Math Quest(ions)

Co-operative group studies:

As soon as we entered the class we were handed a Popsicle stick that was both coloured and had a number. This immediately got my attention and I already started to wonder what math activity we would be exploring today. There were two ways we could have formed groups, either a group consisting of all one colour popsicle stick, or a group with numbers 1- 6. I really like this way of allocating groups as you can get a heterogeneous group of students with different abilities and strengths working together . The purpose of this opening activity was to not only teach us  activities that can be used in math class but also techniques on how to assign groups.

We had three different kinds of math stations with six clues at each station:

1.Toothpicks to create stick figures
2.Hundreds chart to figure out the mystery number
3.Linking cubes to build a figure

Stick Figure

(Khalid, N © 2016) 

Mystery Number

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Build a Figure

(Khalid, N © 2016) 

What made all three activities similar was that students had to communicate their clues verbally without letting the other members see it. I really liked the addition of this rule, as it gets students participating and taking initiative in their learning. Also each member of the group is dependent on the others as they have to work together to solve the riddle.  We also discussed in class how standing makes students take an active role in their learning because they are getting up and doing, making and getting involved. Whereas sitting almost felt passive, or someone may sit down when independently and deeply processing information. Our group mainly stood, since we also knew we would be travelling to the other stations. Overall this is a great activity to use as a substitute teacher when you may not have a lesson planned, and I can definitely see myself using these math stations in my future classroom.

Math Activities: The Quest!

This week of activities looked at how to use technology to teach math. Since I was presenting this week, I thought to look at https://www.prodigygame.com/  as it a free resource for teachers to implement in their classrooms to make math more engaging. Students can enter the play prodigy site to make an account and add the class code. Students can pick and customize their avatar, as well as name them to represent their character in the game. They will be prompted through the game as an introduction. As the game proceeds the students are answering a series of questions by battling monsters. There is an in-built diagnostic test set in place to put them at the appropriate grade level. There can also be assignments created for specific days according to the math strand being discussed in class and skill you want your students to practice. This helps teachers to check and see how much the students know, and where they are struggling since their successes and failed attempts are recorded. Having this data helps teachers figure out where students need extra scaffolding to help them in their learning. This is a great platform since it uses the idea Gamification to draw in the students, and gets them involved in their learning. However, I would double check that the assignments placed within the game are in-line with the curriculum.

Another great platform to use is Gizmos: https://www.explorelearning.com/. Similar to prodigy, Gizmos uses technology to integrate math lessons and makes the learning very interactive. Prodigy is already being implemented at my placement, and I hope to introduce the students to math lessons that involve Gizmos to keep the learning fun and interactive.

Teaching students about area
using the chocolate gizmo
(Khalid, N © 2016) 

Student login page
(Khalid, N © 2016) 

I Have… Who Has…?

Using Games to Teach Math

This week in class we began with a fun activity playing the game, “I have…Who has…?” This activity revolves around a specific topic; in our case we continued discussing geometric properties. With the deck distributed to the class, each table group had random cards with an answer (I have) and a question (who has). Within our table group we reviewed each of the cards at our table to make sure everyone at our table was familiar with the geometric property they had, so when the, “who has,” is called out we knew if we had to respond, “I have.” This is a great way for students to collaborate and share their knowledge with students in their group and making them comfortable with their card. As a result, when the game commenced they knew when to respond with their answer. Once the person called on responds, now they ask, “Who has?” to keep the chain going till the game ends. I really loved this game as it involves the whole class and it keeps students engaged because they have to be always alert in case their card is called out.

When I was in school, we played ‘around the world,’ which was similar where one students stands behind another student and answers a math question. The one who answers correctly moves onto the next student till all the students have participated. This game gets really competitive and the students who are not so strong in math feel intimidated to play. What I liked about the previously mentioned game, is how versatile it is in terms of topic selection. This game can be used in many strands of math as well as multiple subject areas. This is a game I definitely look forward to using at my placement for many purposes, especially for reviewing topics covered in math.  

Student Centered Learning:

In this session we covered a new strand in math, measurement. The teaching technique used in class was very hands-on and an experiential form of learning. This type of learning involves students taking an active role in their learning. The teacher acts as the facilitator making the process fun and allows students to engage in their learning. We used tissue rolls to determine the surface area of a cylinder and determine relationships among measurable attributes. It was fun working through the activity sheet, using concrete materials such as tissue rolls and string to measure specific attributes. The whole activity also revolved around a problem to help students make the connection between what was being done in class, and making it relatable using a real life situation.

We Figured out the rectangles, but did not keep
 track of all the variations that we tried.

(Khalid, N © 2016) 

Another activity we explored was the relationship between area and perimeter. We looked at having two rectangles that had fixed perimeters with the areas differing by six units. This is an interesting way to demonstrate to students through inquiry that perimeters can be the same but the areas of the two rectangles does not need to be. They will also soon discover that, “the fatter the shape, the smaller its perimeter, and the skinnier the shape the larger its perimeter,” (Van De Walle, & Folk, 2005). Students are also encouraged to keep track of all their trials, because this helps them make connections and see what works and what does not. I tried this method when I taught a math lesson on pattering using a story book, “Anno’s Magic Seeds.” The pattern in the middle of the story get a little complicated, but showing students how to keep track of data is a great way to help them see patterns without much effort.

Anno's Magic Seeds, a great literature to
 be used in class for patterning.
(Khalid, N © 2016)

Reference:

Van De Walle, J. & Folk, S. (2005). Elementary and Middle School Mathematics: Teaching Developmentally (Canadian Edition). Toronto: Pearson.

Guess My Name?

In this week’s lesson we explored geometric thinking and concepts. Learning about familiarizing students with certain terms and concepts such as, “similar versus congruent.” We began the class by being handed a shape, and students had to form groups with members that all had similar shapes. Through use of inquiry, students and teachers discussed why certain group members in the same group had congruent shapes versus similar shapes. I found this activity as a great way for students to get up and become active in the classroom, ask questions and inquire about what makes their shapes similar and what makes their shapes congruent. Students can retain concepts better when the learning process is engaging, interactive and fun. I learned that in order to understand geometric concepts, students must be able to touch, feel and move around objects through use of manipulatives.

Exploring Simlar versus Congruent
(Khalid, N © 2016)

The van Hiele levels of geometric thought is a theory which depicts the five-levels of processing that individuals use in making sense of geometric concepts. These levels include visualization, making sense of what images look like. Analysis is being able to identify the various classes of shapes through their properties. Informal deduction is being able to understand relationships between properties of geometric shapes. Deduction and rigour are level 3 and 4 geometric thinking that extends from high school and beyond. Advancing through the various stages requires students to gain enough geometric experience through various forms of interactive and engaging lessons.

When we were working on activities using tangrams, it was very helpful for me to have the tangram pieces in order to create the shapes and then answer the question. Students that have a hard time visualizing geometric concepts mentally can use manipulatives to ease their learning process. Using manipulatives in this strand of math is imperative for students at all levels of learning. Since this strand of math is highly focused on students being able to touch and feel the shapes, the use of manipulatives is an asset to all learners. Also to create a learning environment that is as physical as possible.

Using tangrams to answer question
(Khalid, N © 2016)

I was very excited to learn this week about all the ways there are to teach this strand of math. One creative way is through the use of literature. Student engagement is the key to their success, and I feel that students feel captivated when stories are read to them, especially at the junior level. Knowing that there are many pieces of literature that relate to various strands of math, teachers can find comfort in knowing they can be creative in their teaching methods. Books allow students to relate concepts they either learned or are about to learn, making this form of learning easier to understand. Whereas direct instruction causes some students that are unable to engage in the learning process to tune-out. This week we read, “The Greedy Triangle,” through YouTube, which is a great way of adding technology into the classroom.

2, 4, 6, 8….Who Do We Appreciate? Patterns!

This week we discussed one of my favourite strands of math, patterning and algebra. Growing up I have always loved putting puzzles together. This love for solving puzzles was soon re-discovered when the topic of pattering and algebra was introduced to me in math class in elementary school. However my math skills have become a little rusty over time and when asked to play the matching game, it became a little daunting at first. The task was to match an equation to its corresponding t-table, graph and picture. Having the facilitator on board really helped maneuver our thoughts and also helped guide and scaffold our thinking to figure out why we chose certain cards to match one another. It really helped vocalize our thoughts and actions.

Match the following
(Khalid, N © 2016)

I would like to highlight the facilitator’s role in the activity that we had in the beginning of class. It was very interesting to see how this was incorporated in today’s lesson, because as future teachers our job it is our job to facilitate a student’s learning. This is done by asking the right questions, which I know I need a lot of practice within my placement. The article on asking effective question is a great resource and one that I will constantly re-visit to make sure I am helping ‘provoke student thinking.’

Aha Moments:

There were some more aha moments in class this week when we learned how to come up with an equation. For example the equation t= 2n + 4, is related to the t-table. Where the ‘+4’ represents how much is added onto the input (or the constant) and ‘2n’ is the difference between the terms in the output. This made figuring out the equation for the t-table simple and easy to understand.

So far four parts of algebra have been discussed the graph, equation, t-table, and picture. The final part is to solidify that knowledge further by creating real life scenarios for students. This will help them conceptualize and hopefully make connections to the different parts of algebra.

At my Placement:

Next week in placement I have to come up with a lesson plan to teach an introductory session on patterning. I am really nervous because I will have to create a lesson that is both interesting and interactive to captivate and engage the students. I plan to use the activity in Dr. Small’s “Making Math Meaningful.” The activity in the textbook describes solving an equation by maintaining a balance where an unknown number of tiles are placed in the bag and students must figure out how many tiles are in the unknown bag. Through trial and error students figure out how many tiles by putting certain number of tiles on the other end of the scale till it becomes balanced. Students then make the connection as to how many tiles were in the bag and can come up with an equation to represent the situation. I really liked this activity and I hope to fit it into my lesson plan as it uses a very interactive approach and every student can participate in the learning process

Balancing Act
(Photo captured from Dr.Small's textbook 'Making Math Meaningful')
(Khalid, N © 2016)