Log 10

Teaching Secondary and Middle School Mathematics Chapter 9

General notes on chapter 9 - Principles of Assessment Practices:

The chapter starts with a discussion of NCTM recommendations on assessment.  This breaks down into 6 assessment standards:

  1. The Mathematics Standard - Assessment should reflect the mathematics all students need to know and be able to do.
  2. The Learning Standard - Assessment should enhance mathematics learning.
  3. The Equity Standard - Assessment should promote equity.
  4. The Openness Standard - Assessment should be an open process.
  5. The Inferences Standard - Assessment should promote valid inferences about mathematics learning.
  6. The Coherence Standard - Assessment should be a coherent process.

The NCTM Assessment Principle states that "assessment should support the learning of important mathematics and furnish useful information to both teachers and students."

The next thing the chapter talks about is equity and assessment.  This mostly breaks down into assessing students multiple ways so that students who are weak on tests don't get punished for it.

The chapter then spends quite a few pages on Homework Assignments.  How much homework should be assigned, and how often?  It then talks about different types of homework assignments:

The chapter then discusses different ways of grading homework assignments (having students write them on the board, only checking the most missed ones, etc.).  The book has a nice list of advantages and disadvantages to each method.  Then there is a section on assessing homework (complete, incomplete; rubrics based; checking selected problems; etc.).

Finally, the chapter discusses overall assessment, and argues for multiple assessment methods.

Question 4 - What is a reasonable amount of time for homework?  How can you tell if you are assigning right amount and if it is beneficial?

I think math teachers probably shouldn't give students more than 30 minutes of homework (on average) each night.  Students may have up to 3 or 4 classes that have regular homework, and I believe that kids shouldn't have more than a couple of hours total homework each night.  Kids need time to do other things than just school and homework, and more than two hours homework each night may be only moderately helpful to their academic development, but could negatively impact their growth in other areas (social, athletic, personal, etc.).  Maybe in a block schedule you could give 40 minutes of homework because they have fewer classes.

One way to tell how much homework you are giving kids is to ask.  You can have them write down their start and finish times, for instance.  Another good idea is to do the homework yourself and assume that it will take the students perhaps twice as long as it takes you.

One way to tell if homework is beneficial or not is to give frequent small quizzes to see if they are mastering the material.  Sometimes the quiz could just be in the form of a class warm-up or random Q&A - it doesn't always have to be formal assessment.  I like the idea of doing quizzes with networked computers or calculators to get the quickest feedback possible.

Question 9 - What do you value in math class and how is that reflected in your grading?

Personally, I value understanding the concepts and being able to problem solve more than anything else.  This is why I tend to value tests and quizzes pretty highly, and why I only value homework at a level that is high enough to a actually motivate the students to do it.  I don't believe that math students should be rewarded primarily for effort - which is the sort of philosophy that would lead to a high valuation for homework.  If a student can master the concepts, I don't really care much how much work they put into it.

I think this reflects the reality of the engineering and science world where these math concepts are used.  I don't care that much if an engineer works harder than the others, I care if he can generate a sound design or solve a problem that the other engineers cannot.

On the other hand, I also place some value on the ability to communicate, collaborate, and follow through on a task.  That is why I would consider adding some sort of project into the grading scheme - and why I might reward students for helping other students in their grades.