This section tests your knowledge on how students think about math and how you, the teacher, should teach math (aka “best practices”).
Student thinking and instructional practices questions make up about 26% of the Mathematics subtest.
There are three pretty big concepts to know:
- Major Theories of Learning
- Teaching Strategies
The first big concept to know is the major theories of learning and how they can be applied to math. First of all, there are a lot of theories about how children learn. But here are some important ones to read and think about:
- Social Learning
- Sociocultural Learning
More specifically, take a look at these theories:
- Piaget’s Four Stages of Cognitive Development
- Bloom’s Taxonomy
- Levels of Geometric Thinking (van Hieles)
Be sure to know what each of these are and how they can be applied to math.
You should also read over Florida’s standards for each grade level. You can do that by clicking here.
The next big concept is teaching strategies. Remember, as I’ve said a few times before now, there are “best practices” for teaching each subject.
Take a look at this publication by National Council of Teachers of Mathematics (NCTM). They outline some effective teaching practices for math.
Also, be sure to know what manipulatives are, why they are important to use, and be aware of some specific manipulatives like geoboards, pattern blocks, number lines, base ten blocks, tangrams, etc.
You also need to know the importance of using small groups to differentiate math instruction.
Finally, the last big concept to know is how to assess students’ knowledge in math. Know these types of assessments and when to use them:
- progress monitoring
Remember, assessments should guide your planning and instruction and help you differentiate for each student.
So, those are the big concepts to know concerning student thinking and instructional practices.
Let’s take a look at some pretty specific concepts that are likely to appear on the test.
Problem-solving is a critical skill that students need to master in all subjects, including math. Let’s take a look at a particular problem-solving model called Polya’s Model. Here are his four steps to problem-solving:
- Understand the problem
- Devise a plan
- Carry out the plan
Now, there are a lot of problem-solving methods out there, but all of them are basically some form of Polya’s original four steps. And there are several strategies you can use to devise a plan (Step 2) like working backward and using a formula.
Be sure you are able to use the four steps to solve a math problem.
You really need to know the different components of math fluency and why it’s important for your students to be fluent in math. The components of math fluency are:
These components are a little bit different than reading fluency.
Accuracy means solving problems with the best method, the right steps, and in the right order to get the correct answer.
Automaticity means knowing the answer to a problem right away. You’ve done it so many times that its almost just an instant reflex. An example is knowing right away that 10 x 3 = 30.
Rate is all about being efficient. You can complete the steps of problem-solving quickly. You know exactly what step to take next and don’t waste time being “lost”.
Finally, flexibility means that you are comfortable using more than one approach to solve a problem. You understand numbers and operations well, so you can manipulate the information and think critically. If you don’t know the answer right away, you know a way to figure it out.
These are some words you need to know. How do I know? Because they appear right in the description of the skill that you will be tested on. It’s like the state is handing you a little gift. Take advantage of this gift and learn these words!
Subitizing is a way of instantly counting (example: you see a group of dots and know immediately that there are ten, without counting).
Transitivity. Okay. Stay with me here. Think of three elements. We will call them A, B, and C. Transitivity means that if A is related to B, and B is related to C, then A and C must also be related to each other. Get it?
Iteration is when you repeatedly solve a problem using a result from a previous problem.
Tiling is when you put individual tiles together with no gaps or overlaps.