Conducting an activity with the entire class may be a difficult task to accomplish. Students may be at various math levels. It is very probable that when a question is asked, a student may not know the answer, or even understand the concept as to how to achieve the answer. Therefore, it is important that the questions being asked do not only escalate in difficulty but that they decrease in difficulty as well, for those students that need extra help. It is crucial that the teacher does not make it obvious when he/she is increasing or decreasing the difficulty of the math question. Although students should not be ashamed of the level they are at in math, they may get embarrassed if they were pointed out. If there are students that are unable to answer many of the questions that are posed, it is important that the teacher notes these difficulties so that he/she can help the students develop to the level that they should be at. Students have various learning styles; it is important to cater to these various learning styles as a teacher. Visual pieces, as well as dialogues, or songs can be used in conjunction with the lesson plan.

     Using blocks is a great way to count. They allow students to handle objects, allowing them the opportunity to see what the number 5 looks like and feels like. A number can be a tangible thing, something that can be grasped and understood...it’s not just a symbol that is generated by ideas, but instead the number can be created by using things to represent it. The blocks can help represent other objects that will aid in the developmental process of understanding a certain number’s worth. For instance, the teacher may want to demonstrate that twenty-five apples and thirty-six oranges, when added together, make the number sixty-one. It is easy to demonstrate this by using words, but if the teacher wanted to use objects, it would be a difficult task to try and bring in the exact number of fruits to represent the number that is being taught. So, the bocks can be a useful way of representing objects (such as apples and oranges) that are not always readily available. Teachers are still able to make their lessons engaging, colourful and interactive with a bit of imagination.

Observation: Giving instruction to one student may be difficult. They may not understand or abide by the rules that are enforced. Imagine giving instruction to twenty-five or thirty students, or asking them to do something you’ve requested...it is difficult! Making the transition from one lesson to the next is one example of when a teacher can encounter situations where one lesson ends sooner than planned, or a method of teaching isn’t working. This is when the teacher can either choose to let the class do what they wish for a few minutes or bring in an engaging activity or game.  An activity where students can physically get involved is ideal.

Reflection 1: The activity is an ideal way to get students involved and interactive. Whether the lessons being taught are math related, it’s great to include a little activity, and why not have it be math? The game “Down Goes the Groundhog” is an example of an interactive activity teachers may choose to use as they transition from one lesson to the next. The teacher can divide the class into groups. The teacher asks each group a math question (addition, subtraction etc.). The questions asked escalate in difficulty. If the group answers correctly, they are safe for that round. If not, one member of their team must sit down “down goes the groundhog” (all other students will be standing) last person standing wins a prize for their group.  Depending on how much time the teacher has, the activity may be minimized by dividing the class in two. When the time is up for the next lesson to begin, the side with the most people standing wins.

Observation: There are many ways to engage students in learning, to name a few; textbooks, technology i.e. Smart Board, interactive activities. In class this week, we were taught a way of engaging children in a math lesson; get them to interact with math materials; thereby allowing a harmonious collaboration between students with various learning styles. The materials that were used were simple counting blocks. The professor gave teacher candidates a number; we grouped together the blocks to represent the number, keeping in mind that each block represented one unit. As the lesson continued, the numbers that were given to us became harder and harder to demonstrate by using blocks. For instance, two separate numbers were given to us, thirty-four and twenty-two. We were asked to portray these numbers with counting blocks, without adding the counting blocks for each number together, and while only using 5 groups of blocks of ten units to represent both numbers. We were unable to fulfill the task. As a group we were trying various ways to create the numbers with just 5 groups of blocks, but we came to the conclusion that the only way of doing this was by rounding each of the numbers so that we got 3 blocks of ten units for thirty-four, and 2 blocks of ten units for twenty-two.

Reflection 1: By using an interactive activity, where counting blocks were used to demonstrate the lesson on rounding, we as students were able to see for ourselves the meaning of rounding. I understand that it can be hard to imagine what something means, especially when it comes to math. Having objects to demonstrate actual numbers/units helps in the process of understanding a specific concept, in this case it was rounding. By taking objects (things) and using them to represent the idea of rounding, it helps in demonstrating the existence of a certain number (symbol) and its worth. It is alright to write the number 5  on the board, but it is better learning and teaching, if the teacher demonstrates what the number five looks like, how it can be created using things, and therefore how it can be used to make larger numbers which lead to various lessons on addition, multiplication etc.

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The world of math is a vast one! Wherever you go, there is always math clinging at our fingertips. It is true that students learn abundance within the classroom, but students are continuously learning outside of the classroom. My encounter with math at the grocery store was a tremendous surprise. The child noticed that certain groceries, and signs had one thing in common, that they were all multiplied, subtracted or divided by the number 12. Students learn in an environment that is welcoming and not constrictive. Just like when mom or dad cooks at home, children always want to put their fingers into the batter and dig right in. The best classroom setting is one that allows for an interactive and collaborative environment. Baking a cake or making brownies can be a great way to bring a math lesson to a whole new level.

    It is important to engage students as much as possible. We encounter math every day, and it is important that we not only acknowledge this, but understand how math relates to our everyday lives. My cousin enjoys the subject Language Arts; she loves Art and enjoys reading as well. As a visual learner, she tends to remember ideas, and lessons as pictures. For her, a week means 2 soccer practises etc. She makes the connection between numbers and events that are occurring in her life. I suggest that we should include activities that are hands on, and catered to every type of learner (i.e. visual).

    We all know that technology is an ever changing thing, well it keeps evolving and the technology that is out today is fast, simple and effective! As we have been discussing, math is all around us, whether it is in the classroom, outside on our local streets, or in stores, it’s there. Today you can upload apps that teach math, one of which is called “Counting with the Very Hungry Caterpillar” (https://www.google.ca/imgres?imgurl=https://appsforipads.net/wp-content/uploads/2011/12/Counting.png&imgrefurl=https://appsforipads.net/educational-apps/childrens-apps/counting-hungry-caterpillar&usg=__lmeIQ5fF2mUgJbNiCSugU7y9dkA=&h=389&w=504&sz=169&hl=en&start=12&zoom=1&tbnid=q7_Aekg6inyogM:&tbnh=100&tbnw=130&ei=MrNUUMLWNKa9ywHAsoCABw&prev=/search%3Fq%3Dcounting%2Bthe%2Bdays%2Bof%2Bthe%2Bweek%26hl%3Den%26gbv%3D2%26tbm%3Disch&itbs=1).

    Learning does not stop once teachers send their students off for the day. More than ever, parents are interested in the new technology that will allow them to interact with their children in a learning environment, whenever and wherever they find themselves ready and eager to learn.  

Observation: I went out for a walk today, and thought I`d pass by the local grocery store for some fresh vegetables for tonight`s dinner. While trying to find all of the groceries I had in mind, I came across a little boy who was shopping with his mother. By observing him, I learned that kids enjoy grouping things, numbers and groceries alike. After listening to the conversation he was having with his mother, I couldn`t help but notice how similar everything became in the store. He pointed at certain groceries and signs and shook his head at certain things his mother touched. Who knew a trip to the grocery store could be a math lesson all on its own? For a few minutes I felt like I was back in grade 4 and a kid again! Green peppers and red peppers, eggs, cookies, even signs seemed to be interconnected. Eggs reminded me of the number 12, the red and green peppers were 84 cents a pound (7x12) and the sign said 6 items or less(12 divided by 2). The child was thinking of like numbers; how the number twelve could be divided and multiplied and so forth. It was his way of learning and understanding numbers in relation to the world around him.

Reflection: Students are very good at making connections between things. Most times, making connections is the only way a student can remember and understand certain things. A great lesson plan on multiplication could be on the identification of the number 12 as a number that can be used in a variety of settings, and therefore used quite frequently. We all remember those multiplication tables, teachers asked us to write out, cut out and paste in our binders. We were encouraged to memorize the table by a certain date, a dreadful thing nobody looked forward to. I remember that only three quarters of the class memorized the table, and for the part that did memorize the table they could barely reach the 12 time tables. We were in higher grades, and were expected to know the table...dice, play money, and blocks were for “small children” and weren`t used.

                The other day at one of the orientation lectures, a teacher suggested that learning strategies and lesson plans at the junior intermediate level are surpringly looking more and more like those from a primary junior level. Just as the boy in grocery store grouped groceries into categories that related to numbers that equalled the same number when divided and multiplied, students should be able to do the same thing within the classroom. If it means that the student can get a better grasp of the symbol, why not use blocks and pictures. Another way to engage students into learning and understanding numbers is by relating the subject of math to subjects that they really excel at (considering that math isn`t their strongest subject. For instance, students who`s subject they excel most in is History, a visual timeline, with pictures along with small characters that move along the timeline to show the addition or subtraction of years. By connecting two subject areas, students can take what they know and enjoy from the subject they excel at most, and use the information and knowledge they have of it towards understanding another subject such as math.

Observation: This week in math class, we learned that students better understand math when the lesson is conducted in a simple and straightforward way. Being able to identify the number 2 can be a daunting task for students who are unable to understand what the number represents, or on the other hand, what represents the number. For instance, 2 is a symbol that represents the idea of 2. The idea is then represented by objects or things like apples, and cars. It is important to not only identify but understand the number 2. The student must relate the symbol to the world in which they live. It is important to relate math to everyday life, allowing for a more open minded learning of math and the various ways in which it can be taught to every student.

                In relation to the above observation made in class, I had a surprising encounter with math a few days ago. I emailed my little cousin who is in grade 7, asking her to send me a list of books she enjoyed reading or looks forward to reading soon; as part of information I am collecting for a project. I had asked her to email me back as soon as possible, preferably by the end of next week. In observation of her reply to my email, I noticed that she took the idea of “next week” which is represented by the number 7 (as in 7 days) and dissected the number into smaller, tangible sections. To her, she believed that after attending 2 soccer practices, 1 movie night, and 1 birthday party she would reach the end of next week. Although she understood what I meant by next week, how many days there are in a week and therefore how long she had to write back, she felt comfortable in relating the requested date for her reply, to things she had to get done and therefore could relate to. She took the number 7 and made a connection to the events occurring in her life.

Reflection: The lesson should consist of steps that lead the student towards recognizing symbols, such as the number 2. Students, who are learning about numbers for the first time, will not look at the symbol and understand its signification at first glance. In order to identify the number and understand its meaning questions should be posed. What does 2 mean? What creates 2? This is when objects, pictures, or simple diagrams come into play. It is important to adhere to all learning styles, whether it is kinestic, auditory, or visual. The teacher must show where the idea of “two” comes from. For instance, two oranges, two cars, two birds (these things can be presented in various ways; by words that are read out loud, building blocks, or pictures) represent the symbol 2, which therefore represents the idea of 2.

                My cousin, who is in grade 7, chooses to relate numbers and time to specific events that may be occurring in her life. Whether a student is at the primary or junior intermediate level, the ability to relate numbers and therefore math to everyday life creates a sense of security for the student as they encounter the world of math; a subject that can be connected to their own daily encounters and events.