Power of Yet

I did not know the importance of the growth mindset until the first day of classes, when all our classes addressed this concept. This is a powerful mindset to have, but in my opinion it takes time to get used to this type of thinking. This style of thinking is not only for teachers and educators to inculcate into their daily lives but to also teach children this powerful way of thinking. It requires one to re-wire their brain to always think with a positive lens, no matter what the outcome may be. It is to teach students to stay motivated despite their failures and to keep persevering until they get the answer. This is something I have observed being taught to the students daily; when they are frustrated and they feel like they want to give up, the teachers have taught them, “The Power of Yet.” Students are taught not to say, “I do not get it,” but rather, “I do not get it YET.” This teaches students not to give-up, that struggling is a way of learning and when they do get the answer they will remember it, compared to when they get the answer right away. It is also important to keep students motivated with not only the attitude they have towards math but also as they work through the math.

One way to keep students motivated through their work is to design the math problems in a way that intrigues young minds to keep working until they reach a solution. As educators it is our duty to provide students with multiple ways of representing their work. It is also important that math questions are designed to allow students at all levels get started working through the problem.  Here is a list of what makes a good math problem:

• Relevant: It is important to pose question to students that they can relate to
• Wide base: The problem is set-up and is doable by a wide range of learners
•  Initial success: They offer initial success, motivating the learner to push beyond their limits
• Low threshold and High ceiling: it has an opportunity for students of different levels of challenge to be able to tackle the problem, but also the potential for learners who like the extra challenge to extend the problem
•  Engaging: The questions are set-up to engage the learner and draw them into solving the problem
• More than one way: The problems have more than one way of arriving at the solution; thus sharing these different ways allows students to deepen and broaden their thinkin

Another aspect to consider when looking for a good mathematical problem is to think about the mathematical processes that will be taking place as the students work on the problems such as:

•   Problem solving: Structured to include an inquiry problem where students have to investigated to figure out the solution, by making connections to previous concepts and making new discoveries.
•   Connecting: previous experiences in problem solving help in my making new connections to new mathematical concepts
• Reasoning and proving: As students develop new ideas and concepts they also develop reasoning and proving skills
•  Representing: Students can represent work using concrete materials, pictures, diagrams, words and numbers
•  Reflecting: Questions posed by peers and teachers are a good way of getting students reflecting on why they may have chosen a certain method to represent their solution, or why they think their solution works, etc.
• Communicating: Students are able to prove their solution visually, orally or through writing
• Selecting tools and computational strategies: Students are able to use a variety of tools and strategies to represent their answer

It was really important to know these seven mathematical process when observing students doing the problem-solving assignment. This was definitely my favourite assignment to observe students trying to solve math problems and how they used variety of mathematical process to find their solutions. One conclusion I would like to draw from the assignment is that the students I observed really took their time answering the questions. They also asked clarifying questions to make sure they were on the right track. I find that in the classroom sometimes there are students who may know the answer, but because they are too shy to ask, end up making mistakes on a test or assignment. As educators we must create a climate where students feel encouraged to ask questions to clear their doubts and fears and where enough time is allotted to deepen their mathematical concepts.

To conclude, this has been a very interesting class, I have learned a lot over the past twelve weeks and I continue to work on my growth mindset when working on creating my lesson plans. As I work to make them engaging and meaningful for the students at my placement. The work can get overwhelming at times, but having learned all the great techniques to make math subject students look forward to, and on way is the use of literature. I had the opportunity to use this technique and found that students were really captivated by the storytelling technique and I hope to use this and many other techniques learned in class this year!

Level-up

Estimating

We started this week’s class trying to figure out how many cookies in the cookie jar! This activity helped us to gather data for all the estimated values and were plotted onto a stem and leaf graph. I first started my guess with 126 cookies, and the way I reached this number is by counting the number of cookies on the bottom layer (18) and multiplying it by the number of layers (7). The more I looked at the cookie jar as it was being passed around the room; I felt the number was too high of an estimate. When I looked at the jar again I saw 4 layers instead of 7, giving a total estimate of 72 cookies. Now I felt the guess was too low, so I took an average of between 126 and 72 and came to a conclusion of 99 cookies. This was a better estimate since it was very close to the actually number of cookies, 105 in the jar. It was really interesting doing this task to show students the importance of estimating. We make estimates all the time, whether it is in cooking or trying to get ready in time to catch the bus.

How many cookies in the cookie Jar?
(Khalid, N © 2016) 

Graphing

We then took the data and plotted everyone’s estimates on a stem and leaf graph. Something interesting I learned is that two sets of data can be placed on the same graph side-by-side to compare and contrast the data. In one class most people guessed around 72 cookies, while in another class there were around 84 cookies as the estimate. It was nice to compare the data that was taken from other classes. We simply started out with guessing the number of cookies in the jar, which lead us to make many more discoveries. We learned much lessons on gathering data, such as graphing, finding the mean, median and mode and their significance. So many lessons can be taught using this simple activity, which I found very interesting.

Talking about the mean, we were also shown how to demonstrate to students what mean would look like. We learned it is the same as leveling and distributing the bars evenly. It was easy to show this using manipulatives such as blocks. Demonstrating to students that if something is distributed unfairly; how can we level the bars to show a fair representation of that distribution.

Uneven Distribution
(Khalid, N © 2016) 

Evenly Distributed (That's Mean!)
(Khalid, N © 2016)  

Using technology:

Another method of comparing and contrasting data was on a really interesting website called Tinkerplots. This software helps students visualize and model the data to show differences and relationships between various attributes. This software seems a little hard to work with due to all the complex features that it has, but with a growth mindset it should be easy to overcome it with a little practice. I feel that this is a cool tool to use in the classroom and students will enjoy being able to visualize the data. 

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

(Khalid, N © 2016) 

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)

Let’s Congress

We explored a unique way of fostering student’s thinking by exploring the technique known as a math congress. The congress was a combination of last week’s kitten problem and then using the solutions in what is called a math congress (developed by Dr. Cathy Fosnot). I really liked this method as a congress allows for students to be engaged in the math problem, and in trying to figure out “a” solution, which is not necessarily the “only” solution. We began with the kitten problem of comparing 12 cans for $15 at Bob’s store versus 20 cans for $23 at Maria’s store. Then we began with thinking and reflecting on our own to figure out a solution, followed by sharing with our elbow partners to figure out a solution. As a group of four, we had to collectively decide on one way of solving a problem. This allowed for each of us to collaborate by sharing our ideas, thoughts and perspectives. This great technique used in classrooms is known as, “think, pair, share.” These solutions were then saved to be used in the class to conduct a class discussion the following week.

Once each group had a solution, this is when the math congress came to life. Each group joins another group to form a mini congress, where two students facilitate and guide the discussion. Each student uses their respective solutions to share their groups thinking to the rest of the congress. This goes on till all the solutions at the congress are understood and the thinking of each group has been made visible. The teacher also carefully picks which groups should work together to display various samples of thinking and problem solving, allowing for a rich understanding from various perspectives. One solution that really stood out to me was one that was presented in another class. Students developed a strategy to assign a dollar value to each can and compare which deal is better using both pictures and numbers. Although I did not think in this way, I really like their strategy of figuring out a unit price to compare. Overall it was great to see all the brilliant strategies that can be discovered if math focused more on the depth than breadth of a student’s understanding.  Once our thoughts, ideas and perspectives were shared, we did a gallery walk to see all the other solutions. Once again, it was incredibly fascinating to see all the various ways of presenting the solution to just one problem.

Finding unit price of each can at each store
(Khalid, N © 2016)

Numerate vs. Innumerate:

In the following video Dr. Cathy Fosnot discusses the kitten problem and shares solutions that students in a math class discovered and presented. At the very end of the video, she explains that numeracy is when an individual looks to numbers first and comes up with an, “elegant, efficient strategy given those numbers.” While, “someone who is innumerate uses the same strategy for all problems no matter what the numbers are.”  I have to agree with her, although like I have mentioned previously, it is hard to think differently when various algorithms have been drilled into our heads. These new techniques make it apparent the need for change in the way we approach and teach mathematics. 

Cathy Fosnot - What is numeracy? from LearnTeachLead (1) on Vimeo.

Fun with Fractions

This week we continued exploring other methods of engaging students when teaching fractions.

Red Light, Green Light:

A stimulating technique is to use games to teach fractions. This activity is played by having the teacher at the finish line and a group of students at the starting line. It is green light when the teacher at the starting line is looking away from the students and red light when the teacher faces the students. If any of the players are caught moving while teacher is facing them they have to return back to the starting line. At the end of the game, each player is a certain distance from the teacher. They now have to communicate in fractions, describing the distance they are from the teacher. I found this game fun and engaging and I could see this being used at my placement.  The teacher at my placement has allotted ten minute energizers where she allows the students to play an outdoor activity. Depending on the weather this activity could work really well. Since this grade 6 class is taught in a portable it allows for the students to easily enter and exit the class without wasting much time.  

When describing the distance, students would be encouraged to use a variety of descriptive terminology to explain how far from the teacher each of them are. This is known as using soft math terms such as; close to, far from and about half-way, just to list a few. When students are comfortable with this terminology, they can be introduced to fractions such as 1/2, 1/4, 8/9, and 2/47. Students can then be given a number line to see if they understand where each fraction would be placed. They can also work in groups to share ideas of why certain fractions fit in certain places on the number line. This allows students to communicate and collaborate with other students and gets them comfortable with using fractions and math terminology.

Mr. Tan’s Tile:

Another engaging way to develop a student’s understanding of fractions is through the use of stories. Many students enjoy listening to stories especially the junior grade. Incorporating stories into instruction captivates the attention of the students and helps in processing information.  A story can be constructed to get students to help Mr. Tan put all the broken pieces back together to create a complete tile. Students can relate each of the pieces to represent a fraction or a portion of the entire tile. I think this is a great introduction to fractions and proportions. Students can also have fun by using the tiles to create various other images.

I created a house with a chimney (Khalid, N © 2016)

Each tile of the tangram representing a fraction
of the whole tile (Khalid, N © 2016)

Making Fractions Meaningful:

Dividing fractions same
as multiplying (Khalid, N © 2016)

This week in class we learned the meaningful way of dividing and it was as simple as using the same technique of multiplying fractions. The numerators are divided and then the denominators to give an answer. If the denominators cannot be divided evenly, we can find a common denominator. This basic way of dividing fractions is easier and similar to multiplying fractions. When dividing fractions, I never really understood why we used the technique of inverting and multiplying when we could skip one step and just divide numerator by numerator and denominator by denominator. The cool thing about this method is that since the fractions are divided to give a smaller quotient, reducing this answer is much easier. Whereas the invert and multiply gave us larger equivalent quotients making it hard to reduce the fractions and adding multiple steps when dividing two fractions.

Overall this was an insightful class that opened up many possibilities to making learning and teaching math engaging, fun and most of all meaningful. Here are some great websites students can explore to make their experience of learning fractions even more exciting and fun:

http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.FRA&lesson=html/object_interactives/fractions/use_it.html

http://www.mathplayground.com/index_fractions.html

Identity Crisis

There is no escaping the realm of fractions! We are bound to encounter fractions in every aspect of our life. Instead of avoiding fractions, it is best that we as teachers are comfortable in this area of math. In class this week we tackled the number sense strand of math and specifically explored the identity of fractions.

We started the class with picking our favourite fraction, and I chose 1/2. I was thinking of picking another complicated fraction but decided to stick with this easy and more common fraction not knowing what adventures lay ahead. The fraction was then represented using a variety of manipulatives. I then had to add the fraction my elbow partner had, and we both happened to pick 1/2.  This made it easy as our sum added to a whole or 1. I appreciated the class discussion that later took place where I got to observe why certain individuals chose their particular fraction. Some chose mixed fractions (which I had not even considered), while others chose numbers like 5/8 just because it was a complex fraction. Fractions come in all forms and are quite a diverse form of numbers just like the diverse range of learners in a classroom. Fractions are found in percentage, as whole numbers, mixed numbers, proper and improper fractions. Getting students comfortable with the various identities of fractions and their special trademarks will allow them to easily recognize their various forms.

Different ways to represent 1/2 with reference to yellow block
representing a whole (Khalid, N © 2016)

With the abundance of manipulatives to represent fractions, students can explore in ways that allow them to engage in their learning. Possibly every child’s favourite and mine off-course, chocolate! We were generously offered a bar of chocolate per table of four and were asked to cut the Hershey’s chocolate bar into 12 pieces. We could then follow along with the book that was being read to us by the teacher.The book represented all the fractions that dealt with 12 parts of a whole. This book makes the listener, not only engaged in the story but also take an active role in representing all the various fractions with the chocolate in front of them. Who knew fractions can be so delicious! However, if I chose not to use chocolate in my class, I could also use an inexpensive manipulative such as egg cartons or clocks printed out on paper. I personally did not know there were so many ways of representing fractions and was pleasantly surprised!

Chocolate used as a manipulative (Khalid, N © 2016)

All the activities were great, the colourful plates used to represent fractions really stood out to me. Children like nice bright colours and things they can touch and feel. What was interesting was that musical rhythms were incorporated in this activity to show that fractions happily exist in the world of music as well. Musically attuned children can easily engage in this activity, and with a great introduction, the whole class can be engaged in this activity. The deck of cards was used as a competitive game to see which student got the highest fraction. However at my placement I saw the deck of cards used differently. Students had to generate the highest number only with the cards dealt to each player. It was great to see a variety of different ways to use a deck of cards. I walked away from this class with a hope that with all the wonderful tools and techniques available for our use, the journey to teaching fractions will be stimulating and an engaging one.

Differentiated Instruction

This week in class we continued learning the different strategies in which we can add numbers. As well as learned various techniques of subtracting and multiplying. The purpose of having multiple ways of doing the same problem is to allow students to explore various paths of arriving at one or few solutions. This goes back to the purpose of differentiated instruction, since we have a range of learners in class, it only makes sense that as teacher we have multiple ways of arriving at a solution.

So what is the purpose of alternative algorithms?

When learning is done instrumentally, a student does not know why they arrived at that solution. As mentioned above, everyone learns in different ways and we should compute a variety of methods in finding a solution. Differentiated instruction creates a safety net that students fall back onto when they feel like they are struggling. This form of instruction also gives our teaching a creative touch, broadening the way we think, and at the same time respecting the various learners in the classroom. Having this method of instruction allows for students to be engaged in class while helping them relate to the problem.

An example of differentiated instruction is “Skip Counting.” This allows students to visualize their adding and subtracting problems by drawing them out a number line. The students break the numbers down in chunks that are easier for them to add or subtract by skipping in small and easy chunks on a number line. However, ground rules need to be established when teaching this method; the number line increases to the right and decreases to the left. As long as students are aware of what they are doing, the bumps illustrated on the number line are up to the student as to whether they correlate proportionately to the amount skipped.

Skip count to add demonstrated in class (Khalid, N © 2016)

We continued to explore open math problem investigating the different ways we could achieve an area of 8 m². This math problem further demonstrated that a good math problem allows students to relate, thus captivating their interest. It gives everyone a chance to start on the problem no matter the learning levels. Another benefit allows for collaborative group work, observing different points of view and reasoning. When students are engaged, they involve themselves and ask supporting questions to understand the problem better. Student engagement and interaction results in reflection, making it easy for students to recollect not only the ‘how,’ but also the ‘why’.

Activity demonstrated by Fellow teacher
candidate: Using missing numbers from 1 - 9
 to solve math equations (Khalid, N © 2016)

Finally we explored math activities demonstrated by fellow teacher candidates. One of which was to use dice to perform various numerical expressions. While at my teaching practicum I saw a similar activity being implemented by my associate teacher. The activity involved students rolling a dice 5 times and recording the numbers that appeared on the dice onto each of the five blanks, with a decimal between the last two blanks. This process was repeated nine additional times. Next a random draw was made to multiply or divide each of the ten trails in blanks by 10 or 100. This activity tested their ability to multiply, divide and round numerical values. Overall as teachers we need to realize that when students are focused and engaged learning manifests itself.  

Student Engagement

The first couple of classes have completely transformed the way I perceive math. Math is not necessarily one of my strengths, but I have always enjoyed math class. I cannot imagine how someone who struggles in math would feel when taught concepts they have a hard time comprehending. Making math meaningful not only engages the students but also maintains a healthy learning environment to keep the learning process ongoing. Various concepts, strategies and insights were explored to make math more meaningful.

A new concept of open math problems was introduced in class. This is a completely new way of teaching math concepts as it moves the learning process from teacher oriented to student driven. Math questions such as, “How many people can fit in a room if you allow the maximum number of people?” forces the students to come up with supporting questions that allows for student engagement. With an increased level of interest, students try to figure out a possible solution. Another advantage to open concept problems is that it allows the teacher to use real world scenarios and incorporate it into the learning process. Math problems can also be designed with a story line that draws the interest of the students. An example of a math problem based on a camp story makes it much more relatable as many students may have experienced such events in their lifetime, once again engaging the students.

Another point of reflection that changed the way I think about math is that different strategies to solving a problem can produce the same answer. Algorithms are step-by-step processes that result in an answer regardless of the numbers used. Although different algorithms can produce the same answer, some are easier to comprehend than others allowing students to grasp the concept much faster. An additional strategy to engage students is allowing them to work with partners or groups and provide manipulatives to help students of all levels of understanding better visualize the problem. Letting students collaborate, feel and play around with the manipulatives further deepens their understanding of a concept. 

An example of how math
 manipulatives can be used in class (Khalid, N © 2016)

Many myths surround math class and one very common one is that most students feel they are just not “good at math.” This is not true as everyone has the innate ability to do math. Experiences related to math allow the brain to grow by building synapses or connections and is referred to as the plasticity of the brain. As teachers we need to create a strong and healthy environment that builds and promotes the growth of a healthy brain and a healthy mindset. A great insight into the work by Carol Dewek who beautifully explains the power of, “yet”. The idea that when faced with a hard question students should not feel they cannot do it, but rather they cannot do it, yet. This idea is another way to motivate students to have a positive mindset towards math.

As teachers it is important to know that although we do not need to be a genius in math, we do need to know how to teach math in a way which is engaging to the students. We need to be able to see the larger picture as well as make small connections. Finally, it helps to have an open mind towards those with different perspectives and ideas, including those of the students.