# Formative Assessment In The Math Class: How To Weave It Into Your Daily Practice

Often when we teach math we don’t really know if students ‘get it’ or not until we give a quiz or test and then it might be too late as you are moving on to new material. Sound familiar? This dilemma is something I hear often from teachers and it is how many students fall between the cracks in math and just get further and further behind. Want a better way of assessing so that you know DAILY who ‘gets it’ and who doesn’t? Try imbedding formative assessment into your daily practice. It’s actually not difficult to do and it doesn’t take away from valuable teaching and learning time.

I recently attended the Pearson Ati summer conference in Portland with five colleagues.Learning with them and from them elevated this conference experience immensely (and we had a blast together in the conference and out!). I’m feeling very inspired and grateful. So, on to the good stuff – what did I learn?

So much! I’m going to focus on formative assessment for this blog post and how to imbed it into your daily teaching. Formative assessment can come in any form; activity, questions, quiz, ticket out the door, etc. What makes a task or activity a formative assessment is what is done with the data. If the data is used to make changes in instruction, it is formative assessment. Formative assessments that are graded or counted for marks are not formative. The whole purpose is to inform instruction that helps students to get from where they are to where they need to be (learning targets or standards).

Here are some examples of formative assessments that you will recognize from our Educating Now videos:

- Use individual white boards and give a problem to be solved – students solve and write their answers on the white board. I can scan the room and see quickly who ‘gets it’ and who doesn’t. Just moving on without doing anything differently would make this activity pointless so from here I make decisions such as: work individually with the small number of students who are not yet understanding the concept, pair these individuals with others who do understand, or if there are a large number who don’t understand, then I need to re-teach the concept in a different way. When all students have a solid understanding I can move on or allow them the opportunity to practice the concept (now that I know they will be practicing correctly – we do not want students moving onto practice if they are going to practice incorrectly).
- Exit slip with stems such as: What I understand well_____________, What I’m still not understanding ______________, or a couple of questions from the lesson’s concept such as: Find 30% of 75 (show all of your thinking). Now that I have the data, I will need to decide whether I need to give more time and opportunity to learn the concept to some or many, or I may need to re-teach or I may be able to move onto the next concept because they all have mastered this.

Let’s look at a detailed example that will illuminate the purpose and power behind using formative assessment well. This is from a grade 6 class that I worked in this year:

Our learning goal was to understand the relationship between mixed numbers and improper fractions. Once we began to explore using the Cuisenaire Rods (see our video and detailed lesson plan for how to teach this concept), I asked students questions like what does 15/4 look like? How many wholes is it? What two whole numbers is it in between? Which is it closer to? How do you know? I asked students to show me what 15/4 looks like using the rods and then asked them to write 15/4 as a mixed number (always reminding them that this means how many wholes and parts). I did several examples asking those who answered correctly to explain their understanding and asking them how they figured out the mixed number and I asked those who did it incorrectly the same thing. We then had mathematical debates until one by one the students understood the connection and could explain in words, in pictures and using symbols (numbers), the relationship between mixed numbers and improper. Next lesson, we would start with mixed numbers and do the whole process again with converting mixed numbers into improper fractions.

Using the manipulatives and the white boards allowed me to assess the whole class quickly and then I could decide how many examples to do, what questions I needed to ask to root out the misunderstandings and allow students the chance to explain their ways of viewing this concept. In some classes I only need to do a few examples and the vast majority understand it, which means I give them the opportunity to practice while I can support the few who were not yet grasping it. In other classes, I’ve had to do many more examples and this lesson would be stretched out over two days (we have 57 minute blocks) and for those students who mastered this concept quickly, I gave more open tasks like: what number between 2 and 2.5 has an improper fraction with a denominator of 6? There are many correct answers and I challenge them to search for patterns in their solutions and to come up with their own open questions.

The point of using formative assessment is to meet your students where they are at and then use the data you’re getting from viewing their manipulatives and white boards to move them towards the goal of understanding the relationship between mixed numbers and improper fractions. Note that there were no grades, nothing was for marks, but everything was for learning. Students are now given PENALTY FREE PRACTICE. This is a term I heard at the conference and loved–we need to give our students the chance to practice without marking it. Homework is for practice or reflection, not for marks. Math is often the most assessed subject, so much so that it has become all about performance. The perils of this are vast and range from crippling math anxiety to lack of willingness to learn conceptually. We need to allow time for LEARNING, not just rehearsing procedures. Structured partner talk or using collaborative math teams help students with their mathematical reasoning skills, which in turn help them to develop conceptual and procedural understanding.

Mistakes are a very important part of learning and need to be made, not punished. If we are grading based on standards and criteria, then punishing students for making errors in homework is inaccurate at best, and harmful at worst. This conference reminded me of how damaging our often traditional way of grading, especially math, can be for students. It helped me to see how our assessment practices affect mindset and can either grow or stunt learning. I will write more about this conference in a few weeks but wanted to share with you the importance of using formative assessment, throughout your daily lessons to gather information about the true level of understanding of your students. This type of assessment works extremely well once you’ve established a culture in your math classroom that is based around the goal of learning – not performing. We want to cultivate an intrinsic motivation to learn in all of our students and we can do this best by tuning into them, their learning needs and formative assessment is a way to do this daily. I also find it is easiest to do formative assessment effectively when I use collaborative math teams as using the math teams frees up so much more time in the classroom to actually assess students.