Unit Plan + 3 Lessons (Draft)

 Link to the Unit Plan Draft

Giant Soup Can Problem - Solution and Extension

My Solution:

I started off by estimating the size of the medium-sized hybrid bike's frame to be 43cm, which falls in the range of the suggested hybrid bike frame size for a medium sized bike. Then, measuring the scaled length of 43 cm, we can use it as a scale factor to estimate the potential size of the giant soup can. Once we measure to scale, we can use the volume of the giant soup can to calculate the amount of volume of water, and compare with the amount of water needed to put out a house fire.

Extension:

One extension to this problem is to look at the amount of pain needed to paint this water tank. Maybe even go deeper into how long would it have taken to dry the paint depending on the angle of the sun on Hornby Island. This would be a question that, just like the original question, requires some research and connection to science within math. It will require lots of estimations and assumptions, focusing on the different methods that students can use to approach this question. This can be a good math question where teachers can promote math-thinking and communication where there are no correct answers (however there could be a range where reasonable answers should fall).

Group Curricular Micro-Teaching Reflection

 Reflection

Our lesson was on linear regression from FOM 12, and we focused on an interactive activity-based learning for the students. It was my first time going through the FOM 12 curriculum, and I noticed that many topics are different from what is covered in PC 12. 

As we worked our way through the lesson into the worksheet activity, each of us (without making a group decision beforehand) walked around making sure students were on task, asking them questions, giving assistance if students were unsure of the task, and keeping them engaged. It was fantastic that we all knew what to do and how to be present in the classroom during the activity, despite the lack of practice time we had. 

After reading through the peer-assessments, some improvements we can make for next time would be:

• Including additional scaffoldings for clear worksheet instructions: This could be written on the worksheet or verbally communicated before assigning the worksheet questions

• Explain instructions before distributing worksheet: A student mentioned that a couple of students missed instructions because they had their attention on the worksheet in front of them.

• Lesson run-through before lesson: We did not have enough time to do a full run-through of our lesson. Despite most of it being organized and smooth, there were areas where we could definitely improve and gave advice to each other if we went over what we were going to say in the lesson.

Self-/Peer-Assessments

Group Curricular Micro-Teaching Lesson Plan

Group members: Yuki, Ross, Katarina

Subject and Grade Level: FOM 12

Curriculum Big Idea: Modelling data requires an understanding of a variety of functions

Curriculum Competencies: Reasoning and modelling, Connecting and reflecting

Curriculum content: Regression analysis

Learning objectives: Students should understand what a line of best fit is, know how to choose the function that yields the best fit, and think about what the error is

Materials: Whiteboard markers (for teacher explanations on board), calculators (Desmos), worksheet

Teacher	Student	Assessment	Timing
(Set up) Co-teachers hand out activity worksheets.	Students offer what functions they are familiar with Ask the class to use their hands to show what those functions look like	(Accessing prior knowledge)  Setting the stage and asking students what functions they remember learning in previous units or grades.  Note: We will have been studying linear, quadratics, exponential, logarithmic, and sinusoidal functions throughout the year	3 min
(Matching Activity) Teacher asks students to have a look at the dataset and match the type of function to the dataset. The matching activity will be done as a think-pair-share.	Students match on their own, discuss with partner, and then share as a class (Think-pair-share)	Teachers check in with groups, ask them to describe their thinking, see if there are any functions that are challenging to match	6 min (1 min think, 2 min pair, 3 min share) Note: move on to class-share if pair discussions start to  drift off topic
(Error activity) The teacher asks students to have a look at the three sets of fits on one of the dataset from the matching activity. Discuss with partners: which fit do you think is the ‘best fit’? Could you provide a measure of which one is best? (Could do TPS but it might be hard with time)	Students work in pairs to think about which fit is best, and measure error (in a non-sophisticated way).	Teachers check in with groups, ask them to describe their thinking, see if students are recognizing that the best fit is connected to how large the error is. Use an exit ticket to check understanding – Which fit they think is best and why?	4 min
Teacher introduces Pearson correlation coefficient as a measure of error	Students listen		2 min

Extension: Factorial Function

Earlier in the year (likely) they will have done a unit on combinatorics. Note that we do not have a function y=x! because we know it only works with integers. But if we put for example (0.5)! into a calculator we do get a result. 

• Have students use desmos to plot y=n! for integers n = [0,6]

• Use function regressions they have practiced to see how close you can fit the curve and the various values of R^2. Try plugging in (7,7!) and calculate the error, as well as different non-whole numbered inputs.

If short on time, we will not introduce Pearson’s correlation coefficient and end with the exit ticket. 

Reading Response: Battleground Schools

    The section on math phobia and negative stereotypes stopped me the most. It's definitely true, and I've personally experienced it being said to me. Many people are not fond of anything math-related and would, probably thinking that it's not offensive and more as a joke, to give the "ew"-reaction. Some people will give respect to those who are proficient in math, recognizing how others can do something you aren't as good at. And of course, some adults are not hesitant to say that they can't do math, because everyone else is also open about it. However, if you replace these conversations with the subject of literacy, would it still be heard as a joke? Or would saying that you are illiterate be different, and why? These are some questions that made me want to ask as I read.

    Another point was how mathematicians, and people who are simply good at math, are generally stereotyped to be male. I've heard about this before, but never believed it until I gradually saw the proportion of male students in math courses rise once I got to upper-level courses. In elementary and secondary, many of the "smart" kids were female students, and I would find more male students struggling with math throughout my high school years. This was an interesting finding for me, but I never took the time to look through any research or articles, so maybe it will be a good chance to search now. 

    The third point that made me think deeply was about the reality of unqualified or math-phobic teachers working in the secondary level. I remember that, in our Math Assessment course, we were told that there are many cases where districts don't have enough qualified math teachers and had to ask other subject teachers to teach math. This lead to teachers not knowing how to assess their students well in math, and some had to just "do their job" which lead to the disconnection of students to mathematics. Even with the demand of the number of math classes just as much as English and Socials courses (i.e., having Math 8-12, AP), there's a lack in math teachers, which is also very evident in the number of TCs in each subject cohort. 

Reading Response: Lockhart’s Lament

I was amazed by how Lockhart started off by used the word nightmare to describe the current situation of math education. His strong use of vocabulary (like destroy, soul-crushing, and rotten) truly speaks where he is standing in this discussion on our education system. 

I would definitely agree that math can be seen as art and that our curriculum and education system is not delivering this idea in their lessons as much as we think they should be. From my experience with high school math, I only did math-art-related assignments in grade 8 and 9 but never showed up in higher grades. We would talk about conics, but that's it, and we move on once we take the unit test. I also want to point out that Lockhart's statement on not needing to put math in context to have relevance in life was interesting. I don't know if I completely agree with this, but I understand that some math questions on worksheets and textbooks can be very odd and unrealistic situations, making students question ABOUT the wording or question rather than thinking of how to solve the question. 

Despite the significance of thinking math as an art, I disagree with how preparing for tests is a complete destruction of the concept of artistic math. I think art in math is amazing, but at the same time, I strongly think that the mastery of foundational skills, like memorizing formulas, applying and solving problems by hand, and studying for tests, aren't an enemy of creativity. They are important skills and preconditions to working in and succeeding in STEM careers. Utility-based teaching should not be removed from math education if teachers use thoughtful assessment strategies that look at students' competencies for advanced learning or professional paths. Without some form of testing (or assessment), how can we ensure that these professionals are capable, reliable, and accountable? I don't like to think that schools and education systems are human factories that produce young adults that are ready to work for the community, but instead, education should be a way to open up the countless paths that students can take in this world after graduation. 

Skemp and Lockhart:

Both Skemp and Lockhart share the big idea that we must put emphasis on the discovery and reasoning (i.e., knowing the 'what' and 'why') rather than just remembering how to plug things into formulas and memorize to survive tests. Lockhart explains this as the art of mathematical thinking, and Skemp calls this the relational understanding, which they think is not present in a school where everything is determined by tests.

Micro-teaching Reflection

Self- and Peer-evaluations

    A big idea I learned from this activity is that it's very easy to get myself engaged in teaching the content because we chose a topic that we are passionate and have knowledge in. This made me realize how important it is to have passion and solid knowledge in what you are teaching (whether it's teaching/training a skill at work and tutoring academic subjects, to explaining someone about the details of some breaking news), to be an effective instructor for your audience. If I'm not having a fun time talking about something, how would it be possible to keep the students engaged in what I say? Not everything teachers teach is "fun" (like certain historical events, since those should be treated in a respectful manner), but the significance of being able to show how much we care and think it's meaningful will reach the audience. In the math context, this definitely reaffirmed my values as a teacher, on the importance of mastery while creating a positive learning environment for all students. 

    My micro-teaching lesson went smoothly, having enough time to go through the key slides and information needed to complete the assignment at the end. I think the layout of the lesson was very clear, especially because I took the time at the start to go over the lesson objective and learning objectives with the students. While teaching, I noticed that all of my students were very engaged in the content. With this, I made the choice to allocate more time to the end-of-class activity. The choice to make this change ended up being successful, even though I made the decision on the spot. I'm happy that I was able to make flexible decisions as I saw how the students were doing. 

    One thing I should work on is my voice projection, especially when we have many groups talking at the same time. I've always had a hard time adjusting my volume to the adequate loudness of the environment, since I either speak very very loud in a large room to teach karate, or I talk softer with my friends in a smaller group setting. I hope I can practice this during our other teaching opportunities in the program or during the upcoming short practicum. Something that I could have added to my lesson was another very small check-in question or activity. This could've been a short Check-Your-Understanding question mid-lesson to connect with students and see if they are on the right track with the material. Even if I didn't have to use this check-in question, I could have added a slide just in case I had students who were struggling to understand the lesson.