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.

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. 

Inquiry math: Estimation

One of my challenges as an IB PYP teacher is how to design authentic opportunities for inquiry using mathematics. I think it’s due partly to the fact that the outcomes tend to be predetermined but also because upper elementary mathematical skills aren’t often prominent in the students’ own inquiries.


My solution has generally been to provide an inquiry provocation to introduce a concept with related skills to be practiced in subsequent lessons.

Estimation

Recently, we completed a unit on estimation. The initial challenge was simply to estimate the number of various objects in various containers.

Invitation

//platform.twitter.com/widgets.jsAfter my students discussed different strategies and submitted their estimates, we engaged the school community by setting up the jars and forms in the corridor and inviting other classes to join in.



The added social element was invaluable. The observations my students made about the strategies employed by the younger students had particularly strong metacognitive value, as they stimulated us to reflect more deeply on our own approaches.

In reflection, this activity might have been better provoked by a question like ‘How do people estimate?’, providing students with more flexibility to inquire in different ways into the mathematical thinking of themselves and others.

Challenge

Finally, to bring the inquiry to our target of using very large numbers, I challenged my students to formulate an estimation question that would result in a very large number. I’ll share two of the standout projects:

How many ants weigh the same as a ten year old girl?


The student who created this poster struggled mightily with her inquiry. I appreciated her creativity in first making a moving seesaw, especially because it was likely inspired by her participation in our school’s Maker Club. Considering her first guess of 100 ants being equal in weight to a child, it took a significant cognitive effort, a fair amount of peer support, and some careful teacher coaching to arrive at a more realistic estimate.

How much more ingredients would you need to make a classroom sized cupcake?



The giant cupcake was beautifully presented, but illustrates the importance of action in inquiry. This student’s work was hypothetically interesting, yet I don’t believe that any of the questions or ideas were actually pursued. When the idea was introduced, I was hoping that an abnormally large cupcake would appear in the classroom one day!

Practice

After creating posters to share their estimation inquiry processes, students embarked on a traditional unit of estimation practice and application in different situations. Their learning was certainly enhanced after completing their individual projects, and resulted in a clear connection between the academic and practical aspects of mathematics.

Reflection

This was an interesting mini unit that resulted in meaningful learning, but I would like to explore ways to tie it to a greater and more general theme.

It also raises a question for me about the role of purposeful practice in inquiry learning. After all, learning outcomes are, by definition, predetermined. Is it enough to view them with suspicion when designing learning experiences, or should I actively try to eliminate them from my planning?

SAMR v Smart-Board

In October, the dry-erase whiteboard in my classroom was replaced with a Promethean ActivBoard. The children at school aptly described it as a ‘giant iPad’ as they explored the functions of dragging and dropping with their fingers and writing with the provided styluses.

It was a much anticipated change, and now that I’ve had opportunities to integrate it into my approaches to teaching, this is an ideal opportunity to assess how I’ve utilized it according to the SAMR model of technology integration.

Listening to Richard Wells speak about SAMR on the BAM! Radio podcast, Using the Four Step SAMR Model to Update Your Teaching Practice, was particularly helpful as he emphasizes the SAMR model as a tool for changing one’s mindset toward technology in the classroom.

Substitution

Say goodbye to dry-erase dust!
At first, and with no additional training or time to prepare new activities, I used the ActivBoard as a substitute for a low-tech whiteboard. Although being able to use a myriad of colors and line thicknesses provides more expressive functionality, it could still be accomplished with dry-erase markers, albeit without all the grungy dry-erase dust.

Augmentation

Documentation
After using the ActivBoard as an inkless whiteboard, I realized the potential to save work in a variety of digital formats, including as a ‘flipboard’ that could be opened and edited later or simply as a screenshot for archival purposes. Gone are the days of photographing the whiteboard at the conclusion of a discussion!

Visible thinking
This was particularly useful for KWL charts and other digital visible thinking artifacts. The ActivBoard software can import PDFs to be annotated, a feature we have used effectively for interactively reviewing quizzes. Another interesting application is desktop annotation. During an inquiry into visual literacy, we used this to discuss and make notes on the design and layout of our favorite websites.

Engagement
Thus far, the most noticeable augmentation relates to student engagement. The futuristic appearance of the ActivBoard and its similarity to familiar tablet computers has motivated students to participate more actively in discussions and contribute to visual media created in class.

Modification

Virtual tools
Discovering the capabilities of our ActivBoard revealed many useful features. In particular, the Math Tools enable presentations and demonstrations to be completed with virtual versions of the same tools students are using at their desks.

Digital music
One application that was successful occurred in music class. To introduce a Grade 4 inquiry into digital sequencers, we used the ActivBoard to co-create a piece of music to practice the functions and features of the Online Sequencer.

In the past, I generally introduced new applications by first using a digital projector to make a presentation to outline key features, then providing time for independent or small group exploration. The ActivBoard allowed for a bridge activity between teacher presentation and independent practice that is visually, physically, and socially engaging. It also has a good audio system!

Redefinition

Can the ActivBoard redefine learning?
A common thread running through the discourse on ‘modification’, and my primary goal for technology modification, is student agency. Technology provides unprecedented opportunities to personalize learning and empower learners to take ownership of their learning processes.

To use the ActivBoard to achieve the goal of increasing student agency requires a mindset change with which I am still grappling.

After all, it is still a screen mostly suitable to presentation. Perhaps it can be used to redefine ‘presentation’ into an interactive experience, but that would require an in-depth inquiry into tools beyond the ActivBoard itself. Perhaps those are the exact tools students and I should be learning.

Is there a way to connect learning on the other ubiquitous touch screen devices like iPads with the touch screen ActivBoard? A quick inquiry revealed a post, What Can I Do with an iPad in an ActivBoard Classroom? (Part 1), from the Promethean Planet community blog, and Apple Kills the Interactive Whiteboard with iPad 2.

In both posts, hints of the benefits of iPad/ActivBoard compatibility are mentioned. Evidently, however, those ideas have yet to be realized.

Next steps
My own plans focus on using the ActivBoard to redefine ‘presentation’. As an inquiry teacher, curating and presenting thought-provoking media is critical. Thus far, that seems to be the primary strength of the ActivBoard and the most obvious line of inquiry for me to pursue.

EdTech Unplugged

Educational technology has become synonymous with computers. However, I often remind myself that any tool is technology, and different tools work better for different people for different jobs.
Late 20th century classic, the individual whiteboard.

I’ve never met a class that didn’t enjoy creating word problems for their peers on individual whiteboards and voraciously solving each others’ problems.

Water Resources Inquiry

To inquire into the effects of access to water around the world, we gained perspective by graphically representing water resources per capita in various countries. The bars at the bottom represent the data.

The lowest bar for Iceland stretched over three meters!

It was supposed to integrate mathematics (division & ratio) into a mainly ‘social studies’ unit, and worked brilliantly except for the fact that the numbers we used were extremely large and not exactly appropriate for early in fourth grade.

Is my classroom mastery-oriented?

Having spent the past year trying to understand and utilize the International Baccalaureate Organization Primary-Years-Program for the first time, I’ve applied a great deal of planning and instructional time to inquiry. I strongly believe in the model and its apparent intention to emphasize much more than academic performance in the education of children. It compliments my previous experiences perfectly and my students and I have enjoyed our journey thus far.

Last week, however, I received my class’ results from the International Schools Assessment. Results in Mathematics were impressive, Reading were acceptable, but the Writing results were disappointing, especially non-fiction.

What happened?

This guy is clearly master-oriented.

I have already identified one problem: When our Language Arts curriculum was correlated with the PYP sample Program-of-Inquiry, the units on persuasive and informational writing were pushed to the end of the school year, after the testing in February, although we did practice essay writing as part of every History unit and the entire class made documented progress in every domain on our own formal summative assessments.

There were also several school events in the same month as the tests, which may have contributed to fatigue or a lack of focus, and certainly interfered with opportunities for explicit test-preparation.

Certainly this will be an area of focus for me in the near future. Perhaps it’s time to pull up on the inquiry reins just enough to allow for more formal writing development and mastery of grammar techniques which seem to be the focus of that assessment, but have not been our focus this year.

Should they have been?

Being mastery-oriented means a great deal more than simply meeting learning objectives. At least that’s my new understanding after beginning to read Carol Dweck’s Self-Theories.

It’s a state-of-mind, intellectual and emotional. The PYP is clearly oriented toward developing mastery-oriented people willing to pursue goals and take risks. While I believe that is much more important than marching through a mastery-oriented curriculum, perhaps my emphasis has been askew.

I would like to explore the possibility of a writing program which not only motivates and inspires children to write, but also ensures that they master the grammar and vocabulary they need to be truly confident and fluent communicators.