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.

Math and Science Go Hand-in-Hand

THOUGHT

Hypothesis: If I follow a recipe for Gluten-Free Pancakes, the final product will turn out perfectly.

Problem	Solution
Pancake mix is too watery.	Add more flour.
Pancakes are too flat.	Add one egg.
Pancakes aren't cooking well.	Cook them one at a time.
Flip pancake too early.	Ruined a pancake.

Findings: With some additions to the recipe, and through experimenting with cooking time, the pancakes were a success.

Conclusion: Basic Math and experimentation are important in our daily lives.

REFLECTION #1

Would a deeper understanding of math make me a better cook? Would every mathematician (or scientist) be a world-class cook? I would say no to both.

When it comes to math - like cooking - it can be fun to experiment with amounts and try to figure things out for yourself. I think it is important in Math, and education, for students to have a sense of curiosity, which can be modeled initially by the teacher, to encourage curiosity. Still, (cooking) classes are also beneficial.

REFLECTION #2

Does the fact that one can't cook make one a hopeless case who will never be good at it? Should we just give up on someone who doesn't get it?

No! So why wouldn't we help our students until they get it? We may need to try different approaches - different ingredients - but eventually we will reach a day when the recipe (student) succeeds.

Also, it would be unfortunate if an individual decided to give up on cooking altogether because they were not successful at it the first time. We, as teachers, must keep students engaged (read: curious) in their learning, to achieve a successful result.