Simply Manipulatives

THOUGHT

Manipulatives can be brought into the classroom to improve student learning.

REFLECTION #1

BUT... manipulatives have to be taught properly in order for students to understand what they mean and how they work. For example, with pattern blocks, a red block can equal a half of a yellow block, but it is more complicating to say that one yellow block represents half of two yellow blocks.

REFLECTION #2

Albert Einstein is quoted for saying: “If you can't explain it simply, you don't understand it well enough.” If the teacher does cannot teach students, in a simple way, how to solve more complex ideas with the blocks, such as how to multiply and divide with them, then it is best for the teacher to first understand this. If it cannot be taught simply, a lot of confusion will result from the attempts at explaining what the teacher may not fully understand themselves.

“If you can't explain it simply,
you don't understand it well enough.”
-- Albert Einstein

Luckily, there are many resources available online to help educators understand and implement manipulatives into their lessons, which can be found through a simple Google search.

As Long As It Takes

THOUGHT

How long it takes to teach math is insignificant.

REFLECTION #1

Math needs to be taught to the students through quality lessons, and perhaps very differentiated ones, but there is no point in moving on to new lessons, which often build on previous knowledge, if students are not comprehending the material. While some students may not be able to comprehend the material, a teacher's responsibilities can be conflicting. On one hand, we want our students to understand the ideas that we are teaching them, but on the other hand, we are expected to cover many areas, which can create pressure on the teacher to keep moving forward, however, this is a disservice to the students who are unable to keep up, or are at a standstill in their learning of the mathematic concepts, for whatever reason.

REFLECTION #2

If students do not understand the most basic concepts, this can cause them to not understand entire units, because they do not have the foundation of knowledge to support the rest of their learning. Therefore, I would agree that it is crucial that students understand a math concept before moving on, otherwise it is likely that they will lose confidence in math, and develop a dislike for the subject because their teachers never took the time to properly explain the basics in words/ways that the student would understand.

Educator to Learner

THOUGHT

We must practice non-attachment as teachers and be willing to explore new territory, in order to move away from what we know, toward what we don't know and have to learn.

REFLECTION #1

If we look at the curriculum from only our own perspectives, and what we LIKE to teach in math, then we are quite probably failing students by limiting the range of mathematical topics, or not spending enough time on areas of math that some students might find fascinating. We cannot let our own bias come in the way of fully exploring some areas in the math curriculum.

REFLECTION #2

By challenging ourselves, as educators, to explore areas of math that do not come as easily to us, or that we do not enjoy, we may discover, as learners, that there are aspects of these units that we can find something to like about it. Even if this enthusiasm for a topic is forced in the beginning, if students become excited about the unit, and are discovering new things, this can be enough to encourage the teacher to continue to find ways to keep the students engaged and learning in this area. Thus, the teacher is an educator, and a learner, in this endeavour.

Here are some (American) links I found to be an interesting read on the teaching of math:

Mathematics Education
Barry Garelick Myth

Base Ten Blocks

THOUGHT

Base Ten Blocks have many different functions within the math classroom.

REFLECTION #1

Base Ten Blocks, with a brief explanation of their function to students, are a great tool to help students when they are beginning to learn addition and subtraction. Upon doing a Google search for Bass Ten Block resources, among the first websites that show up are Base Ten and Base Ten Blocks. These resources are fun ways to get students interacting with digital Base Ten Blocks.

REFLECTION #2

There are many online resources for teaching math, and making it more interesting and engaging for students. Some more, related resources are: The Learning Box and Build-a-Block.

A screenshot from the Base Ten Blocks website.
One of many online resources for teachers and students.

I Can't Do Math

THOUGHT

Student's, and people in general, use the word "can't" a lot, as in, "I can't do math."

REFLECTION #1

It was brought up in my Science Methodology class that students also use this phrase, replacing "math" with "science". As a teacher, we must not tolerate these types of defeatist concepts in our classrooms. If we tolerate these beliefs about what one can and cannot do, we are perpetuating the negative self-talk, and non-verbally telling children that it is OK to write something off because you cannot do math YET!

REFLECTION #2

To help remove this negative talk from students' vocabulary, the teacher might seek out intelligent speakers to invite into the classroom to speak positively about math, the possibilities of math, and why it is important. This can be especially empowering for female students, who are generally more likely to state these beliefs about their math and science inabilities, if a female mathematician visits the classroom. This is one way to change students' minds about negative perceptions.

One does not have to look far to find the noteworthy female mathematicians. These figures could even be brought up when students do a unit on biographies in Language Arts.

Sofia Kovalevskaya, one of many
noteworthy female mathematicians.

Show and Tell

THOUGHT

When looking at numbers, how does the teacher explain to the student that one number is bigger than another. For example, how can we explain that 199 is smaller than 301?

REFLECTION #1

Have the kids SHOW instead of telling them how this is true. When students build it with blocks, they can visually see that this is true, because 199 will only have one hundred base block, while 301 will have three.

This method of showing one's work with blocks, makes sense.

REFLECTION #2

This works extremely well with subtraction, for example 58 - 29. "Take away 29 blocks" is far more easily understood by students than, change the 5 to a 4 and carry the one (and reflecting on this information at this time I, myself, can't figure out how to explain why this is a the case in simple terms). So we should allow students to use tangible objects to represent mathematical equations, so see the visual representations of the.

THE Solution

THOUGHT

There are multiple ways to find a correct answer to a math equation.

REFLECTION #1

When we tell students that there is only ONE way to find an answer in a math class, this limits their thinking. People, especially children, can be very creative and there are often multiple paths leading to a correct answer. Telling students that there is only one method, or one best method, removes this creativity, and I would go as far as to say that it affect their creativity in all areas of life.

REFLECTION #2

Students' discovery of different routes to a solution should not only be allowed by the teacher, but also encouraged. In thinking creatively about the various ways to find mathematical solutions, students further develop their broad thinking, and they might even think of "better" ways to solve equations than what the teacher might have knowledge of. Imagine if some of the most influential mathematicians and scientists of the past had restricted their thinking and problem solving, because there was only one "right" way.

There are multiple ways to represent 15÷3.

Note: In the above entry, I never refer to a solution as THE solution. This is done purposefully.