Exit: Micro Teaching feedback

I taught Multiplication of Fractions with Julie. We had allocated the time fairly accurately, however the structure of the lesson was a bit poor. Our prior knowledge check was a bit rushed and awkward (as we were all just pretending). The teaching of the material was also quite rushed and there was no time at all for any development of skills, only an introduction (due to having about 6 minutes for it). I would add to this and remove part of the participatory activity if this was real students, and do the activity the next day.

The activity itself for the second half of the teaching was quite effective and fun. The students enjoyed it and it reinforced their skill-set. I would do it again, but I would do it later in the lesson.

Here is my feedback:

Entry: Micro Teaching in Pairs

Micro Teaching Criteria

Name: Jacob & Julie

Topic: Multiplying Fractions and Mixed Numbers

Objectives & Goals	The purpose of this session is to introduce the students to multiplication of various fractions, including mixed numbers. The subsequent lesson (which we won’t do) would teach them about division.
Hook	I will introduce the lesson by showing them a fraction of the board (eg. 5 x ⅓) and ask them what this means in math. I will then explain that it is the addition of ⅓ five times (ie. ⅓ + ⅓ + ⅓ + ⅓ + ⅓), just like regular multiplication.
Materials	To teach this lesson, it is suggested that you have a whiteboard and marker.
Prior Knowledge Check	I would check that students: a) Understand what fractions are and b) Know how to add and subtract fractions. If these are met, we can continue the lesson after a short refresher. If not, we would spend a bit of time on that a it is a required prerequisite.
Activities	2 Minutes: I will explain that multiplication is just addition. I will say that this is also true of fractions and that they know how to add fractions. 2 Minutes: I will do an example. (6 x 1) is just 6 units by 1 unit If you count the boxes, you will get the answer of 6. Now for (6 x ½) you can simply cut this in half either way: If you count the half boxes, you will have 6 of them, which equals 3. 2 Minutes: I will show them that it works for only having fractions as well, such as (½ x ½): 2 Minutes: I will show them the formulaic approach that they will apply, now that they see the methodology: You simply cross multiply. If there is a mixed number, just turn it into an improper fraction first. 6 Minutes: I will give them an activity on Kahoot and review at the end.
Ideas and Skills	They will learn the basics of multiplication of fractions. It will be a culmination of addition of fractions, multiplication, and mixed numbers/improper fractions. This will reinforce algebraic skills.
Closing	The closing section will be at the end of the Kahoot activity. We will check their learning progress and use it to prepare the subsequent lesson.
Assessment	I will assess the students’ learning by seeing if they understand the method during Kahoot. This assessment will be used to determine the amount of homework to assign as well as if the following lesson should advance to division of fractions or further development of multiplication.

Exit: Thinking Mathematically

 If we treat the red circle as being stationary and I rotate the yellow circle around, every quarter rotation flips the face (as is represented by the rectangle) of the rotating circle. So every semi-turn will be a full rotation about itself.

Entry: Dave Hewitt

   According to Hewiit, arbitrary facts of mathematics are similar to postulates. The facts and concepts with which we assume to be true but which you need to be taught before you can thoroughly explore any deeper meaning within. They are concepts which must be stated and are not able to be found, and are not consistent through different frameworks.

   On the contrary, necessary aspects are, according to Hewitt, those facts and ideas which can be constructed through our arbitrary concepts. These are things which everyone will find to be true when based on the same framework of arbitrary ideas and through which are able to be known without being told. They are able to be 'discovered'.

   His idea is obvious in retrospect, but makes you become aware of something important in the classroom. You need to teach arbitrary ideas and let the students become aware that these are not capable of being discovered and need to be memorized. This will avoid frustration when students don't understand the idea or can't reproduce it. In addition, you should let them see which ideas are necessary and show them the steps to creating them using your arbitrary set of ideas.

Exit: Museum SNAP Fair

   I thought that the museum visit was quite interesting. After having presented at 3 math fairs this semester, it was a nice change of pace to attend one as a participant. It was a great idea having the fair at a museum, where the projects were based around exhibits. Though many of the projects were only loosely linked to their corresponding exhibits, it was a good way to encourage the students to learn more about the museum as well as the attendees, while forcing the students to add some creativity to their project.

   The puzzles themselves were very well done (better even than my own presentations). I liked that there were several puzzles which obviously were based upon the same concept yet were presented quite differently. It was great to see the kids adding their own twists and ideas to well established math fair problems. Not only that, but I loved how the students had clearly spent a lot of time with their projects and were able to show us multiple methods to solve it.

Entry: SNAP Fairs

I think that a SNAP Math Fair would be feasible at my practicum school, though I would need to verify it before-hand. I would most likely test it out with 1 block of students to test the waters. I could give the class a list of projects appropriate to their age and skill level, and let them each choose one in small groups. Maybe something like letting setting aside 1 class to set them up and then letting them work on these projects once a week when they have a double block (they have an extra 40 minutes of class-time after lunch). Give them a month or so and they can host a small presentation of their projects. I would need to investigate further into the logistics of the presentation, but it does seem like an interesting way to get the students interested.