“Planning for math assessment” is a phrase that we might not use that often. PLANNING for instruction? Isn’t it just something we DO? I think a proactive approach to assessment leads to better instruction, less stress, and more efficient use of our time. I want to bring up some different topics related to math assessment as food for thought.
Math Content Assessment
We all know that we need to measure how well students are learning the content we are teaching. If our standards dictate that students need to be able to “round numbers through hundred thousands to a given place”, then we have to have the tools by which we check for that math understanding.
Often math series, if used, have this type of assessment–in varying degrees of quality. Here are some points to ponder!
- Do your content assessments ask students to showcase their understanding in more than one way, with more than one or two problems, and in multiple attempts? (So often series only provide end-of-unit assessments and many standards are measured with maybe one or two questions)
- Are many of the questions multiple choice or matching? Do students have to actually DO the math to get questions right or could your data be inaccurate because students can guess or narrow down the answers because of how they are written?
- Do the assessments really tackle the content at the level or depth of understanding needed to really show they have learned it?
- Are there opportunities to measure understanding throughout the unit or just at the end?
Math Practice Standards and Student Self-Assessment
Whether or not you GRADE the standards for mathematical practice (more on that later!), I do think it’s important for us to be not only tuned in to our students’ math content understanding, but the math practices as well–and that we are making that public to them! Students can only hit a target that they can see, so we need to make these math practices visible and meaningful.
I have found a few things to be true.
- Students often don’t realize how important math “behaviors” and practice are to their learning.
- They often feel that speed and accuracy are the most important components of math work.
- Students often overgeneralize–they don’t realize how complex math is and we need to help them realize their strengths and goal area.
- Students need help finding ways to measure their own progress and successes.
As I alluded to earlier, I am huge believer in formative assessment. I don’t EVER want to get to an end-of-unit assessment and be shocked at how a student performs. A few nuggets to think about as you plan for your formative assessment:
- Formative assessment doesn’t have to be all paper and pencil (see “Observation”)
- You do not need to only assess what you taught that day. Bring back concepts from weeks earlier to check for understanding.
- Try doing an “entrance” slip when students walk in the door and use that information to group students.
- No need to grade and score all assessments…as students turn them in, sort them into “Got it!”, “Maybe” and “Oh my!” to help you know who to work with later.
- Thumbs up/thumbs down can give you a quick “check”–as long as you have built the culture where students are comfortable admitting that they are stumped
- Student self-assessment can be formative as well!
- One way to informally assess students is to make an optional “coaching session” for students wanting help…students can self-select (or be placed by you!) into this review group.
- Be mindful that you don’t simply mimic the questions on the end-of-unit assessment. Present things in as many different ways as you can and make students really show they understand!
Exit and Entrance Slips
Sometimes I want to assess something in a different way (or in a different subject!), so I use these to make my own! I make a copy of the page I want…write in my content, and then make copies!
I think it’s really important that we realize that math assessment doesn’t need to be written down. A huge percentage of what I learn about students happens as I watch, listen, ask, and notice. In order to get good information about students and their thinking, we need to put students in situations where they will do the type of work we want to see.
If we want to see if they can compute accurately, we can give them a page of problems to do. If we want to see how they think, how they process, how they explain, or where they go wrong–we need to get them doing rigorous work so we can see how they tackle it.
This work can be done as a part of a whole class activity…in a small group…as a center that we are facilitating, as we walk around and coach. This is really the BEST kind of assessment because we can intervene at the time of difficulty rather than wait for students to struggle with misunderstandings that they then show us on paper later.
One of the trickiest parts about assessing in this way is record keeping. There are a ton of different ideas out there for tracking your anecdotal notes–but before you stress out about how much work this is, let me just ask a question.
Is this information you will need to remember later?
If it is…then you will need to find a way to document it. You can use sticky notes. A Google doc. A spiral notebook. Whatever works for you…but keep in mind that good teaching involves constant assessing…so be mindful that spending more time writing down what you see than COACHING what you see isn’t, in my opinion, the best use of time. Instead, use your time and energy to refine your observation skills–and I hope the freebie I’m sharing with you below will help you with this!
Depth of Understanding
When we are looking to assess student understanding, I feel I would be remiss if I didn’t ask you to do some reflecting on the types of problems, questions, and tasks you are giving your students. If we ask students to fill in the blank on a problem like this, does this tell you how well students understand equivalent fractions? If they can answer 2 of these? 8 of these? Will you be convinced that they understand the concept of equivalence? What other questions might help you really determine how deeply they understand equivalent fractions?
As an interesting exercise, take one of your summative assessments and study it. How many questions are basic recall? How many require only computation? Are there problems that allow students to use multiple strategies? Can students show their work in different ways? This is a great activity to do with a team–have a discussion about what you are assessing and HOW you are measuring. Do your assessments match your instruction? Do students need to do novel tasks where they apply the skills that have been taught?
What about a question like this:
There were two pans of brownies at the baseball picnic. The coach cut each pan of brownies into equal portions. Jamal had 2 portions from one pan, while Daniel took 4 portions from the other pan. They both took the same amount of brownies. How is this possible?
Write two fractions that are equivalent. Prove they are equivalent using at least three different methods. Explain your thinking with words and pictures.
Sam said 4/5 and 9/10 are equivalent because each fraction is one piece away from a “whole”. Is he right? Explain your thinking.
Or how about a combination of all of them! My point is this…if most of your assessment tasks are asking students to fill in a blank, generate an answer, or come up with a computational response, it might be time to do some research about how to assess students at a deeper level. (NOTE: Many students will put the number “6” in that white box because it is a logical guess…it doesn’t in any way guarantee they understand equivalency.)
Another way to assess the depth of student understanding is to give them a much more open-ended assessment option. I use these throughout the year…and it really helps me see if student understanding is superficial or more in depth. I have a blog post where I show more about if you are interested–just CLICK HERE. The image below will take you to my fourth grade math assessment set if you want ot check them out!
Math Assessment and Grading
I just want to preface this section by making it clear that math assessment and grading are related but not equivalent. I think we often use the terms interchangeably–and shouldn’t be. We use math assessment as teachers to help us understand how our students are doing–and for students to assess how they are doing.
We also need to be cognizant that we DO have to report out–in some format. Whether we have to be ready to talk to parents at conferences, do report cards–or even just send parents an email, we must be able to take the information we observe and collect to make our decisions. We then need to communicate with families and students about how students are progressing.
A few hints:
- Remember that finding “averages” of scores doesn’t necessarily show where students are NOW.
- Often, scores mean very little to parents, so finding ways to EXPLAIN with comments, checklists, or other more clarifying examples.
- Getting students involved with their own assessment and grading makes a difference in how students understand why their grades are what they are.
- We want students to understand that grades are a VERY small representation of who they are as students and people!
I hope this post has gotten you thinking a little bit–and might give you inspiration to make your assessment practices more in-depth and varied.
Want to grab the freebie to help you with some math assessment planning? CLICK HERE
Looking for more guidance?
Want to read a post about observation in math class?
Want to read a post about student self-assessment?
How about a post with some formative assessment tips?
Have you missed the other posts in this series?
Click HERE for Challenge 2 (math talk and mindset)
Click HERE for Challenge 3 (word problems and problem solving)
Click HERE for Challenge 4 (math organization)
Click HERE for Challenge 5 (math assessment)
Click HERE for Challenge 6 (meaningful problem solving)
(And make sure to answer the screener questions!)