Maintaining Intrest in Content

THOUGHT

Students can complain about math a lot, so why make it more painful for them by strictly using the old textbooks, which can include examples which are dated, at best, and contain little variation.

Math textbooks in schools today are the same ones that I used
when I was in elementary school.

REFLECTION #1

By bringing topics, statistics, data, examples, etc, etc, into the classroom, that are actually relevant to the lives of students, the teacher had a better chance of engaging students in the math lesson, and keeping them actively engaged.

REFLECTION #2

It isn't a novel concept that people enjoy talking about themselves and their interests. In order for the teacher to bring in material that is relevant for the students, the teacher must first know exactly what their students are interested in. It would be a great idea if the teacher were able to bring in a variety of activities over the course of a unit that would engage all students and their interests. Or the teacher could set up math centres with differing activities, like literacy centres, and allow students to either pick the centre that most interests them, have them rotate throughout the class, or put students into groups of similar interests, and assign them to these centres.

Students can be organized to complete activities at different math centres.

Tools For Teachers

Ones and Zeros

THOUGHT

Digital data is all 1's and 0's. How can this be used in a classroom?

REFLECTION #1

While completing my undergraduate degree with part of my combined major in Multimedia, I took a course in which I had to build a computer. We also studied binary codes, and the translation of 1's and 0's into numbers as well as hexadecimals. Putting my fear of failing this class aside, I think it would be a neat idea to bring binary code into the classroom, and have students create messages, on any given topic, in binary code.

REFLECTION #2

I think the introduction of binary numbers to students could be a fun way of looking at a different kind of math. This website brings up a positive point: "[...] even though I didn't like math much at that age I spent a lot of time for a while playing with converting from one number system to another."

Below are some resources I have found that could bring binary code into the elementary classroom:

Counting in Binary on Your Hands

Binary Counter
The Socratic Method I would like to look more in-depth at this method in the future.
Binary Numbers Contains videos on the exploration of the binary system.
Binary Counting for Kids
Text Convertor
Decimal/Binary Convertor

Twelve Days of Christmas

THOUGHT

The Twelve Days of Christmas can be used as a math activity that can be taken into the classroom.

REFLECTION #1

Until it was mentioned to me, I never thought that the recipient of their "true love" in the popular Christmas song, acquired any more than the ONE partridge in a pear tree. However, on the twelfth day of Christmas, the recipient will have 12 partridges in a pear tree! I hope that bringing this into a classroom would be as shocking a realization as it was for me.

REFLECTION #2

Teachers can use this song, and other forms of pop culture, or situations that are more relevant to the students lives, than just resorting to the math textbook, when teaching math. Students can use the information provided in this song to visually represent, in a chart, graph, or other form, the way that the song displays patterns. The prior knowledge of the song, makes it an excellent resource to use around the winter holiday. When the teacher uses these types of things, students can become more receptive to learning, as they may forget that they are actually learning, once they are engaged in the activity that is somehow relevant and connected to them.

Learning and Importance

THOUGHT

How do kids learn, and what how do they learn what is important? And what IS important?

REFLECTION #1

Children learn by connected new knowledge to prior knowledge and experience. If a child cannot connect a new piece of knowledge to prior knowledge, it will be very difficult for them to understand the new concept. This is why it is so important for the teacher to connect new concepts to things that the students are familiar with.

Students must be interested to be engaged.

REFLECTION #2

It is not the presentation of the concepts or answers that is important, but it is the developing of the concepts and answers that is important. While we might like students to arrive at the "correct" answer, the path that they take to arrive there, is just as important as their solution, if not more so. The path allows the student to display their thought process, while also allowing the teacher to see what the student's thinking about a math equation is.

These Are The Groupings

THOUGHT

Students learn concepts best by attempting to find solutions by themselves.

REFLECTION #1

This is not to say the teacher does not have any part in student learning, but when students are given some basic instructions, it can be best to let them experiment with finding a solution on their own. For example, when using manipulatives, students can be given the freedom to work with the blocks and using them to find the solutions to equations. When working on their own, they are given the opportunity to develop their own concepts, and ways of working with objects that they might understand better than the a method that the teacher might further explain to them.

REFLECTION #2

"Work on their own", this does not necessarily mean individually. It can simply mean without the lead of a teacher, so that the lesson becomes more student-directed. There is a reason that more and more teachers are moving away from the typical classroom setup of students sitting in rows, toward seating students in groups with their classmates. This arrangement suggests the growing importance, and support, of peer-to-peer learning. When sitting in groups, the teacher can encourage the students to teach concepts to their peers, the way that they understand them. Some students may be more open to the suggestions of their peers as well, and the teacher can facilitate this kind of learning by discussing the different methods that the students have come up with as a class.

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.

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.