Learning in Progress! Our class chart for height measurements.

“Wait a second,” I said, “are you sure he’s 10 inches taller than you?”

My student’s brow furrowed.  I’m not sure if it was because I insulted his pride, suggesting that another child was, indeed, that much taller than him, or if it was because he’d realized the inaccuracy of the measurement.

We were embarking upon a short-term math project, one that was inspired by an Illustrative Mathematics first-grade measurement task.  The children made a tracing of themselves and measured their heights, arms, and legs in four different units, from large non-standard units like wooden blocks, to small, standard measurements like inches and centimeters.

I walked over to the cabinet to grab a ruler, to demonstrate just how big of a difference 10 inches was when discussing height.  None of my children, not even my most advanced, were able to spot this error in our data.

I had the two children in question stand next to each other, showing my children, very concretely, that they were practically the same height, perhaps a fraction of an inch distinguishing the two of them.

“What does this mean?” I asked my group of twelve mathematicians.

“The measuring wasn’t accurate!” one child shouted out.

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A few of our math practice cards.

“Exactly. We have to remember that all mathematicians must be ac-cur-ate, ac-cur-ate, ac-curate,” in a rhythmic, sing-song voice, intended to reiterate a message from one of our mathematical practice cards.

“When we’re not accurate, our data will be off. And it’s important to remember that mathematicians use math to figure things out.  If we’re not accurate, the data will tell us a story that’s not true!”

This lesson on accuracy ended up serving as my math workshop mini-lesson today. It invited my children into a lesson that all of them could learn from, despite their varying ability levels.  And as I finished the lesson, my thoughts converged and coalesced, helping me to realize a few very important things about project-based learning, especially in the context of math.

Truth be told, I’ve really struggled with this over the past two years, especially with the lower elementary age band.  My classes have been expansive multi-age classes, with this year’s class spanning from junior kindergarten to second grade.  Not only has the task of personalization felt monumental in a class with this range, but the mere notion of creating a project-based math workshop has been challenging, as well.  Math requires a focus on concrete skills that are oftentimes best met by direct instruction, which has always felt antithetical to the notion of project-based learning.

In fact, I used to think that direct instruction was at odds with project-based learning, but through adhering to a few basic principles, I’ve learned that I can balance project-based learning with direct instruction and competency-based assessment, still creating a learning environment that is inviting, engaging, and authentic, all the while holding children accountable to the skills they need to learn–and at their level.

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Just a snapshot of my competency-based assessment, which has laid the foundation for my feedback in this project.

1) Build your assessment criteria first.

Too often, progressive education and project-based learning are conflated with a lack of structure and/or expectation.  In a project-based environment, constraints are necessary, and in many cases, these constraints can actually enhance the creativity or unique learning paths that each child will take.

To start this unit on measurement, I built a number of measurement-focused assessments, spanning from proficiency levels in junior kindergarten through second grade.  This not only aligns with the practices of backward design, but it also allowed me to figure out where each of the children would fit within the context of this project.  These assessments are still framing my thinking, my feedback, and my responsiveness to each child as they navigate the project.

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This student made groups of 10 to measure her arm.

2) Create a project with multiple entry points and paths for discovery and inquiry.

Personalization is frequently mistakenly conflated with individualization. This project may be generalized to the whole class, but it is personalized in terms of what the children do with it.  By building my assessment criteria first, I was able to understand the breadth of skills that I would be dealing with and engineer the project specifically to that breadth. I chose blocks as the most basic unit of measurement, appealing to my youngest children who were emerging into a concrete stage of measurement, while I chose inches and centimeters to be available for those who needed a challenge.

3) Focus mini-lessons on thinking and habits of mathematicians.

Content is important in mini-lessons, but it can sometimes be limiting, especially if you’re facing the range of children I am.  Simply working on one skill per mini-lesson may lose some of your children for obvious reasons. The chosen skill could be too easy or too challenging, leading to disengagement or boredom. That said, if minilessons are focused on thinking and inquiry, as my minilesson today was, the more likely your children will stay engaged.

With today’s lesson, the mere discrepancy between the two heights created a problem that the children wanted to solve.  They had uncovered an inconsistency–a story that wasn’t true–and it was important to them to make sure that this wrong was righted. Note, too, that it wasn’t absent of content; the content simply served as the medium for inquiry.

4) Allow children to practice skills they’ve already mastered, and remind them that it builds fluency.

Especially in environments that are considered personalized, many are victim to the misconception that a child must be operating within his or her zone of proximal development at all times.  To many, this means that if a child has shown mastery on a topic or skill, that having them re-practice this skill may be considered a waste of time.  But this is simply not true.

Not only is constantly working within this just-right level exhausting, it also neglects the importance of fluency.  A popular suggestion for building fluency in reading is to have children read books that are below their just-right levels, allowing them to build speed and prosody at levels that feel less taxing.  The same goes for math: by allowing children to build speed and prosody with already mastered skills, we create space for them to intuit patterns, making these skills more automatic and laying the foundation for more complexity later on.  I saw this in my children just to say, as some were practicing counting by 1s, 2s, and 10s to measure themselves with unifix cubes.

Lessons Learned

None of this could have been possible without my initial step in the process.  This step is rather simple, but too often overlooked.  Intentionally defining objectives and building competency-based assessment criteria around these objectives builds a strong foundation for the project itself.  Not only does it allow for the educator to collect data on the knowledge with which the children are coming into the project, but it also creates a map on which an educator can navigate the unique learning journeys of so many children.

Too often, we conflate project-based learning and personalization with a severe degree of student autonomy.  This autonomy can actually become limiting without a clear sense direction.  But by defining objectives and success criteria ahead of time, one gives the project shape and structure, making it possible for all sorts of children to engage.

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