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More Good News

11/20/2014

Yes. Good news. And it's about math and teaching.

But first, I must set the context: Today was one of those days where I seriously considered quitting my chosen profession and taking up ranks in the private sector... wait staff or floor host at a trendy, upscale vegetarian restaurant was looking good. Assistant manager for an eco-friendly retail outlet was also a contender as I perused the job postings in a feed I subscribe to. I even considered a position in -- oh, never mind!

Don't get me wrong: It's not that I don't love public service. It's more the slavery aspect that doesn't appeal to me. Long hours (haven't seen bedtime before 1 a.m. in weeks!), largely thankless (and sometimes even accusatory) clientele, systemic challenges that complicate an already-near-impossible job... when you're part of the over-forty crowd like I am, there are times when you want to taste success. More often.

So I sometimes fantasize about a job where the people can choose. Rather than being stuck with me, they can choose whether to come into my shop or not. The accountability factor has immediate ramifications, and GOOD service is rewarded quickly.

But then, I'd miss the intellectual rigour that teaching can provide. I love assessment that drives instruction. I love always trying to make it better. I love planning in ways that I think and hope will engage my learners, even the most reluctant ones, and I love partnering with colleagues to share ideas and design new and interesting learning challenges. It would be hard, too, to find a job that matches the opportunity for impacting social justice in the world in ways that public education does.

Nevertheless, when I watch a student who struggles to pay attention at the best of times pull out yet another can of pop and two bags of fuzzy peach candies for "lunch" (no, that wasn't desert, that was the whole lunch!!!), I feel sometimes, well, helpless and overwhelmed.

SOOOOOoooooo, it was very exciting when I opened an email this evening from OTF, to whom I had submitted -- some weeks ago on behalf of myself and two colleagues -- a funding proposal for 1-2 netbooks in the classroom and a few days of release time to facilitate my/our learning about and planning for the centers-based approach I've been exploring in math to find that (drum roll please.....) despite the extremely high number of submissions this year, OUR PROPOSAL WAS ACCEPTED AND APPROVED!!!! :))))

So, maybe I'll stay in the game for a few more months.

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Engagement for the reluctant math learner

11/19/2014

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Today something happened in math class that illustrates those moments we career teachers live for...

For a few weeks now I've been engaging my intermediate students in learning through Math centers. The idea is that they work independently (either alone or in a small group) at various guided learning stations while I do some precision teaching with individuals and small groups of students, based on diagnostic and observational data (currently geometry).

Although some students took quickly to the model and are relishing the independence (and using it wisely; a small group today presented a self-designed power point on Pythagorean theorem to the rest of the class), others have needed a little more convincing.

One gal in particular has been desperate for spoon-feeding. "Please, can you just teach us?" she pleaded one day in a winy voice, as I checked in on her while she wandered listlessly from one station to the next, seemingly unable to get started on any meaningful task. My mini-lecture about needing to become independent learners capable of choosing wisely from the learning buffet of life did not convince her.

But today, today I think my little friend embarked down the road of self-inspiration: Asked at one center to identify and construct the five platonic solids, she and a peer set out half-heartedly to build an octahedron out of the plastic polydrons provided.

The "net" just didn't click for her at first, and she came over to me and ask if I would build it for her. When I declined, she nearly gave up, but with a little encouragement she suddenly saw the task for the achievable challenge that it was.

"Okay, let's DO this!" she decidedly announced to her partner.

Not long after that, they arrived to show me their completed octahedron, and insisted that they be allowed to put it back in the center as is for all to see and admire, rather than tear it apart when it was time to tidy up. :D

I am looking forward to observing and fostering my new convert's progress as she continues to discover the joy of meaningful, self-directed learning.

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Oh Yes, I did!

11/19/2014

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Biked home in the snow tonight. Yup. 14 km.

Other than a few frozen eyelashes, I was warm; thankfully yesterday morning's headwind adventures taught me to remember my proper biking boots and a few extra layers to add/shed as needed. And Claudio Monteverdi carried me through to Queensway and Islington, where my iPhone finally died. But boy, was it ever tough going... cold, wet flakes stinging my eyes, slow skidding tires all the way home: My 42-minute ride took nearly an hour and half!

It didn't help that some drivers seem compelled to share their personal (uninformed) perspective on winter biking with me while whizzing past way too close; one charming fellow -- all the commentators were men driving large vehicles, as an aside -- rolled do the window of his SUV and yelled out some obscenity to me as he splattered past on the Dundas turn-off to the 427.

I responded with an equally hostile tone, and added some choice words for good measure. While I'm doing my best to stay reasonably fit and trying to offset my carbon footprint at least somewhat (yes, even on snowy, crazy days like today), it would be helpful if my car-driving fellow planet dwellers could simply move over a bit as they're passing, or least just drive by and keep their horns quiet and their mouths shut. What I don't need while I'm biking by as safely as I can under extremely challenging conditions is you to roll down your window and spontaneously share your personal opinion about winter cyclists, or give me a naive lecture about helmets, or yell at me to get off the "#%^&*@!" road and scream at me about road use and right of way (last time I checked, the tax rate I pay for roads and infrastructure is the same as yours!!)

I supplemented my angry verbal response with an appropriately-paired hand gesture, though admittedly, since I was wearing mittens, the effect may have been lost on the guy.

Once home, I left my trusty steed to drip dry onto the floor while Simon and I walked over to the Indian place for dinner. It (the bike, not the curry) made a pretty good mess, but was easily cleaned up with a rag and a bit of warm water after we got home.

A fun adventure for sure, but I can't say I'm not glad to be taking the bus to work tomorrow!

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It seemed like a good idea at the time...

11/16/2014

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A few weeks ago, a Grade 7 colleague and I cooked up this "brilliant" plan: As we were drawing to a close with our study of Ecology in Science, we thought it might be neat to assign the students a comprehensive, cross-curricular culminating task. They were to select an audience (a younger class, in grades 2, 3 or 4), and design and promote a "field trip" to our school's courtyard.

The assignment included media and written components for Language (students chose to design a poster, announcement or brochure advertising their proposed field trip, and wrote letters persuading the younger students or their teachers to come, or wrote explanations of what would be learned on the trip). Also included was a Science component (they had to prove -- in writing and through the details of their planning notes -- their understanding of biotic and abiotic interactions and in particular, the effects of human interactions on the environment) and even a Math component (they were asked to use the per pupil cost they had decided on to calculate how many classes they would need to process through their "trip" in order to pay for a new laptop for our classroom, or for a visit from Scientists in the Schools for three Grade 7 classes).

All great... until I ended up with a GIANT stack of marking which took over my life for three days straight!!!

In addition to the Science and Math components for two classes this weekend, I also had two class sets of math journal entries on square and cubed numbers to read and assess. Oh, and Alex and Simon were with me this weekend.

WHAT WAS I THINKING???!!!

Thank goodness my partner is currently out of the province, so I was able to incorporate her desk when space on the dining room table became scarce! ;-P

And truthfully, this assignment really does separate the wheat from the chaff... while some of the work is relatively superficial, a few outstanding assignments really demonstrate a deep understanding and real life application of both the science we've been studying since September and specific application of math problem solving skills. So, overall, I am glad I undertook it.

But... perhaps I ought to have waited on the math journals?

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Nurturing growth mindset in math

11/8/2014

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Last year I read "Mindset" by Carol Dweck; now it seems the word is everywhere, especially in math education, where many have long felt (erroneously) that one needs some sort of innate skill or "talent" to be good at math. (Dweck argues, "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", and that the research on neural plasticity supports this idea, and further, that certain types of parenting and teaching promote growth mindest, while others inhibit it.)

This evening I watched a math webinar with Maria Vamvalis from TC2. Nurturing a growth mindset was on the agenda. I plan to keep this in mind as I prepare for a math workshop I am facilitating for teachers in Guelph in a few weeks, but also in working with my own students in class.

Based on a slide from Vamvalis' presentation, I've developed the following "exit ticket" to use as a self-assessment and learning encouragement with my Grade 7 and 8 students over the coming weeks; I'll use their feedback in addition to my own observations in class to develop next steps for each student.

exit_ticket_growth_mindset.docx
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My goal is to communicate effectively with my students that it's okay to make mistakes, and that the critical feedback I give them I do because I believe in their ability to learn and grow.

P.S. Check out Jo Boaler sharing research about the impact of "I believe in you" statements on student work!

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bedtime...

11/8/2014

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Geometry Centers

11/7/2014

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In an attempt to practice the Board/ministry's mandate to teach math using a more balanced approach, and meet the needs of a variety of learners more effectively in the math classroom, I have been exploring teaching through centres.

Those familiar with the Daily Five and Literacy Café and their mathematical counterpart will have a sense of what "centers" can look like at the primary level, but there is precious little to support guided teaching and independent learning at the intermediate level, I have found. Researchers I have read wax poetic about helping students develop growth mindset, and supporting a variety of learning needs, but the "how to" manual seems to be missing.

So, inspired by a math workshop I attended this summer, and supported by my school's instructional coach and another grade-level colleague at my school, I set about developing a set of generic "centers" earlier this year. The idea was to use the curriculum expectations for each unit to develop specific learning activities for said "centers", so that once students were "trained" in the classroom management particulars, they could monitor their own learning, freeing me up to focus on guiding small groups of students with similar needs and conferencing with individual students to teach and assess.

It's been a work in progress, to say the least.

A Rocky Start

Given that I had six classes to teach, many of which -- pre-reorg -- were quite large, and given that my LCD didn't work for a week, and given that I was still acclimatizing to a new school, things did not begin as smoothly as I had envisioned. :)

But, knowing how important the process is for students to develop their identity in relationship to math, especially at the Intermediate level, I pressed on, determined to make enthusiastic, independent math learners out of my students!

After completing a whole class introductory unit from TIPS as well as some real life problems in Number Sense, my school's instructional coach and I sat down to map out a series of Integers learning activities, and hunt down an end-of-unit test to measure growth.

Permitting students to choose which center(s) they wanted to spend time at allowed them to become key players in their learning, and to develop more metacognitive skills. (I.e.: What do I know? What can I already do? What am I struggling with? How can I improve this skill?)

students who develop a sense of identity which resonates with the discourse of mathematics are more likely to continue with their studies than their peers who do not develop such a sense of identity."
- Jo Boaler, Stanford

Learning Goals and Success Criteria

It quickly became apparent that for many of the students (especially those in my grade 8 class), this was a new way of doing business in math. We therefore provided them with the learning goal and success criteria, rather than co-constructing these. Hopefully we will move into co-construction of criteria later in the year, as students become more comfortable with self-assessment.

Providing a learning goal up front helps students to focus their learning throughout a unit, and the success criteria offer specific language which students and teachers can use for descriptive feedback as they work through the various learning tasks within a unit.

Assessment and Evaluation

As per Growing Success and current assessment practice, teachers assess students using various tools and methods. Watching students work through a problem and taking anecdotal notes, questioning students about their mathematical thinking and listening to their responses, conferring with individual or small groups of students, and -- sometimes -- providing paper and pencil tasks such as a quiz or a test are all pieces of evidence that can be considered for assessment purposes to drive instruction, or to formulate a summative mark at the end of a unit.

A Baseline for Geometry

One thing we learned from our first attempt with Integers was that we needed to get a sense of what students already knew and could do, skill- and strategy-wise, in order to plan for instruction in small groups.

We therefore developed a short, simple "Show what you know" diagnostic with tasks that would demonstrate to what extent students already knew some of the necessary vocabulary and end-of-year expectations.

(The grade 7 one is shown to the right.)

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After being introduced to the learning goal, students completed the diagnostic, knowing that the expectation was that they probably would not do particularly well, since this was a beginning of unit task, and that the results would be used to drive instruction and measure growth at the end of the unit.

Developing Small Groups

My Grade 8 class surprised me. Many of them had a fairly solid foundation in geometry already, and a few of them did exceptionally well, leading me to consider how I could best differentiate for their learning needs (With the help of my instructional coach, I developed several problems -- based on Marian Small's work as well as the curriculum and the textbook -- and also challenged these students to create a center or lesson to show what they already knew in a particular area to another group of students. We will see how that unfolds in the weeks ahead!)

The students who did not "ace" the diagnostic fell into three primary categories:

those who needed help refining their use of protractors
those who would benefit from some guided instruction with 3D shapes to help develop their spatial sense
those who need to develop their mathematical vocabulary in order to communicate with clarity and precision

I proceeded to develop a series of small group and individual meeting sessions, which I post on the overhead at the beginning of each class so that students know who is working independently, and who is meeting with Ms. Teschow.

A reminder of the unit learning goal and success criteria is also posted. (See below.)

Knowing and Supporting Student Skills and Knowledge

Meeting with students in small groups provides an excellent way to really get a sense of what they know. I am finding that this way of teaching helps me to clarify mathematical misunderstandings in the moment and do some on-the-spot precision teaching as needed for individual students.

Working through centers also allows the more mathematically advanced students to work on math of interest to them, rather than being held back by their peers with other needs.

Students Knowing Themselves

As the work of Boaler, Dweck and others researching mindset shows, students need to develop an understanding of themselves as learners in order to authentically improve as thinkers. Regular, specific self-assessment opportunities can help to develop metacognitive skills.

Descriptive Feedback & Communicating Progress

One challenge I am finding is communicating progress effectively to families. Whereas in previous years, I have had one class for whom I teach most/all subjects, this year, I have several classes, not all the same grade and subject. Much as I would like to, it is impossible to make weekly or even monthly phone calls to 120 or more parents! And yet, the progress report in November and the First Term Report Card in January don't seem adequate tools to share all the learning that's happening in Ms. T's classroom!

I am still working on ways to communicate descriptive feedback in ways that are effective for students and parents, and manageable for me as a teacher.

When meeting with students, I record observations about their work and/or our conversations in my marks tracking binder (well, on a clipboard this year; I'm finding it more effective to have multiple clipboards to manage so many classes). I also provide oral feedback to students as we work together.

This allows me to see many students each day/week, and balance recording progress and communicating next steps with accomplishing the personalized teaching of as many students as possible. What it doesn't allow me to do is communicate regularly and in great detail with families, many of whom may be wondering what strange things are happening in Ms. Teschow's math class! :)

In response to this need, I've recently developed a feedback recording sheet (above), where I can copy specific notes from my clipboard and conversations onto a slip of paper that students can share with their families. While this won't work for everyone, I'm hoping it will help with some students who benefit from written rather than oral feeback.

I'm still searching for ways to communicate effectively while allowing the time needed to have meaningful conferences and check-in points with students throughout the week.

A Work in Progress

Our reflections from the somewhat scattered process from the inaugural Integers unit resulted in a far more organized Geometry Unit; I am tremendously enjoying the teaching and learning happening with my Grade 8s in math, and am looking forward to beginning geometry with my Grade 7s. But there is still lots to learn. Will a traditional unit test at the end be enough to capture the growth from the baseline? And if not, how can I incorporate choice into the alternative summative tasks so that students can effectively show what they know in the way that best suits them as learners?

I look forward to answering these questions and many more as the year unfolds, and plan to seek ongoing feedback from the students as to how to improve as we go.

Geometry Centers

For those interested in trying this approach, or looking to supplement their own work in Geometry, feel free to download, modify and use any of the centers below. Please note, you will require polydrons or paper nets, and power polygons. Center 7 for this unit is Blokus.

Grade 7 Geometry 1 Centers*

Grade 8 Geometry 1 Centers

2_-_manips.docx
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3_-_online_math.docx
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6_-_problems_challenges.docx
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8_-_journal.docx
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2_-_manips_as_thinking_tools.docx
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4_or_8_-_understanding_lines.docx
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6_-_problems_challenges.docx
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Resources:
The ideas for the learning activities in these centers come from the Ontario Math Curriculum document, Marian Small's "Big Questions" and "Eyes on Math" books, and the Grade 7 & 8 "Math Makes Sense" text books.
* Transformational Geometry is coming in Term 2

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Post-Progress report Family INterviews

11/6/2014

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Preparing to meet with families to discuss the progress report? Looking for a few templates for interview letters or for keeping your 15-minute conference on track?

This is the first year I am not able to do my usual student-led conference schtick (the school I teach at this year is on full rotary, which means I see over 120 students, usually just for one subject, and so interviews are held collaboratively in the gym, with one or more teachers in attendance, as able).

In an attempt to customize the experience for students and their families as much as possible while maintaining some semblance of organization for myself, I've developed the following templates:

1. Interview Confirmation Letter Home
A letter is sent from the school earlier in the week to collect preferred meeting times from families. Over a few chaotic lunches, teachers dash madly in and hour of one another's rooms and attempt to coordinate who's meeting whom when. Then the homeroom teacher sends a note home with the report card, confirming the student's interview time.

2. Interview Planning Sheet
With only 15 minutes per time slot, there isn't much margin for guesswork. Get yourself organized for the conference by preparing notes about each student's meeting and family situation and including student, teacher and family perception of strengths, learning needs and next steps. A space is also included for follow up. Page Two is a "fill in the blanks" letter that parents can complete and give to their child some time after the interview.

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interview_notes_and_letter_from_parents_to_kids.docx
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progress_report_student_reflection_and_goals.docx
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3. Student Reflection and Interview Prep Sheet
Even with only 15 minutes to meet, I think it's important for students to be present at the conference. After all, it's about them! :) This template helps students reflect on their progress and consider what they might want to share with families at the interview. (Modified from this pdf, sent to me by a colleague at school.)

Hope these templates are helpful to my teacher readers -- feel free to modify and use as you wish. Good luck, teachers and families, with your upcoming student-led conferences and interviews!!

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