{"id":22387,"date":"2024-07-02T05:00:00","date_gmt":"2024-07-02T12:00:00","guid":{"rendered":"https:\/\/www.nwea.org\/blog\/?p=22387"},"modified":"2025-06-17T10:45:41","modified_gmt":"2025-06-17T17:45:41","slug":"how-to-use-student-discourse-as-a-formative-assessment-activity-in-the-math-classroom-and-beyond","status":"publish","type":"post","link":"https:\/\/www.nwea.org\/blog\/2024\/how-to-use-student-discourse-as-a-formative-assessment-activity-in-the-math-classroom-and-beyond\/","title":{"rendered":"How to use student discourse as a formative assessment activity in the math classroom\u2014and beyond"},"content":{"rendered":"
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Have you ever had one of those experiences where you use a word and soon realize your listener had a completely different interpretation of it? One of the most memorable of those communication breaks happened to me when my wife and I were newly married. We talked about how our apartment needed cleaning, then set off to do exactly that. I went after the irritating clutter; she went for the dirt. To me, \u201cclean\u201d meant getting things in order. To her, it meant wiping down baseboards. I hadn\u2019t even noticed the baseboards. Ever. And I certainly didn\u2019t think her notion of \u201cclean\u201d was as pressing as mine. We thought we were talking about the same thing, but we each meant something quite different. It led to a playful routine where we would stop and play a quick round of \u201cwhat I said vs. what you heard\u201d when we had unexpected responses from each other during conversations.<\/p>\n\n\n\n

Words are funny that way. We like to think that the other person is hearing certain words in the same way that we mean them. We want our meanings to be shared. Often, though, that is simply not the case. And while misunderstanding each other\u2019s meaning of the word \u201cclean\u201d is innocuous, other occasions of mismatched meanings could be far more, well, meaningful.<\/p>\n\n\n\n

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Formative conversations can illuminate student understandings<\/h2>\n\n\n\n

In educational settings, formative conversations can serve to help teachers and students better understand each other, just as my wife and I have tried to do since that fateful cleaning day. Consider the mathematics classroom. There are all sorts of ways people might talk past each other. The word \u201cfraction\u201d is a great example. When I say that word, I have a certain meaning that is grounded in how I think about that term. My listeners, on the other hand, all bring their own ideas to it: I might be thinking about a fraction as a point on the number line. Someone else might be thinking about circular foods. Another might be thinking about part\/whole relationships while yet another might completely shut down due to a history that lacks any healthy, meaningful ways to think about fractions. It might look like we are talking, but given our different meanings  one might argue there is very little communication actually taking place.<\/p>\n\n\n\n

\u201cThere are certain kinds of higher order thinking that only really express themselves when we talk to each other,\u201d says former NWEA researcher Chase Nordengren while describing the strategy of using student discourse as formative assessment<\/a>. It\u2019s the ninth of ten transformative instructional strategies<\/a> grounded in his research into what approaches work best in high-growth schools<\/a>.<\/p>\n\n\n\n

Chase is right on in the study\u2019s accompanying white paper<\/a> when he calls out that \u201cgetting students talking to one another is one of the most important things that can happen in any classroom.\u201d The need to \u201cfacilitate meaningful mathematical discourse\u201d is also strongly urged by the National Council of Teachers of Mathematics (NCTM). It\u2019s one of the eight mathematics teaching practices listed in their Principles to Actions<\/em> document<\/a>. I often emphasize that meaningful mathematics discourse must focus on mathematical meanings. That is, to enable true communication, we must establish that we are meaning the same things. The trick, however, is to find ways to get such conversations going and to know what to listen for.<\/p>\n\n\n\n

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How to improve communication with formative conversations<\/h2>\n\n\n\n

In line with Chase\u2019s take, my colleagues and I thought about the formative space as a valuable place to drive powerful conversations. After considerable effort, we ended up building a series of eBooks called Formative Conversation Starters<\/a> that are available for free on the NWEA website. There, we provide what we call \u201cBig Ideas to Nurture Standards Sense-Making,\u201d or BINSS, as a high-level framework of things to listen for, along with clusters of questions that invite opportunities to uncover meanings.<\/p>\n\n\n\n

For example, when it comes to fractions, we aimed to highlight the importance of thinking about fractions as a number on the number line: \u201cFractions: A fraction is a single number. It is a number just as 1, or 100, or 37,549 are, and it has a location on the number line. Students should be able to think of a fraction as a number and treat it as such. The fraction  can be thought of as  copies of , where  is the length of a single part when the interval from 0 to 1 is partitioned into  parts. Two fractions are equivalent when they share a location on the number line.\u201d<\/p>\n\n\n\n

Then, we provide question clusters that poke at the big ideas. The clusters are organized around individual grade-level tasks, but instead of asking what mathematics is directly needed to answer a given task, we ask about the other mathematics that also plays a role. A particular task may focus on a single idea, but it will require meanings and ways of thinking from a collection of mathematical ideas. Our aim is to never let go of those other big ideas.<\/p>\n\n\n\n

Here\u2019s one set that invites conversation from page 16 of the eBook for grade 3<\/a>:<\/p>\n\n\n\n