In this reflection piece I assess and analyze an activity I did with the students and what I learned from it in terms of pedagogical knowledge, prior knowledge and previously learned information 

Teaching math (or any other subject) requires understanding of the nature of the student’s content understandings and their ways of representing knowledge. It is important to understand how students represent knowledge. I, as a teacher need have a good understanding of the common learning difficulties and preconception of students.
I want to talk a little about a lesson I did, which was dividing decimals.

My vision:
 present the question on the board
how do I divide 1.5/2.5
before telling them the rule of dividing decimals, ask them how we divide 15/25 
let them solve it
the answer is 0.6
notice how 1.5/2.5 is equivalent to 15/25 (multiply both sides by 10)
so 1.5/2.5 = 0.6
Write another example on the board 0.25/1.5
before we solve it, ask students to solve 25/150
the answer is 1.66…
notice how 0.25/1.5 is equivalent to 25/150, they have the same value so
so 0.25/1.5 = 1.66
Ask them to solve 2.1/.3 don’t give them any hints, walk around the class and see how they Solve it. Find out whether or not they have figured out the pattern.
Solve the example on the board: 2.1/0.3 is equivalent to 21/3, so the answer is 7
Explain the rule, make sure they understand how we can find the equivalent (multiply by 10 or 100) give few more examples and let them solve it, walk around the class to give one on one help.
I wanted the students to see how we can easily divide decimals by changing them to something that we know how to divide. Since they already know what equivalent fractions are, I thought presenting the lesson that way was a good idea, and it would make dividing decimals easy.

How it went:
the students have already learned dividing decimal in pervious grades (I think grade five). When I asked them to solve examples, many of them tried to use the method they learned in the past: which was move the decimal of the denominator, then divide and move the decimal back)

As I was walking around to see what they are doing, many were solving it using their way. And those who were trying to solve it my way were asking me “when do I move the decimal back?”

It is clear that as I was presenting the lesson, many were trying connect what I was saying with what they learned previously, which created a big confusion.

I think teaching math takes much more than knowing the material. It takes  knowing how to present it as well as knowing how the students think and how they will perceive it.

In this reflection piece I talk about an activity I did with the students and how I assessed myself and the activity in terms of student engagement, what they learned and how they feel about their learning, my interaction with the students, and what I learned about classroom management

Although the activity that i did with the class didn't go as great as i thought it would, I have learned many things from it and I take it a s a valuable experience

I wanted to do a review for the class, and I thought jigsaw might be a good way to do so. There are a couple of advantages of the jigsaw method. The teacher is not the sole provider of knowledge. Students take ownership in the work and achievement. Students are held accountable among their peers. Learning revolves around interaction with peers. Students are active participants in the learning process. 
Lesson plan: Divide the students to groups of 5, hand each group coloured cards. The card indicates what topic each group is responsible for (Equivalent, Reducing, adding, ext). That is if one group gets the reducing card, then they are the “experts” at reducing, they have to explain what reducing is and give examples. After most groups are done, shuffle them based on their coloured cards. So the purple card students are in one group and the yellow card in another group and so forth. Each student will explain to his new group about what he discussed earlier. After all students have had a chance to talk with their group, have a class discussion about fractions. Ask questions like why do we simplify fractions? How do we add fractions of different denominators? Where do we see fractions in real life?

So the lesson started, I gave them instructions to get to their groups and work on their topic. I went around to each group and explained to them that they have to know their materials really well because they will explain it to everyone else. As I walked around it was nice to see some discussion going within each group. One student was not really good with subtraction. His group members were explaining it to him and he was paying attention to them and asking them questions, he was finally getting it. It was nice to see him come up with his own examples about subtracting fractions; he was struggling with it for a while, but now I see that he is getting it. It was really nice his group working with him and helping him out. I think all the expert groups did really in working together. I think this is because they knew exactly what was expected from them. That is, they knew they had to teach the other kids about their topic, so they had to be prepared. After about 15 minutes some groups were done and waiting for more instructions while others were still working on examples. It would have been better if I didn’t limit the examples to only five. Instead, make them come up with as many as they can. This way the groups who were “done” wouldn’t have thought they were done, and they would have kept on working. Also, since there wasn’t a specific time frame, some were working slower than others. It would have been better if I made it clear from the beginning that there will be a time frame of 10 minutes, and if they are not done, it’s ok as long as they have some examples we can move on. After about 15 minutes I shuffled the groups and they started sharing what they know. I told them to try and challenge their new group members and give them some hard examples to work. I also told them to write down notes from their group. This is because I wanted to give them a reason to pay attention to their group. I must say this didn’t really work out so well. As I walked around I see some groups working alright and others not so much. In one particular group, two kids were arguing and getting on each other’s nerves. I walked over to them and tried to calm them down and help them resolve their issues. The thing is, usually in this class, kids pick their own groups, so naturally they work with their friends and group working goes smoothly (most of the time). This time they don’t get to chose; they are stuck with people that they might not get along with so well. There were definitely some different personality issues. When it was the shy kid's turn to share, he talked very quietly. It was very hard to hear or pay attention to him and he was completely ignored by other kids. It must have been overwhelming for him to be around those very strong personalities. I think it would have been better if I assigned each group a leader. It would reduce the problem of dominant student. The leader is responsible for being fair and spreading participation evenly. The students weren’t as engaged as they were in their expert group. Other than personality clashes, I think they weren’t very clear on what was expected from them. 

As mentioned by Mr. Long, it would have been a nice idea to get a big poster and let them explain using it. It would be easier for the group member to look at and pay attention to it. We could have them decorate it and hang it on the wall, I’m sure they would have been more engaged if they knew they would have to share it with the class. After maybe 20 minutes it seemed that most groups were done, and every student got to share what they know. I wanted to start the discussion, so I grabbed their attention and started asking them question and passing out candy, unfortunately we ran out of time.

overall I think the activity went well. The biggest issue that I still have to handle is time management and transition between activities. Explaining from the beginning how everything will go, and setting time frames for the kids will keep them on task and keep us on schedule. Also it would make transition easier since they know what to expect. This was the first group activity I did with the kids. The most important thing I learned is that they need to have group rules!

classroom management:

I think the thing I do well the most when it comes to classroom management is giving students attention. Some need it more than others, but all kids need and want attention, especially positive attention. In this activity, there was some tension between some group members, but as I walked over to them things calmed down a little bit and they were able to get back on task. When students behave badly sometimes all they want is attention. Giving positive attention is an effective strategy that I observed in Ms. Johal’s class. There is one particular student who is considered by his previous teachers to be a “trouble maker”. He was constantly saying inappropriate things and acting up in class; she started by listing to him, asking him questions in class discussion, making run errands for her, making him feel needed, and acknowledging his presence in a positive way. His attitude has changed a lot from the beginning of the year to now. I like what Mike said in our field seminar class. When a student does something right, give them three times as much attention as when they do something wrong. If all a student hears is yelling and negativity and nagging about not doing his work, he would eventually stop caring and it would become a habit. Like the self-fulfilling prophecy “she thinks I’m bad anyways, why bother?” It is better if we invest in encouraging them about an improvement and making them feel proud when they do their job. That is what will push them to do better. This is something that I have trying with one of my students. This week for the first time he had finished all his math homework, I was so proud of him I kept on praising him about it. He was so happy too; he looked at me with his big bright eyes and said "since I'm being really good, can I have some candy?" well, unfortunately I didn't have any candy with me that time, but next week I will give him some, just to continue the encouragement. I hope he will continue to do better.

Giving individual attention to students is extremely important. Everyone in the world needs their own attention, especially kids. We all need to know that we are special, we are unique. I try to spend time with all the kids in class, not just the ones that are easy to get along with. I try to give individual attention to each one. I see it as an affective classroom management strategy. Because it shows the kids "I care about you. You are important to me" it makes students feel wanted in the class, which is important to make them thrive. There is one student who started out to be really shy. He wouldn’t really talk much and didn’t really care about doing his work. I always joke around with him and teas him and try to bring him out of his shell. I feel like it works because he has improved a lot. Now he teases me as well. Just the other say he was  saying how he would "mess things up" when my "boss" comes to visit me... which he didn’t.

Something interesting happened on Thursday at the last period. Ms. Johal gave the students work period. The class desks were divided to four tables, so the students were sitting in four groups. Right after she assigned them their work, she walked around the groups. Her presence was very important to get them focused. The class was quite and everyone was working. Then she stood right in the middle, two steps away from every group. The class stayed quiet for a really long time and everyone was right on task, even as she went back to her desk the class stayed quiet. This doesn’t happen very often. I think because she was with them from the beginning, they had to be quite to show her they're busy at work. She stayed around them for a very long time, their minds were put on working mode, so even after she went, their minds were still set on working mode.