While there may be an overlap between some types of formative and summative assessments, and while both informal and formal means exist for assessing students, in this article I will primarily offer suggestions for informal formative assessment for the mathematics classroom, particularly in the third. of the three categories suggested by Clarke & Wilson:

1. Knowledge of the student’s mathematical content.
2. The student’s mathematical processes, such as reasoning, communication, problem solving, and making connections.
3. The student’s mathematical disposition, such as attitudes, persistence, confidence, and cooperative skills.

Disposition is defined as “one’s usual state of mind; temperament, a habitual inclination, tendency.” With teenagers, it’s not always easy to determine their disposition or temperament regarding anything, including math. Too often, if your reference group has decided that “school is not great,” then it is mandatory that they use all of their body language and facial expressions (and sometimes words) to indicate their disdain for our beloved subject. We must not accept this at face value (no pun intended). The ideas in this article will allow you to determine the mathematical dispositions of your students (sometimes without their knowledge!).

The first idea I want to offer came about almost by chance. Another teacher and I were creating an assessment tool for some research we were doing. We had about half a page left on this eight-page instrument, and we didn’t want to waste the paper, so we decided to deliver the message shown below. It turned out to be the best question of the entire evaluation! Consider using this message at the beginning of the year, and then several times during the school year to get an idea of ​​the changes that are taking place.

As a math student in this class, I rate myself on the following scale (put an X on the scale you rate yourself on). 1 = Probably worst in class; 5/6 = Not bad; no good; 10 = Totally amazing! Maybe the best in school

The reason I rated myself a / a ____ on the scale above is because:

I have found that teenage students are willing and able to be more honest when asked to write than when asked to share their thoughts publicly. For this reason, I use the learning logs as often as possible to learn about students’ dispositions towards mathematics. The term “learning log” is not one that I originated, but it fits my philosophy of what writing looks like in the math classroom. The first part of the phrase “learning record” states the purpose of writing: to learn. The second part of the phrase “learning record” connotes a particular format, that is, a continuous comment. A record is not meant to be a polished writing, drawn up draft after draft. Commander and Smith (1996) define the purpose of learning records as “reflections on specific cognitive aspects of learning … (emphasizing) personal connection or commitment to academic skills and techniques” (p. 447).

Using learning logs provides you with a variety of ways to assess students’ attitudes, beliefs, and stereotypes about mathematics. The following are some writing prompts that I have found helpful:

• What does a mathematician look like?
• My ability to do math is …
• When I’m in math class, I feel …
• Mathematics has good and bad points. This is what I mean …
• I study, I pay attention, I take notes, I read my math book, but I still don’t understand math. True or false? Explain your answer.

Student responses to questions like these provide information to the teacher as he plans for instruction. Ignoring student dispositions toward mathematics is done at the risk of teachers and students.

Nobody thinks that formative assessment is something that is ‘added’ to our already completed curriculum. Formative assessment is part of good teaching. There must be a fluidity between instruction and assessment. Note that the word “formative” comes from the Latin word for “form.” The formative assessment is intended to shape the next instruction. Use and / or modify the ideas offered in this article. You will find that your instruction is more specific and effective. Then come up with more ideas of your own and share them with as many other teachers as possible.