WELCOME!

Welcome to Stephanie's Math Blog: "Surprising Math Encounters."

This is a place where I document my thoughts and thinking about the teaching of Mathematics. My reflections are often based in theory, and theoretical perspectives, but I also provide some practical tips, tricks, and activities which can be brought into the Math classroom, or in many cases, any classroom.

I hope readers will find something hear that will assist them in their own classrooms.

Yours in education,
Stephanie

Estimation

THOUGHT

Estimation is inherently difficult to do.

REFLECTION #1

Students must understand that in estimation, there is always "something" to go by. For example, when estimating how many grains of rice there are in a cup of rice, students can use estimate how many grains of rice fit into a 1 cm Base Ten Block, how many 1 cm Base Ten Blocks of rice fit into a tablespoon, and how many tablespoons of rice fit into a quarter cup. From here, students can use multiplication to estimate approximately how many grains of rice are in a quarter cup, and thus, how many are in a cup.

REFLECTION #2

This type of estimation experiment is best done with physical rice and objects of measurement (cups, spoons, etc). This way, students can understand how more "accurate" estimates are found, and they will be less likely to believe that a trillion grains of rice will fit into one average-sized room.

Approximately how many grains of rice WILL fit into an average-sized room?

Our Beliefs Control Us

THOUGHT

Students would rather not try, than get the answer wrong.

REFLECTION #1

I think many of us have experienced this on one level or another, and it can be an extreme debilitating belief. When it comes to math, or any other subject, teachers must do their best to keep this belief as far from the students' minds as possible. By engaging students in the material, and allowing them to explore topics on their own, as well as within small groups, can dissolve some of the pressures that students feel to find, or say, the "right" answer.

REFLECTION #2

One way that the teacher can extinguish this belief in students is my creating a safe environment where students feel comfortable enough with themselves and their peers, that they can express their thoughts without the fear of ridicule. Teachers can also encourage positive, empowering beliefs in the classroom by telling students that their are NO wrong answers, but this statement must be backed up with actions, and must be truly believed by the teacher to be effective in establishing trust and confidence for the students within the classroom.

Giving Math a Chance

THOUGHT

Forcing students to learn, use, and show that they know how to use a tree diagram (or other diagram used to visually represent data) should be more of a suggestion.

REFLECTION #1

Students should be shown these ways of visually representing information, so that they are aware of them, but then students should be given the choice to use these diagrams to show their thinking, or be able to choose if they would like to represent the information in another way.

REFLECTION #2

Maybe the underlying idea of conformity to one norm in math (if one looks hard/deep enough), is one of the things that turns some students away from math. If they were allowed to have more options, and allowed to use more creative means of representing data, then they would be more likely to give math a chance. This leniency from the teacher would also help alleviate some of the stresses that students have when taking a math test (or a test in any subject, for that matter). When students know that they do not have to mimic the "right" way, this can allow students to focus on the math equation, rather than on the way that they represent the data.

Probability

THOUGHT

What is the probability that students will understand probability?

REFLECTION #1

Probability can be very difficult to teach, and is quite possibly undesirable to teach for teachers who do not have a firm grasp on the topic. This means that many teachers either do not explain probability correctly, or teach it too quickly and breeze through it.

REFLECTION #2

Probable ways to make probability more exciting for the students AND the teacher are as follows:

1) There are many games (e.g. using spinners and relevant topics for the students) and magic tricks that the teacher can bring into the classroom, that will help the students not only understand probability more thoroughly, it will also engage them more within the lesson. When my teaching partner in the first placement played probability games with the students, they became very excited, and wanted to compete with one another to win the game.

2) When you use tangible objects (such as playing cards), it is easier to explain to students what the probability is. For example, when a teacher holds 3 cards, and shows one to the student, so that 2 cards are left, and the student must pick the "correct" card, they have a 33% chance of choosing the correct card, and not 50%, even though they will be choosing 1 of 2 cards.

Some probability games and resources:

Johnny's Math Page
Basic Skill Practice Games
MrNussbaum
The Mathematics of  Magic

Student Involvement

THOUGHT

Students should be physically involved in the "creation" of math.

REFLECTION #1

By getting students out of their seats, they are more or less unable to doze off and forget about the math at hand. One example where students can be used in the math classroom, in an active way, is when introducing pie graphs. The teacher could have students with various likes and dislikes stand together in the classroom. After students have been separated, the teacher can have them form a circle, so that students are still standing beside the other students with similar likes. Next, the teacher can give one student standing on the edge of each group a string, which will be held together in the centre of the circle. This will have created an actual pie graph right before the student's eyes, and the activity is differentiated enough so that all types of learners' needs are met.

REFLECTION #2

In this sense of the "creation" of math, the math classroom becomes more akin to a drama classroom. Having a Dramatic Arts background, this aspect of the classroom, where students are involved in the learning process is extremely important to me. I believe that when students are involved in activities like this, they are not only learning the necessary skills and knowledge, but they are also creating a sense of community within the classroom, with their peers.

Graph That Data

THOUGHT

Computer programs like Excel can be used to introduce the concept of graphing data, and representing it visually, when students first begin learning how to create graphs.

REFLECTION #1

Giving students data and then asking them to create a graph from scratch seems a little backward, not to mention confusing for students. "Where am I supposed to do with this data?" students might ask, and "How does data become a graph?" If we allow students to input data into an Excel sheets, and allow them to see how the computer generates a graph from the data, students will discover how to use the data to make their own graphs.

REFLECTION #2

Technology is used for virtually everything these days. If the use of technology can help students to better understand a concept, then I believe we should take advantage of these technologies. This especially the case with Excel, because it is a very inexpensive program, and is probably already on most computers. Generally, children are so accustom to using computers everyday, that teaching graphing with technology should come very naturally to students. This is only one basic example of the many ways in which technology could assist in the math classroom.

Visual Presentation

THOUGHT

 It is very important for students to be able to visually represent their thinking, and solutions (e.g. in charts, graphs, etc).

REFLECTION #1

Visual representation help students to organize their thinking, and explain their thinking process to others. Teachers can help students to become accustomed to representing data in this way, so that it becomes a skill that students can use, not only in math, but across curricula as well, such as web diagrams when brainstorming for a piece of creative writing.

REFLECTION #2

These skills are not only helpful to students, but being able to represent ideas in visual ways can benefit everyone. With the everyday use of technology, the internet, and other means, we are constantly representing ideas to others in visual ways. One example is the creation of an itinerary for a trip. This can be a visual way of representing information from one person to another, and there are certain aspects of this, that allow people to know exactly what the information means, so it can be "decoded" and understood.

An itinerary provides information so that others can
understand what is going on, and at what time.