Division models

One of the best ways I’ve found for infusing inquiry into my approach to teaching mathematics is to introduce new topics and concepts with a challenge. Recently, we explored Division by asking volunteers to share on the whiteboard techniques for visually modelling the division expression 21÷3.

Taking the time to do this has many benefits, including:

  • providing an opportunity to build confidence through peer to peer teaching
  • introducing, highlighting, and discussing a variety of accessible strategies
  • developing mental models which can be referred to as learning continues
  • initially assess general understanding of the concept in a zero pressure setting
  • review learning that may need to be refreshed before engaging more deeply.
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Student Survey analysis 2016

This year, my Student Survey results held few surprises (link to view last year’s Student survey analysis). Items directly related to me, such as ‘My teacher cares about me’, were positive. Generally, 70-80% of students answered ‘usually’ with very few, most often only one student, answering ‘no’.

Listening to students

One surprise was the response to the statement, ‘My teacher listens to me.’, to which 48% of my students think I only ‘sometimes’ listen to them. Slightly baffled, I reflected on my practice and identified a few of my behaviors that could lead to this result.

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First, as a rule, I ignore students when they suddenly shout across the classroom, begin asking a question without saying ‘excuse me’ or otherwise catching my attention, and especially interrupt other students. I can easily understand how a child could perceive that I am not listening to them because in some cases, I intentionally don’t listen in order to cultivate a culture in the classroom of politeness.

Of students who responded ‘sometimes’ or ‘no’, their overall average response was only 69% positive, meaning that those who responded negatively to this item were also negative to most of the other items. Of those who don’t feel that I ‘usually’ listen to them, 69% also don’t feel free to ask and answer questions, a tenuous correlation.

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As a simple action plan, I would follow the steps below.

1 Observe if and when I don’t listen to students.
2 Make more explicit that I sometimes ignore students speaking to me if they are acting disrespectfully or impolitely.
3 Reinforce our classroom essential agreement – which was composed, synthesized, and signed by all of the students – about being Open-minded Communicators.

We are Open-Minded Communicators.

We have a right to share our opinions and feelings.

We have a responsibility to show respect by listening and practicing empathy.

I would also note that of all of the classes I have taught in nine years, this is by far the most needy. During any written assessment, there is a constant queue at my desk and barrages of hands in the air asking for help. My email box is also consistently populated by emails from students asking to send PDFs of lost homework and other requests for favors which I politely decline. It is possible that their concept of the role of a teacher is significantly different than mine.

Choice and agency

A difference in expectations might illuminate another perplexing survey item result to the statement, ‘My teacher allows me to demonstrate my understanding in various ways.’

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For their first unit Summative Assessment Task, students had the instruction to ‘Present your research findings in an appropriate medium of your choice (written report, video, poster, dance, cooking, etc).’

Almost everyone in the class chose to do an oral presentation with a poster or PowerPoint for visual support. The remaining two students submitted written reports. Although this may only be a case of carefully reading and following instructions, I feel justified in being somewhat annoyed.

Respect and classroom behavior

I was shocked to discover their responses to the statement, ‘Students are respectful to each other in my class.’

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Only two students think that their peers ‘usually’ treat each other with respect, and almost a quarter feel that their class is always disrespectful. The same holds true for their perceptions of classroom behavior.

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When I asked if anyone wanted to learn in a class like the one shown above, no one responded.

I have discussed these results with my grade level team, administration, and the precious grade teachers. All assured me that the students’ feelings about their community are absolutely about complex social dynamics. In brief, this class has too many ‘alphas’ and not enough empathy. This is a case study to test my ability to cultivate social and emotional intelligence. And a fair and timely challenge it is.

A future post will detail the reflection and data informed action plan I have set into motion to help this learning community to become more Caring.

I would certainly appreciate anecdotes and suggestions that might more brightly illuminate a path forward.

‘Level up’ transdisciplinary skills

In the IB Primary years program, ‘Transdisciplinary skills’ play a critical role in planning, teaching, and assessing student learning. However, they are not often explicitly taught and when they are, it is usually in an isolated manner. For example, one might teach a mini lesson about ‘gather data’ as part of a unit of inquiry.
To reinforce the transdisciplinary nature of the skills and provide more opportunities for students to reflect and discuss them together, I designed a slightly gamified system.
Each skill is posted on the wall with an eight by one square grid underneath.

 

Each square represents a level. Every Friday, students are invited to nominate a skill to ‘level up’ and support their choice with examples from the week. For instance, a student could suggest that we have increased our ‘organizing data’ skill by learning how to use a new type of graph.
Each colored box represents a brief class reflection and discussion of a particular way to practice a skill.
The learning around this simple chart in barely ten minutes per week has been incredible, and occasionally students comment during class that we are practicing a certain skill.
Another benefit is that as our skill levels grow, it becomes more difficult to achieve higher levels. In the photo above, ‘Listening’ is at level seven with only one space to go. Many nominations have been made, but I have had to politely decline and explain that to achieve the final level of Listening, a new innovation will need to be discovered. I’m holding out for some expression of active listening, questioning or paraphrasing to improve clarity and understanding in communication.
Our skills reflection routine, for its minimal investment of time and materials, has provided opportunities to explore the nuances of each skill and highlight the importance of applying them in diverse contexts.
Perhaps before the end of the school year, we will finally level up the elusive Metacognition.

 

Integrating public speaking, peer assessment, and data handling

As a formative assessment task within a unit focused on advertising, my class recently completed a learning engagement which integrated persuasive writing, public speaking, peer assessment, and data gathering, organization, and analysis.

Public speaking

The first step was for students to apply what they had learned around the central idea, ‘People create and manipulate messages to target and persuade specific audiences.’, by presenting their own persuasive speeches.

One of the most powerful tools we explored were TED talks about children.

We followed a typical writing process which featured prominently rehearsal and peer feedback.

Peer assessment

By emphasizing peer evaluation, there were many opportunities for me to model sensitive and effective critique as well as coach individual students and groups to develop as assessors.

When the day of the presentations drew near, students contributed their ideas about features of a persuasive speech which I synthesized into our Persuasive speech peer assessment rubric

Every student in the class used the rubric to evaluate every other student’s speech.

Data handling

This provided an authentic data handling exercise as students used a Persuasive speech peer assessment data organizer to gain deeper insights into their peer feedback.


I believe that the authenticity and social elements designed into the activity led to every student being extremely motivated to learn the concept and application of average.

Reflection

A further step that I considered including but decided against would be to teach the students how to use Excel or other spreadsheet software to organize and analyze their data. However, it didn’t seem appropriate at the time and I would prefer that the students experience this process in the old fashioned analog manner before introducing digital tools. 

Negotiating rubrics

In our first unit of the school year in Grade 4B at KIST, the Summative Assessment Task was to prepare a proposal for an exploratory expedition.

One of my favorite informal formative assessments is to empower students to collaborate to create the success criteria for each of the rubric categories. I simply distribute blank rubrics and provide time for them to discuss and fill in the charts to continue a practice that I introduced in the post Student-created rubrics and have found to be effective in many ways.


As they deliberate, I circulate throughout the room listening for opportunities to clarify or guide discussions to higher orders of thinking. By nature, this activity practices Evaluation, but students’ discussions do not always reach that goal without help.


By engaging with the language of the unit, especially the Key Concepts, the students complete a formative self assessment of their understanding, even if they are not fully aware of what they are doing.

Finally, on a version projected at the front of the room, we negotiate and build the final draft using the work students have already completed in their groups.

An added bonus is that my evaluations according to the rubric are, and more importantly are perceived to be exceptionally fair. Because they are intimately familiar with the language in the rubric, my feedback is understandable and meaningful.