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...
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.
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!!!)
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.
Communication. It’s an essential component of mathematics, especially when dealing with a student population whose first language is NOT the language of instruction!
A few weeks ago, I wrote about the simplification of criteria in order to help focus students on writing clear and succinct explanations when communicating solutions to problems they solve. That strategy seems to have worked for many of the students in my class: Below is a sample from some multiplication/division problems they solved the other day.
As one can see, it is easy to assess their understanding of the concept, as well as note where errors were made (and by following up with a short conference, one can surmise if those errors were mathematical, or linked to a misreading of the problem itself, due possibly to ESL factors).
Speaking of conferencing, my colleague, Dale, recently reminded me of the value of this: As we finished up our transformational geometry unit a few weeks back, he elected to evaluate students by meeting with them individually to orally assess their understanding of transformation understanding.
Dale showed what he had students do, including a question or to using a grid map from the text book, and a few tasks involving the translation, reflection and rotation of an object on a grid paper.
For each task, he made note of whether they were able to do it independently and confidently, whether they benefited from some teacher guidance, or whether they seemed completely at a loss, even with teacher intervention and support. (I stole his idea and created a recording template -- see photo below.)
In some sense, the conference became a bit of a teaching opportunity as well as an assessment measure. We conference daily or weekly with students for reading and writing as a way to assess and remediate as needed, why not in Math?!
I've often harped on the importance of employing "talk before writing" strategies like "think-pair-share"... Another thing I’ve noticed, both while conferencing AND while using such instructional tactics as “think-pair-share”, is the importance of wait time. It can take a while for students to focus and get on-topic. Giving them a few extra seconds or even minutes to chat with a partner, instead of rushing them through a discussion topic, can really help students to go a little deeper with their understanding. Although I know the research on wait time, I am always surprised when I actually remember to use it, and then students' responses are richer and more focused!
Simplifying success criteria, using oral conferencing as a form of assessment and integrating wait time into the instructional repertoire... three of the many ways we can increase student success as they communicate in math.
Something we worried about when starting this project was how we would be able to effectively differentiate for the wide variety of needs in our classes. But in many cases, differentiation wasn't a problem. Most of our problems and learning activities turned out to be "open" enough to allow multiple entry points.
But with our latest unit, Multiplication and Division, we've hit a bit of a wall!
As Grade 3 is the first year these topics are introduced, we felt uneasy launching right into parallel tasks, since for most students, we first had to develop the concept of multiplication as a more efficient way to add.
So, we gave everyone the same question. (Basically, a 3 x 7 number sentence -- see screenshot above.)
Ahhh... now the difficulties with differentiation finally showed their true colours!!!
The students who were new to multiplication muddled through, using some ideas introduced during our warm-up (arrays and making groups) to attack the problem and show/communicate their work. But for the students who had already memorised their times tables up to 12 at home, or at Kumon, or in the country from which they emmigrated, this simple question was painfully babyish! Even changing the numbers (say from 3 x 7 to 6 x 7) does not provide enough challenge, as, once you know it, you know it, this multiplication business!
The Ontario curriculum for Grade 3 only goes up to 7x7, so 2-digit numbers are extraneous. So, my poor friends who already have multiplication down are bored to tears, and causing all manner of, er, "interesting" behaviour problems while I attempt to guide the newbies to an understanding of this new concept.
Can't wait to move on to something more open-ended again soon... next week, next week!
Earlier this fall, I blogged about our weekly small math groups, which allow those students ready for more of a challenge to work with their intellectual peers, while other students spend time in smaller groups focussed on remediation of basic skills.
My own group fluxiates between 3 and 5 students each week, all of whom face major struggles with language, and demonstrate difficulty with basic number sense. Interestingly, I am finding that even working in a small group, my students struggle to pay attention, and each needs different areas of focused remediation.
Today, I tried a new approach, based on the success of my 1:1 conferences in Literacy...
While two students worked on an iPad app I had brought from home, and another played a 2-digit math game on the classroom computer with headphones, I worked with one student on a paper and pencil task, talking through the math vocabulary he was struggling with, and guiding him in explaining his thinking (we were rounding numbers to estimate).
After 12 minutes, we switched: I sent the student I had been conferencing with to go work with the iPad, and moved one of the students from the iPad to the computer. The computer kid then came to me, and we conferenced on what he needed - developing a firm grasp on the hundreds chart so he could use it to help himself round two-digit numbers up or down.
We continued rotating every 12 minutes so that by the end of the session, I had touched base personally with all four students. Then we played a small group math game together. The students left the session having had fun with numbers, and hopefully having learned a few strategies specific to their needs.
After the session, I reflected on whether I had used technology as a learning tool this afternoon, or merely as a babysitter.
Personally, I think the case could be made for both.
For example, although on one hand one might argue that the computer games and iPad apps were merely glorified worksheets, thus placing this task firmly in the the "substitution" phase of the SAMR model.
On the other hand, the technology allowed me to quickly pull up a math app or game suited to the specific need of a student in a way I couldn't possibly imagine customizing "busy work worksheets".
Further, the technology engaged the students sufficiently to allow me to work in an uninterrupted way with each student for 12 minutes at a time -- a significant chunk of time in which to intensively support specific needs and remediate isolated skills for those students. The "babysitting" provided by a tool which incorporates built-in feedback the way the games and apps do (both included visual prompts for the students whether they were correct or incorrect in their responses to a given math question) was beyond any task of which I could have previously concieved.
In this case, one might argue that the task as designed falls into the Modification phase... or at least straddles the Enhancement and Modification phases of the SAMR model!
At the very least, technology has most certainly caused me to consider how I teach and reflect on the effectiveness of the choices I make in ways that I didn't before I became more involved in its use in my classroom.
In my quest to remediate math skills in ways that don't interfere to heavily with the overall problem-based approach in my room, I’ve come across a series of math apps which I like especially for the visual imagery. iLiveMath by iHome Educator consists of several math apps that generate addition, subtraction, multiplication and division problems at the elementary level, within various themes, such as Oceans, Nature, Farming, etc.
Although in principle I am not in favour of a "skill, drill and kill" approach to math, I have been doing some reading lately on memory and learning, and I am reminded that repetition is one path to consolidation of skills. In this sense these apps and the activities they offer have their place in a more balanced math program.
What I really like about the apps is
One of the best activities parents can do to support their children in math (and in general) is to take them shopping. Although it is of course far easier to just do it yourself sometimes, taking children along for a grocery run, and asking them to consider food choices, costs of items, sales, etc., builds vocabulary and schema.
On of the students in my class this year is very lucky to have a neighbour who does lots of schema building with him She shared this experience with me the other day and -- with her permission (and a few edits to protect privacy) -- I am reprinting it here:
...Nilloah finally experienced real shopping.
As I'm sure you can imagine, this neighbour has the patience of a saint!
When I greeted Nlioah in class the next morning with, "hey, so I hear you went shopping!", he almost fainted. It was like magic! "HOW did you know that, Ms. Teschow?!" he exclaimed!
A little email is a miraculous thing.