendees.
A conference of this size tends to surface a number of common themes; it seems that many of the sessions, key notes and casual conversations with colleagues at lunch generate similar “big ideas”. This year, I came away from the conference thinking about these two things:
1. Social Justice has landed in the math classroom! The keynote on the first day spoke explicitly about this, several workshops addressed the topic specifically, and many others embedded it or referred it in their sessions. I will blog on social justice in math in a separate post.
2. The math processes and “big ideas” in math are critically important to a cohesive presentation of the math program by teachers; we need to stop focusing so much on individual expectations, and rather consider how we can best weave these together to facilitate our students in developing a sense of the grander scheme of things. Already some schools and school boards are using the math processes rather than the overall or specific expectations to report on progress in math. The processes are inter-strand; communication or reasoning do not just live in “Number Sense” or “Geometry” but transcend many or all five strands of math, as do good, rich problems which help students develop these skills.
3. Teaching math well takes time. Well, okay, this was not new learning for me, but rather, a confirmation of reality! Dale and I spent a double session with colleagues across the province developing and doing ONE math problem. ONE! The importance of doing the math in order to anticipate possible student responses was underscored. Taking the time to think about how the pieces fit together, and how best to present different concepts (and in what order) to students, considering how to integrate issues of social justice and equity meaningfully into ones lessons, make math "real" for students, assessing their work and providing timely, personal, descriptive feedback... it all takes time. Dale and I really recognized that this year, as we were blessed with so much release time to think about and address some of these things.
The trouble of course is that as the thinkers in the intellectual organizations and the practitioners in the classrooms come to recognize how to do things well, they/we are stifled by archaic institutional structures. A simple example is the Ontario Report Card. How, dear readers, am I to realistically track and report a discrete mark for five individual strands of math in a program that effectively integrates across strands and processes? How do I transform my detailed, individualized observations of each student's strengths and needs into a generic chunk of text that can be plugged into the limited box provided on a report card designed for the masses?! (I asked one of the presenters at a workshop this question -- her reply was that she "doesn't worry about report cards too much". Easy for her, I commented to my table group; she hasn't had to write them in almost 20 years!) When do I get to meet with colleagues down the hall and across the province, on a regular basis, so that effective practices can be meaningfully shared amongst the people who use them daily with real students in real classrooms?!
Although the impossibility of the task at hand can seem overwhelming at times, it is nevertheless exciting to attend a conference like this and take in some of the many tools, resources and ideas that are constantly being developed in mathematical instruction. I am left with lots to think about.
Thanks to additional release time funding from the TLLP, this morning I had the opportunity to interview Michael Wendler and Jason Rodger, two junior teachers from Ottawa-Carlton District School Board who have been early adopters of IWBs in the Math Classroom.
Jason and Michael teach in a fairly large, K-6 school in Ottawa, with a mainly middle-class, culturally diverse population. Their school has two laptop carts and a class set of iPads which teachers can sign out. Thanks to the efforts of a small but dedicated group of teachers, several classrooms also have Smart Boards in them now.
After reflecting in some detail about the challenges and opportunities that technology presents to teachers at different places along the continuum of tech-comfort, we spoke about how teachers use technology to integrate social justice into their programs, and make learning “real” for students. We also addressed student vs. teacher use of the IWB as an instructional/learning tool in the classroom, and the boys shared some of the different apps and programs they have found useful in their journey with students. It was really encouraging to see two teachers at different stages of SAMR being so comfortable learning from and sharing with one another, and it made me feel more optimistic about my own abilities as a teacher who still uses technology primarily to substitute and augment, rather than to modify and redefine!
After a brief earthquake (no, I’m not kidding; we all felt the tremor, on both sides of the Skype!), we chatted briefly about some more philosophical things, like how some students with an LD can really focus when it comes to video games, and how we can harness that interest and ability with technology, and we also discussed the more pressing matter of TIME, which seems to be in ever-short supply for teachers across this province. (How do you build in the time necessary to be a learner of the “new” tools, for example, and develop a basic comfort and confidence with them, so you can use them effectively in your classroom?)
Before we knew it, our time was up, and we were wrapping up our discussions and trying to figure out the logistics of how to get over an hour of Skype footage edited and up onto the Internet so that others could listen in on our conversation.
It was good to hear from two such engaged educators, and see how colleagues from other parts of the province are using technology to develop mathematical understanding with their students. As Michael noted near the beginning of our Skype session, and Jason concluded towards the end, technology needn’t be overwhelming. Beginning with one small step can open the door to unlimited possibilities not just for students, but for us, the teachers who teach them.
Thanks, Jason and Michael, for your enthusiasm, and for your willingness to share with this new-to-technology teacher!
(Please stay tuned... video and/or audio footage hopefully coming soon!!!)
As EQAO approaches, we've spent some time comparing our written responses to various open questions to exemplars from the EQAO website, using student responses from previous years as anchors, and then considering how to improve our responses.
No matter where they were when they started, every student who agreed to have their work photographed ended up with a Level 3 or 4 answer. My goal was to make every child feel like they could achieve at or above standard, by showing them how small tweaks to what they'd already written could dramatically improve their communication.
Today guest blog is written by Jason Rodger, a CCT and Grade 6 MFI Teacher in Ottawa, Ontario. If you like what you read below, or even if you want to challenge it, please post a comment. I will be interviewing Jason and his colleague, Michael Wendler, this Friday, to talk about Interactive White Boards and Math. Your comments will help engage the conversation. So please, consider leaving a comment below, or contact me here.
I remember in my first year of teaching, looking around my empty classroom, bereft of resources and manipulatives, and seeing textbooks galore, thinking: There has to be a better way.
It struck me finally one day when one of my students asked me about the question in the text.
“Do farmers really count kernels of corn?”
If I was going to teach math I was going to have to teach it differently. I needed to teach math in a way that made sense to me and was going to contribute to my students learning in a more meaningful way. Within a week, I had rolled an unused media cart into my classroom, I had commandeered the little-used computer lab across the hall, and the textbooks were ditched. I was all-in and extremely nervous that -- as a new teacher -- I was going to be “found out” and my choices would be questioned. Six years later and the books have never made their way back in.
So how, as a new teacher, or one wishing to make the transition, do you begin a technology based math program?
Read, Read and Read Some More
There are some amazing digital resources available to teachers, and Twitter has become my chief source of education and technology news. Create your own network of educators and begin to read what they post. Begin following the people whom they follow. Find your board’s technology and math gurus, and ask them to point you in the right direction.
My go-to site for tech education is Clif Mims, member of the University of Memphis‘ Instructional Design and Technology faculty since 2005. His news daily can be read here:
Become the Tech Expert
I hear from a lot of teachers that they don’t have any technology at their disposal. Does someone else at your school? A friend at another school? Can you register for workshops which would be of interest?
You must invest the time in learning the technology. Simple as that. You cannot expect to use technology as a part of your daily math lessons if you have never explored the technology yourself. In using the technology you will naturally think of new and interesting ways of using it as a part of your math program and develop ways to integrate it into the curriculum. Always remember that the curriculum tells us what to teach but not how to teach it.
Here are some links to get you started:
3D Tin: www.3Dtin.com
Google SketchUp http://www.sketchup.com/intl/en/
The National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html
The Medium is Not the Message
Technology is cool. Technology is fun. It is also expensive. The novelty of using technology in the classroom is fleeting. When I began using technology to teach math six years ago, technology had not yet penetrated every aspect of our lives; using technology was enough to captivate students' attention and hold it. No more. Technology in the math classroom has to have a purpose. I hear teachers say it would be neat to have X piece of technology in their room. If it’s neat you are looking for, look elsewhere. These are tools that can be used to create amazing work, whether 3D landscapes and architecture or using an excel spreadsheet to graph student generated survey results. If students are given real work, with a true purpose, incorporating newly acquired tech skills, they will surely fly.
Still not Convinced?
Here are a couple of inspirations for you.
The first is a very well known RSA talk by Sir Ken Robinson about the need to change the delivery of education, and a new talk about education’s Death Valley
The second is a TED talk by British technologist and big thinker Conrad Wolfram. He advocates strongly for introducing tech into maths and makes a compelling argument.
Start with integrating one new item a month to your teaching and before you know, it you’ll be an expert spreading the gospel of tech to your colleagues!
Jason Rodger is a CCT and Grade 6 MFI Teacher in Ottawa, Ontario. He and his colleague, Michael Wendler, will be interviewed by me on Skype this Friday, May 17, 2013. Please leave a comment or question which you may want him to address during our interview later this week. Interview blog will be posted next week.
Probability comprises concepts that many adults struggle to understand. (Not convinced? Just have a look at our booming lottery business!)
How, then, can we engage children in such a way that ensures they build a solid foundational understanding of this important mathematical area?
Since many of my students have developed strong oral language skills this year, especially when working with a partner or in a very small group, I developed a series of lessons that drew heavily on the instructional strategy of "think-pair-share", and banked on Van De Walle's games-rich chapter on probability. We spun spinners, rolled dice, made and tested predictions, played "hockey" and other goal-based games that depended on predicting outcomes. But first, we explored the basic vocabulary of probability: chance, possible, certain, impossible, likely, unlikely, equally likely....
A number of scenarios were presented on the board, and students had to discuss whether each was certain, possible, or impossible. Then we moved each scenario into the appropriate part of a Venn diagram on the Interactive White Board.
Lots of wait time was provided for students to consider and discuss each scenario, and as you can see from the photo above, they were quite engaged: For once, every student was either looking at the screen, or discussing the scenario with nearby neighbours!
Next, students engaged in a "continuum of probability" mini-lesson, in which we moved a series of five different spinners into sequence from impossible to certain. It was a great opportunity for them to see each of the new words they had learned in the bigger context of probability vocabulary and concepts.
Finally, after lots and lots of thinking and rich talk, I asked students to work on their own to write down a few examples of things that were likely, impossible, certain, etc. I used this exit ticket as a diagnostic assessment to see what level of understanding most of the learners were at in order to fine tune my next lesson, which involved a series of probability math games.