Mathematics Week 10 & 11

In this final blog post I will discuss Probability and the Maker Space Workshop, which we participated in as a class. 

Probability

The major concepts of probability in the junior and intermediate level are:

• Collection and organization of data
• Data relationships
• Probability
• Graphing

In the probability strand data can be represent in so many different ways. This can be through graphs, charts, or diagrams, but also through concepts such as, mean, median, and mode. 

This is a very cool activity that a teacher could use in their classroom, which demonstrates how probability works. It is highly interactive and something that would definitely engage students. 

Mathematics Week 8 & 9

For these two weeks we looked into geometry/spatial sense and measurement. 

Geometry and Spatial Sense

In the junior and intermediate level some of the key concepts are:

• Properties of two-dimensional shapes and three-dimensional figures
• Geometric relationships
• Location and movement
• Application of geometric properties in real world 

When instructing this strand of math it is very important to differentiate instruction to target individual learning strengths. It is imperative to present geometry and spatial sense in concrete, pictorial, and abstract forms. Instruction should also include examples and non-examples, for example, when teaching symmetry and technology should be incorporated. 

Here is a game for teaching students about basic co-ordinates on a graph.

https://www.education.com/game/graphing-rescue-mission/

The game is suitable for a grade 5 level and I like how it relates to a map of the world. Use can use the game to encourage cross-curricular development by encouraging students to think about what continent or country the plane lands in based on the given co-ordinates. 

Measurement

Using real world situations is a good way to get students thinking about measurement. 

Measurement relates to:

• Length
• Perimeter
• Area
• Mass
• Capacity
• Time

In Canada and the rest of the world the metric system is what is used to determine measurement, but this is not the case in the United States. 

This is a great video to get students thinking about measurement. It features legendary and future Hall of Fame quarterback of the New Orleans Saints, Drew Brees. Even in a game like football, measurement is a critical part of it and you must advance the ball at least 10 yards to achieve a first down. Quite often the chains will come into measure if the ball has advanced 10 yards. As you can see in the video objects, which relate to real life are used to do measurements as any standard can be used. 



"The Game of Inches" 

Measurement is a math strand with plenty of real world application and something, which is a vital life skill. When building anything or designing blueprints, measurement comes into play and we are using it all the time. Sometimes this is through estimation or visualization and educators must also emphasize this in their instruction of measurement. There are many ways educators can make teaching measurement engaging and hands-on for students and this should be the ultimate goal. 

Mathematics Week 6 & 7

This week we focused on proportional thinking, patterning, and algebra. 

Proportional Thinking: 

Ratios and different types of proportions such as direct and inverse proportions. When thinking about proportions it helps to think about them in relation to recipes for example. If you decide to make a cake larger you must adjust all the ingredients accordingly. Many activities relating to recipes are great for use in the classroom as they are relevant to student's everyday lives and have real world application. 

Here is an activity that I think students will really enjoy as it is humorous and can be related to either Harry Potter or Halloween.

  
You can also adjust the numbers used in the activity to increase or decrease the level of difficulty, in order to make it suitable for the appropriate grade level. For example, you could incorporate fractions for students at higher grade levels. As you can see this version is the bronze level. 

Patterning and Algebra:

This topic is generally introduced in grade 4 and continues throughout high school. When introducing students to patterning and algebra there are 4 things we can teach, which can help students develop an understanding.

• Investigate problems involving patterning and algebra in real life setting
• Extend knowledge of patterns that involve addition, subtraction, division, and multiplication as well as ones involving reflection, translations, or rotations
• Investigate problems involving missing numbers and develop and early sense of variables
• Extend their understanding of equality of expressions using multiplication or division in equations with unknown qualities on both sides

This a great introductory video explaining algebra that could be shown to students. I think incorporating videos and other forms of media when teaching math is good strategy to keep students engaged in a subject that can sometimes be quite dry. 

Mathematics Weeks 4 and 5

This week I will be discussing the topics of fractions and integers. In both cases some 
effective techniques for teaching them are through:

-        Problem Solving

-        Children’s Books

-        Games

One game resource that I wanted to focus upon was one of my favourites growing up and made me somewhat enjoy math class. It is called Math Circus and contains various games within it based on different subjects. Some games are also based on strategy and critical thinking skills. I would think that many fellow teacher candidates also played this growing up. There are many difficulties for each particular game that you can play and progress can be saved. One game in particular on Math Circus that would be great for this week’s subject is balancing brothers. The user must place the people on an integer line making sure that both sides are equal, ensuring that the line does not tip to one side. 

This is the game, Balancing Brothers as mentioned above. 

For teachers using problem solving in the classroom there are some important guidelines to remember. First, start with a problem and then facilitate:

-        Share strategies

-        Explain reasoning

-        Adapt their thoughts

-        Search for meaning

-        Identify, discuss patterns and a range of solutions

Once again, it is important for teachers to highlight for students that a range of solutions can be used and that there is more than one way to get to a correct answer. For teaching fractions and integers as well, it is encouraged to use manipulatives, in order to give students a visual representation of fractions. 

I also wanted to discuss an activity for both fractions and integers that I think would be great to use in the classroom. 

For fractions, using a Hershey chocolate bar to represent them I think is a ‘sweet’ idea that students would enjoy. After all, who does not like chocolate? You could also get a cookies and crème bar to contrast with a milk chocolate one and get students to use them to add fractions or compare them. 

For integers, I really enjoyed an activity that was presented by a colleague in class. It was entitled, ‘Mountain Climbers’ and got students to roll a dice and spin a wheel to see the number they got and whether it was positive or negative. The number they got would then see them go up or down the mountain based on positive or negative. The activity was done in pairs and there was a sense of competition even though the numbers you got were completely random. The activity gave a good sense of adding or subtracting integers. 

As an avid golfer this another activity that I liked and that students can take part in collaboratively. Does a very good job of teaching integers in a real world context. Golf is a great game full of principles and etiquette that you can also teach your students about.

When teaching these subjects and math in general, it is important to use activities that are engaging, multi-faceted, and enjoyable for students. Hands-on, visual, collaborative activities are encouraged and provide students with a good foundation to learn math. I believe some of the games and activities mentioned above would be fantastic for teaching fractions and integers to students. 

Mathematics Week 2 and 3

MATHEMATICS WEEK 2 AND 3

I believe that the overall message to be taken away from learning to teach math in today’s day and age is that it should be collaborative, interactive, engaging, and open to a plethora of strategies for finding the correct answer to a problem. There can be many different roads taken to reach the same destination. However, so far we have delved into some key aspects for teaching mathematics, which are the strands and processes that teachers will impart to their students. The mathematical process is crucial in order to increase the learning efficiency of students. It starts with problem solving, then reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing, and communicating. This process is inherently linked to the Ontario curriculum’s expectations of students as they progress from grade 1 to 8. 

For teachers there is a strategy for teaching math, which can help students understand how to better approach mathematical problems that are challenging. As educators we can formulate a minds on, engaging activity for the students and allow them to work collaboratively in groups or pairs. Students must then be challenged to consolidate and connect the new information that they have absorbed. This can be achieved by encouraging a community of learning within the classroom where students summarize their main ideas, leading to further class discussion. So far in my own experience of learning how to teach math, this strategy is something that we have practiced in the classroom and definitely seems quite effective. Some ways that a teacher can achieve this in a fun, engaging manner is to set up a Math Congress activity or the Bansho activity, which comes from Japanese educational practice. We must help students connect new ideas to previous ones and our lessons should certainly include an engaging, creative aspect.

Another important lesson for educators when teaching math is to always encourage multiple algorithms or procedures when attempting to solve a mathematical problem. Whether it is addition, subtraction, multiplication, or division, there are a variety of methods that a student can use to discover the answer. The Ontario curriculum also specifically states that students must be taught to approach mathematical problems from a wide variety of angles. Not all students think the same and one type of mathematical procedure may only benefit certain students, while other students respond better to a different way. In addition, it also fosters a better understanding for students that there are many different ways to solve a problem, a lesson that can be extended far beyond mathematics. I discovered that there are so many different ways to come up with the same answer when it comes to addition, subtraction, multiplication, and division. Students need to be aware of this as it can be fundamental to a proper understanding of mathematics and can be vital for some students to enhance their learning experience.

WELCOME!!

Welcome! I will be doing a math blog, which I hope will be engaging for students or readers! Math can be challenging but you can discover its possibilities when it is taught in a fun, interactive way with real world application.