There are so many “head nod” phrases in education. You know, the kind of phrases we talk about and all of us easily agree upon that whatever the thing is we are talking about is a good thing. For instance, someone says that “assessment should drive the learning” in our classroom, and we all easily accept that this is a good practice. Yet, everyone is likely to have a completely different vision as to what is meant by the phrase.

In this post, I want to illustrate 3 very different ways our assessments can drive our instruction, and how these practices lead to very different learning opportunities for our students.

**Unit Sized Assessments**

Some teachers start their year or their unit with a test to find out the skills their students need or struggle with. These little tests (sometimes not so little) typically consist of a number of short, closed questions. The idea here is that if we can find out where our students struggle, we will be able to better determine how to spend our time.

But let’s take a look at exactly how we do this. **The type of questions, the format of the test and the content involved not only have an effect on how our students view the subject and themselves as learners of math, they also have a dramatic effect on the direction of learning in our classrooms. **

For example, do the questions on the test refer to the types of questions you worked on last year, according to previous Standards, or are they based on the things you are about to learn this year (this year’s Standards)? If you provide questions that are 1 grade below, your assessment data will tell you that your students struggle with last years’ topics… and your instruction for the next few days will likely be to try to fill in the gaps from last year. On the other hand, if you ask questions that are based on this year’s content, most of your students will likely do very poorly, and your data will tell you to teach the stuff you would have anyway without giving the test at all. Either way, the messages our students receive are about their deficits… and our instruction for the next few days will likely relate to the things we just told our students they aren’t good at. I can’t help but wonder how our students who struggle feel when given these messages. Day 1 and they already see themselves as behind.

I also can’t help but wonder if this is helpful even for their skills anyway? As Daro points out below, when this is our main view of assessment guiding our instruction, we often end up providing experiences for our students that continue to keep those who struggle struggling.

**Daily Assessments**

On the other hand, many teachers view assessment guiding their practice through the use of daily assessment practices like math journals, exit cards or other ways of collecting information while the learning is still happening. It is really important to note that these forms of assessment can look very different from teacher to teacher, or from lesson to lesson. In my post titled Exit Cards: What do yours look like? I shared 4 different types of information we often collect between lessons. I really think the type of information we collect says a lot about our own beliefs and our reflections on this evidence will likely form the type of experiences we have the next day.

When we use assessments like these regularly, we are probably more likely to stay on track with our curriculum Standards, however, what we do with this the information the next day will completely depend on the type of information we collect.

**In-the-Moment Assessments**

A third way to think of “assessment driving instruction” is to think of the in-the-moment decisions we make. For example, classrooms that teach THROUGH problem solving will likely use instructional practices that help us use in-the-moment assessment decisions. Take for example The 5 Practices: for Orchestrating Productive Mathematics Discussions (linked here is a free copy of the book). Here are the 5 Practices and brief explanation about how each might be useful as part of the assessment of our students.

**1. Anticipating**

• Do the problem yourself.

• What are students likely to produce?

• Which problems will most likely be the most useful in addressing the mathematics?

**The first practice helps us prepare for WHAT we will be noticing. Being prepared for the problem ahead is a really important place to start.**

**2. Monitoring**

• Listen, observe students as they work

• Keep track of students’ thinking

• Ask questions of students to get them back on track or to think more deeply (without rescuing or funneling information)

**The second practice helps us notice how students are thinking, what representations they might be using. The observations and conversations we make here can be very powerful pieces of assessment data for us!**

**3. Selecting**

• What do you want to highlight?

• Purposefully select those that will advance mathematical ideas of the group.

**The third practice asks us to assess each of the students’ work, and determine which samples will be beneficial for the class. Using our observations and conversations from practice 2, we can now make informed decisions.**

**4. Sequencing**

• In what order do you want to present the student work samples? (Typically only a few share)

• Do you want the most common to start first? Would you present misconceptions first? Or would you start with the simplest sample first?

• How will the learning from the first solution help us better understand the next solution?• Here we ask students specific questions, or ask the group to ask specific questions, we might ask students what they notice from their work…

**The 4th practice asks us to sequence a few student samples in order to construct a conversation that will help all of our students understand the mathematics that can be learned from the problem. This requires us to use our understanding of the mathematics our students are learning in relation to previous learning and where the concepts will eventually lead (a developmental continuum or landscape or trajectory is useful here)**

**5. Connecting**

• Craft questions or allow for students to discuss the mathematics being learned to make the mathematics visible (this isn’t about sharing how you did the problem, but learning what math we can learn from the problem).

• Compare and contrast 2 or 3 students’ work – what are the mathematical relationships? We often state how great it is that we are different, but it is really important to show how the math each student is doing connects!

**In the 5th and final practice, we orchestrate the conversation to help our class make connections between concepts, representations, strategies, big ideas… Our role here is to assess where the conversation should go based on the conversations, observations and products we have seen so far.**

So, I’m left wondering which of these 3 views of “assessment driving learning” makes the most sense? Which one is going to help me keep on track? Which one will help my students see themselves as capable mathematicians? Which one will help my students learn the mathematics we are learning?

Whether we look at data from a unit, or from the day, or throughout each step in a lesson, Daro has 2 quotes that have helped form my opinion on the topic:

I can’t help but think that when we look for gaps in our students’ learning, we are going to find them. When our focus in on these gaps, our instruction is likely more skills oriented, more procedural…. Our view of our students becomes about what they CAN’T do. And our students’ view of themselves and the subject diminishes.

“Need names a sled to low expectations”. I believe when we boil down mathematics into the tiniest pieces then attempt to provide students with exactly the things they need, we lose out on the richness of the subject, we rob our students of the experiences that are empowering, we deny them the opportunity to think and engage in real discourse, or become interested and invested in what they are learning. If our goal is to constantly find needs, then spend our time filling these needs, we are doing our students a huge disservice.

On the other hand, if we provide problems that offer every student access to the mathematics, and allow our students to answer in ways that makes sense to them, we open up the subject for everyone. However, we still need to use our assessment data to drive our instruction.

#### As a little experiment, I wonder what it would look like if other subjects gave a skills test at the beginning of a unit to guide their instruction. Humor me for a minute:

What if an English teacher used a spelling test as their assessment piece right before their unit on narratives? Well, their assessment would likely tell them that the students’ deficits are in their spelling. They couldn’t possibly start writing stories until their spelling improved! What will their instruction look like for the next few days? Lots of memorizing of spelling words… very little writing!

What if a Science teacher took a list of all of the vocabulary from a unit on Simple Machines and asked each student to match each term with its definition as their initial assessment? What would this teacher figure our their students needed more of? Obviously they would find that their students need more work with defining terms. What will their instruction look like for the next few days? Lots of definitions and memorizing terms… very little experiments!

What if a physical education teacher gave a quiz on soccer positions, rules, terms to start a unit on playing soccer. What would this teacher figure out? Obviously they would find out that many of their students didn’t know as much about soccer as they expected. What would their next few days look like? Lots of reading of terms, rules, positions… very little physical activity!

- How do you see “assessment guiding instruction”?
- Is there room for all 3 versions?
- Which pieces of data are collected in your school by others? Why? Do you see this as helpful?
- Which one(s) do you use well?
- Do you see any negative consequences from your assessment practices?
- How do your students identify with mathematics? Does this relate to your assessment practices?

Being reflective is so key in our job! Hopefully I’ve given you something to think about here.

Please respond with a comment, especially if you disagree (respectfully). I’d love to keep the conversation going.

Hmmm. Before I spent time learning pedagogical content knowledge in math I was almost 100% unit assessment driven. I spent sooooooooo much time reteaching when I did that. Now I spend most of my time on in the moment assessments, but it’s because my focus during instruction has changed from what I need to tell the kids to trying to understand student thinking. I think the “anticipate” portion of the lesson is one of the most important pieces. During that time I need to figure out not only possible student responses, but questions to ask that will not funnel their thinking into the answer, but open up their thinking. I do love using reflective journals at the end of a lesson and responding with a notice/wonder format as Joe Schwartz shared. Of course, the unit tests still come into play, but last year I found that I didn’t even want to give them. Like they were a waste of time because they weren’t strong enough to grasp what I already knew. They became more of a reflection for parents. This year I want to look into Kathy Richardson’s critical learning phases assessments too.

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I think you are on to something here Jamie. The more content knowledge we have, the more likely we are already very clear on our path…then we can start focusing on the particulars to move the thinking of our students forward.

Seems that we need to help everyone continue to learn more math…make more connections…understand appropriate representations…learn more about how concepts develop over time…….

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Before taking the Math 7/8 course I thought that assessment in Mathematics was very much evaluation oriented – data collection to determine gaps and re-teach where students are struggling. In the above quote from Daro he made an interesting point that often the gaps com from confusion caused by the very same methods used to teach students, so the cycle of confusion continues. I think that this course has broadened my understanding of the goals of mathematical understanding and how to effectively apply ideas about assessment practices that reflect assessment as and for learning into the math classroom.

I know that I feel much more confident in my ability to support regular classroom work at the 7/8 level because I have a much clearer understanding of the approaches that encompass critical thinking, that allow students to participate and learn in a community environment that builds on and connects to prior learning through differentiated tasks, and is about interesting real world connections. I can apply principles I have used in my subject area and meld them with practices in the math classroom.

I can’t speak to how students identify with mathematics, but the few instances where I did fill in the attitude was negative. If I can change my attitude about math after all these years then using the tools I have learned in this course I can help to change that attitude in students who haven’t yet ingrained the habit of ‘I’m not good at math’ and open them up to some challenging and amazing learning experiences.

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