Math Songs to Calm the Amygdala

(cross-posted on medium.com)

I have been reading Culturally Responsive Teaching and the Brain and it is fantastic. Lots of nuggets to apply immediately in the classroom, as well as a bigger picture to think about. One of the early gems from the book was about how many cultures are still steeped in oral traditions, and the effect of that is that -- depending on their home culture -- some of our students' brains are primed to learn that way even in the classroom. When we provide instruction primarily through writing, not all students process it at the same rate depending on their home culture's dominant way of passing along information. I was on the plane when I read this particular part of the book, and I thought about how I find myself repeating the same information often to groups of students, instead of resorting to music to help them encode that information. I put the book down and wrote three songs to use with my students next year, that encapsulate some of the basic information that I think everyone should really internalize. I don't think teaching by song is in contradiction to "Nixing the Tricks", because really a song is not able to provide the student with all the things they will need to be able to do. They still need a lot of knowledge and understanding outside of the song to be able to flexibly and accurately execute the skills, but if they can memorize the song, then maybe it will provide them with a starting point to be/feel less helpless when approaching intimidating problems. That's all. It's a way of quieting the amygdala and to encourage students who learn through a different sense, to be more independent.

Here are my songs! I wrote one for linear functions, one for math faux pas's (the mistakes that kids often make in simplifying expressions), and one for solving equations. I am not the most musical person, so they are written to mostly kiddie tunes as I sing kiddie tunes to my baby everyday. My thought is that we would sing them as a class sometimes, and I would give extra credit to students who wouldn't mind performing it in class on some days before the assessment. The idea is really to encourage the kids who struggle with tests to learn the songs by heart before the end of the unit, so that it can serve the purpose of building their confidence before the test. 

http://bit.ly/mathSongs

What are your thoughts? Do you think they are too procedural still? Do you think that songs can be used in the classroom to complement student understanding, rather than to take away from it?

Brainstorming for a Mini-term Course

(cross-posted on medium.com)

To the two of you who still have my blog bookmarked, I am back! Back from maternity leave (see picture below of a tiny person I am now responsible for), and back in school mode now that The Precious has started daycare.

One of my first orders of business is to research options for teaching a new class during a two-week mini-term in the 2017-2018 school year. The format is going to be as such: two weeks straight, 6 or so hours a day in that same class. This mini-term is a feature that is new to our school calendar, and in spite of having some anxieties surrounding teaching a new course in such a compacted time frame, I am excited about the possibilities! As far as I understand, the students don't get graded, so it is purely for enrichment. Which means: 1. Anything goes, as long as there is educational value. 2. No alignment to an existing curriculum is needed. The format also means that it needs to be deeply engaging - because can you imagine being stuck with kids for two weeks doing something that they think is boring?

Okay, so my three ideas thus far are: 1. a coding course 2. a robotics course 3. a social justice and math course. I researched these options and want to just lay out the details, both for me to come back to and to gather some feedback at this pre-planning stage.

Option 1: Coding

I reached out to my friend Sam C., whom I had met at PCMI a bunch of years back. He had recently mentioned on social media that he taught a course using the Code.org curriculum, and that it was fantastic. I looked into it, and it is! They have a free curriculum called CSP, Computer Science Principles. For a two-week course, I would start with Unit 3, which is introduction to computer science. The lessons are thoughtful and accessible -- for example, Unit 3 starts off with kids writing verbal instructions for their partners to draw basic geometric shapes on paper. It is like that build-a-PBnJ-sandwich activity that is very popular. It then progresses to the students drawing basic shapes by giving instructions to a computer -- a smooth transition from paper to coding. Then it asks the kids to find the lowest value from a physical row of cards (as manipulatives), and then again to teach their algorithm to a computer. Slowly, it starts to introduce more functional concepts such as parameters and encapsulated logic. All of this within Unit 3! Then, because of the nature of the mini-term lending itself to doing projects, the kids would move on to Unit 5, which gets the kids to start building apps. Sam also did the same with his class, and he said the kids got really into it! (My husband, who also builds apps and writes software professionally, thinks it's not only an essential skill for our students, but also something they would surely get excited about. He had independently recommended teaching a Build an App course to me, before I talked to Sam!) Anyhow, Code.org makes it really easy. They have a sandbox called App Lab that basically allows kids to drag and drop visual elements (such as buttons) onto a page, so that kids can focus their time on programming the desired reaction in response to the user-action. (Here is a video that gave me a good idea of how it works.) The programming concepts can ramp up fairly quickly from there, which allows for both differentiation and creativity in the students' apps. (I would have to do more specific playing around prior to teaching this, so I know what is realistic within the time frame.) Sam also recommended a similar sandbox from MIT, called App Inventor. I haven't had a chance to check it out yet, but Sam C seems to prefer it a bit more to App Lab. 

Bottom line: Since I have some coding background (it was my undergraduate study and I had worked in the industry for a bit) and the Code.org curriculum is so kid-friendly already, I think I can already hit the ground running and teach this course with fairly high chances of success. It would also give me a chance to brush up on my Javascript programming skills, which admittedly I am very rusty with. (I have been teaching for over a decade! Can you believe it? I have hardly programmed at all in that time.)

Option 2: Robotics

So, back when I first went on maternity leave and thought that it meant that I would have copious time to learn extra skills (Ha! Ha! I die laughing...), I had borrowed a Lego EV3 robot from my friend Danielle, whom I had also met at PCMI. (I mean, if this is not good advertisement for PCMI, I don't know what is.) Danielle, if you don't know, is one of the baddest mofos ever. She went to a robotics camp as a newbie some years ago with Zero prior experience in programming or robotics, and now teaches a robotics course and advises her school's award-winning robotics team. If that's not badass, I don't know what is. Well, back to my efforts to learn robotics. My motivation comes from seeing the cool things Danielle's students do with their robots, and now that our school has hired a couple of new teachers who have experience already with Lego, it seems within the realm of feasibility for us to agree to invest in other teachers to build out our program. 

Bad news: I tried looking at tutorials online, but they're really hard to follow unless you already have a full EV3 set at home (complete with the connectors, which I didn't get from Danielle) and are tinkering along. But even then, I wouldn't feel comfortable running a robotics workshop unless I have BEEN to one, amirite? It just makes sense to me that I would want to see how the pros train teachers to teach robotics, before I would want to turn around to run a workshop for kids. So, I looked into the pricing of such training. I'll list them all here for your convenience. It costs $999/teacher to go to a full-week training course, which has the benefit that they provide all the hardware and run the workshop in person. The drawback is that they don't offer these training courses during the school year, so I would have to wait until Summer of 2018 to go to one. (This might happen, if I get approved.) Alternatively, you can also take an online course, which costs $499/person. The caveat is, of course, that it's online and you have to provide your own hardware. These courses run often, so I could take one as soon as the fall (I think September-October 2017). They also go once a week from 3pm-5:30pm PST, for a bunch of weeks, which is a little hard on the childcare side. (I would probably have to get my husband to pick up Sir Poops-a-Lot from daycare on those days.) Lego also offers trainers to be flown out for a one-day $2500 workshop for up to ten teachers on your own campus, which sounds like it could work out to be a better deal for our school, but my husband reminded me that there is no way they could cover the same depth in one day as in a week or a recurrent class, so it could be pretty rushed. 

Bottom line: I am still super interested in this option, but more as a long-term thing, maybe as a mini-term in 2018-2019. If the staffing numbers work out for me to help teach this course alongside someone who is already fully capable of running the course, that would be fantastic, because then I can learn alongside the kids and maybe run the course the following year. I also think it would be a good idea for our school to really invest in people to build out our robotics program, particularly seeing how it is project-based and goes along well with the mini-term format.

Option 3: Math and Social Justice

One of the visions laid out in the mini-term program is that our course offering is inter-disciplinary. Okay, that makes sense, and it seems to me that our school can really use a bit of social justice math. I know, social justice, so vague and broad. But I sat down and tried to brainstorm today, and I think if I were to choose one issue to focus on, I would choose housing. This is because in Seattle, where I live, housing has reached a crisis point. It's so unaffordable for the average person to live here, and minimum wages are not even close to cutting it.

Okay, so I sat down and did some rough math. Obviously if I were to teach the course, we (maybe the kids) would have to get better numbers. But, just hear me out.

I assumed that a median individual salary in our city for a person seeking to buy a house is $60,000. (In reality I know that there is a huuuuge disparity between people who work in tech, and everyone else. When I looked briefly into it, the median household income is $65,000.) I listed some very conservative annual expenses and concluded that the person could save a maximum of $17,500. (In reality, we know that that's not really possible. That's VERY aggressive saving for this salary. But, let's just say that that's the ideal case.)

It would take this person 10 years to save $175,000. At 20% down payment, this person would technically be able to afford a house that is valued around $875,000. In Seattle, a house can easily cost this much today. (When I looked it up, our median single-family home now costs $700,000 before taxes and fees.) So, assuming that this person borrows $700,000, then his monthly mortgage payment would be close to $3,500. (The standard estimate is that for every $100,000 you borrow, you pay $500 in mortgage per month. So, for $700,000, you pay roughly $3,500 per month. Of course we would do the real math in class assuming 4% mortgage and either 25- or 30-year repayment plan, but it does work out to be roughly the same.)

This causes a problem for the person buying the house, because although technically they had enough down payment, their monthly expense now exceeds what they make after taxes. So, we can work backwards with their new expenses (some good ol' middle-school math) to see how much bump in salary they would need, in order to sustain this lifestyle. It turns out that in my model, the person now needs to be making closer to $80,000 in order to make this happen! WOW! Big salary jump.

So, how can people afford to buy houses? Besides the obvious options (buying a starter property or  pooling together resources with your domestic partner), some people are fortunate to have initial help from family, particularly relevant because I teach at an independent school. We can do the work to see how the math changes if you have more down payment. Obviously, this raises the issue of privilege, and that can lead to a discussion of why economic advantage is a legacy that is often passed on from generation to generation.

This should lead into discussions/research about the rental market. I haven't yet looked, but I think we can pull together some stats on how quickly rental prices have grown in Seattle. We can graph them and research whether that outpaces the general trend in income. In general, as the property value rises, the landlords would need to keep raising the rent in order to keep up with the mortgage on their investment, which exacerbates the displacement of families and communities.

What if someone waits to save up more money to buy a house later? Assuming that the market continues to grow the same way it does (which is exponential and ridiculous... something like 25% or 30% in two years), your savings account which is growing roughly linearly from your monthly contributions, cannot hope to catch up to the market. So you would end up in a worse state in a few years unless your income level changes drastically. That is a very real use case of function models.

(Of course, the argument can be made that that's why couples combine incomes to purchase a home. But it comes back to considering that the median household income in our city is $65,000!)

Other aspects of Seattle's housing crisis that I would want to touch upon in the course, should I actually teach the class, include: gentrification, segregation, and homelessness. 

I found a link from Rethinking Schools that paints some personal perspectives behind gentrification. Why do people sell their house in a neighborhood of rising values? https://www.rethinkingschools.org/articles/whose-community-is-this-mathematics-of-neighborhood-displacement This gives me the idea of reaching out to the community activism groups to bring in housing advocates who work on this on a day-to-day basis, to shed some light on the narratives that affect our specific POC communities. In the article, they also do some easy discrete math — great opportunity to incorporate technology! (A few years ago I worked with my Precalc kids to write explicit equations from recursive forms of similar complexity, and it was challenging but great, because it was anchored in real-world math! That can be a possible math extension for this.)

A little while ago, my husband and I watched a mini-series called Show Me a Hero, that I would love to also show my students as a multimedia link to this topic. It has 6 episodes, so it would take basically one whole day. The show is about how there was an attempt in the 1980s to build affordable housing in a middle-class white neighborhood. It became a racial issue, and (I will spoil the ending for you if you read on...) the experiment worked and the project was a success. I am hoping to use this as a segue to talking about the current homelessness in Seattle, and the various challenges surrounding the sanctioned homeless encampments in our neighborhoods. Granted, I am not very good at leading this type of discussions, so I would probably want to partner up with a humanities teacher for this course in order to up the rigor of our structured sharing sessions.

Ideally, the class can then take a service trip to one of these local encampments! In my neighborhood, there is one such area called Nickelsville. I know that volunteering there is possible, because I have a friend who used to do it often. (Our school's ethos goes along with doing such trips as well. We regularly take kids to food banks to help out.)

So far, all of these are just rough thoughts. If I did such a course (which I would like to at  some point), I would like some project that ties it all together. It could be a reflective assignment, or it could be something like interviewing adults and kids to incorporate their thoughts and voices into our class. It could also be a math project, looking at data from different cities and trying to coalesce them somehow into a meaningful conclusion.

But, regardless of which routes I go down, I would love it if you could point me at any resources that you think might be helpful! What are in my blind spots? I know that, for one, I have not yet considered the appropriate audience for these classes. I vaguely think they would be more appropriate for high-schoolers, but is that necessary and true? Have you taught a mini-term before, and do you have any tips for me in terms of structuring each day? Thanks in advance for any tips you might have! 

Quizster: The Formative Assessment App

(cross-listed on medium.com)

I teach high-school math, grades 9 through 12, with classes ranging from Geometry to Calculus. In the past few years, I have found myself increasingly interested in the structures of formative assessment, because although formative assessment is something we all aim to do in our classes, its specific method of implementation can have varying degrees of effectiveness on improving student learning. During the last two years, I have implemented weekly “No Big Deal quizzes” that contain a couple of questions targeting a recent topic, but without including any scaffolding in the questions or cues hinting at specific strategies. The students tended to fall on a spectrum on these formative assessments. They would take about 15 minutes at the start of class trying the questions; I would then collect their responses and go over the answers as a class as the students took careful notes and asked questions. The next day, I would return the graded “quizzes” (usually worth only 2 to 4 points for one or two questions) and assign similar problems on the board for the students to copy down and complete, in order to make up any points missed via showing an improved understanding on those topics. For some students, just turning this new assignment in is enough to show a thorough understanding and to address previous misconceptions, but for other students in the class, remediation frequently requires a continued back-and-forth dialogue on the new questions until they finally get it and are able to demonstrate that understanding on paper. If they have trouble revising the responses, they would first go to their notes on the initial quiz and ask me clarifying questions during class. If that wasn't enough, I would offer to sit down with them to go over the process again one-on-one. What this allowed me to do was to address real-time gaps in their knowledge, so that by the time I gave a summative assessment at the end of the unit (or halfway through a long unit), I could hold all the students accountable for higher-level complexity in problem-solving. This paper-based formative assessment process worked well and was critical in advancing my students’ learning, but I found myself having trouble with effectively following up with my students regarding their assessment results. They sometimes misplaced the graded papers with my written feedback on it, or they couldn't remember whether they still needed to revise a particular quiz. When they did sit down with me, I often wished that I had a more detailed record of their processes and misconceptions, instead of just a score in my gradebook and an unreliable memory of their errors.

My husband is a software developer, always on the lookout for ways to improve the existing ways of doing things. Sensing my frustration and seeing the hours I put into sorting through paperwork, he and I sat down to hash out the design for an app that would allow me to grade formative assessments in pieces, on the go, while I am on the bus or waiting for a meeting to start. The app we built takes photos of student work and allows the teacher to dialogue with the student, updating their assignment grades incrementally and providing additional feedback until the student completely masters the desired skill. It would also provide a photo record of the students’ progress, to enable effective one-on-one conferencing. I piloted the use of this program last year with 60 of my students during a full school term, and it easily complemented the formative assessment I was already doing. To maintain their focus on the math, the students would still complete their work on paper, but instead of handing me loose sheets during class, they would simply use their phones or tablets to take a photo of their work through the app for submission, which took a matter of seconds. After class, I would sit down and open the app to find all of their submissions, already sorted by question. I would grade a single question at a time using just my fingers and a touchscreen interface on a mobile device, across all students, and upon exiting, the scores and feedback would be published to the students instantaneously. Afterwards, the students would be able to submit further revisions and to receive further feedback until both they and I felt satisfied with the results. This app quickly gained popularity with my students. They loved the camera interface, the instantaneous feedback, and the ability to pull up an entire list of assignments to see which items still needed their attention. The more organized students liked not having loose sheets of paper floating around and to be able to keep track of all of their written work sequentially in a paper notebook, which stayed in their possession. I liked the flexibility to selectively collect a single question from a homework assignment, the freedom to grade anywhere without lugging around tons of papers and notebooks, and the ability to focus on providing quality feedback in real-time without fussing with the overhead surrounding the receipt, recording, and returning of assignments, because Quizster took care of all of those logistics for me.

Quizster has helped to streamline an important part of my students’ learning. In doing so, it has made me a more effective teacher, being able to focus my energy on what matters -- identifying student needs and personalizing my responses. I look forward to reading about how other teachers will implement this app in their classroom. Following 6 months of initial prototyping and testing with a small group of teachers, the app is now ready for release to a wider audience. If you wish to be part of the testing and evolution of this product, you can find more information at http://quizster.co .

Goal

My goal for 2016 is to always respond to a potential conflict by killing it with kindness. I had a situation in class today which I had handled calmly, but in hindsight I don't know how kindly I had come across because I was actually feeling fairly upset in the moment. This goal extends beyond professional settings, but I do want to make sure it is something that I keep striving towards in the classroom. How do I consistently show love to a kid who is misbehaving in the moment? How do I do that with the people who are closest to me? As I prepare for parenthood*, that seems like an ever-important question to explore for myself.

(*Yes, parenthood! Baby on the way, if all goes well between now and June!)

What it Means to Slow Down a Problem

We did a really ambitious activity early this year in Geometry. We slowed down an optimization problem for start-of-year Grade 9 students, in order to get every single kid to understand the process. It worked brilliantly, and we are trying now to help them extend the idea to other optimization problems.

I want to document and share this journey, because I think the experiment that we have started is SO challenging and SO worthwhile. We are trying to get the kids to think like mathematicians. By slowing them down.

Here was the first time we formally introduced optimization (after having the kids play around with building their own popcorn containers). If you read it carefully, you might notice that we tried to emphasize a few things: 1. Tactile learning. 2. Justifying their thoughts. 3. Understanding what x and y represent. 4. Understanding how to analyze the domain. 5. Resourceful use of technology. 6. Interpretation of results back in context.

A little while after going through this, we gave the kids an open-notes test, using a different sheet of paper to start. They did well, which showed us that they really understood the different pieces. Then, on the actual closed-notes exam, we worked backwards by giving them a factored cubic equation, and asking them some relevant questions: 1. What is the dimension of the piece of paper that we had started with? 2. What is the domain of this problem, and why? 3. What is the largest box that can be built here, and what are its dimensions? 4. How many different boxes can we build that would have a volume of _____, and what are their dimensions? Again, the kids did brilliantly!

It has been amazing and humbling to see how far along these 9th-graders have come.

The next question that we gave them, which they worked through in small groups, was an optimization problem involving a known perimeter of a rectangle and in trying to maximize its area. They needed to take the problem from start to finish, in writing a system, combining it into a single function, and doing domain and graphical analysis to find the maximum. Then, as usual, interpreting back in context.

Now, the next problem they are tackling has to do with maximizing the area of an isosceles triangle whose perimeter is 30 units. Not easy. Some kids figured out right away that this follows the patterns of other similar problems, where they will try to write an area equation. Some kids started to make tables -- another really great habit of a mathematician! The class, as a whole, needed a nudge to help them figure out how to get the height of the triangles. We stopped discussions today at writing a general height equation as a class, in terms of x, the length of the two congruent sides, and I asked the kids to keep thinking about the rest of the problem.

A worthwhile experiment, indeed! If by the end of the term, they can do even half of these problems completely independently of us, we will be so thrilled. I think the key is to slow them down. By feeding them the understanding in pieces and then giving them another similar problem, we are building the foundation that it takes to transfer the knowledge.

Stay tuned! 

First Term Reflection

This is a rough brain dump after the recent end of school term, but I am going to try to stay coherent and helpful.


1. This past school term, I decided to be tougher-than-usual and to cut off accepting make-up work a day before the end of the term. It seems like a small change, but it really saved my sanity by so much! I got to get all of that make-up work graded and returned by the last day of the term, and to just focus on the bigger assignments (like tests) once the kids went on term break and I was working on finalizing their grades. It probably didn't save me much time, but it saved me lots in terms of sanity and focus. I wasn't trying to grade a thousand different assignments all at once while trying to re-calculate their grades.

2. Another thing that really saved me is that I created a learning rubric, asking kids to rate themselves on their growth mindset, reflectiveness, responsibility, resourcefulness, and organization on the last day of the term. It was tremendously helpful to me in writing comments for them, looking at how they rate themselves in each category of the rubric! At this point of the year, it allowed me to really incorporate their own self-assessment into their evaluation, while keeping it somewhat objective (action-based, as my rubric was formatted to be, rather than opinion-based, like it would probably be if I gave them an open-form self-reflection). Again, in the end I don't think that I necessarily saved time in writing their evaluations, but I think that I wrote really detailed and comprehensive ones, considering that it is only the first term and we have only had 6 or so weeks of school.

3. At the end of the term, I really liked ending Algebra 2 with choice assignments and ending Calculus with no-requiz-option exams. For Algebra 2, the choice assignments were all regression activities, and all groups ended up learning/practicing the same skills, but offering them the choice meant that we would potentially have richer discussions in coming weeks, and their interest level was also very high during the task. For Calculus, giving them a quiz that does not have any re-quizzing options was a great way for me to ask the students to step up to a "college-level" challenge after a term of slowly ramping them up to my expectations, and to show them that they could still do very well if they would commit to preparing and asking questions in advance. It worked! Although in general, I am a believer of re-quizzes, I think giving one no-requiz assessment every term will actually reinforce their confidence over time, even for the students who initially don't do well on them. It will also make for a more realistic preparation for college next year.

4. In Grade 9 Geometry, we had given an open-notes exam half-way through the first term, and then a closed-notes final exam at the end of the first term. These tests were super helpful, in combination. The open-notes exam was a great informal check-in on how responsible they are as learners, in asking clarifying questions in class and making sure that they had understood a quite complex task. (Their open-notes task was to take a sheet of paper and to write a cubic equation modeling the volume that could be built by folding up the corners into a box. The 9th-graders needed to do domain analysis and to use Desmos to optimize the volume, and then to construct the box accordingly, individually.) The closed-notes exam at the end of the term, then, assessed how well they are practicing/preparing for exams. I loved this combination, particularly in Grade 9. I thought it was a very developmentally appropriate way to introduce them to high-school expectations.

5. Math journals. Love them, but they're so much work! I am still looking for ways to cut down the work load that is to grade these concept journals all the time (often twice, if the kids are doing revisions on their entries). Any tips?

6. Overall, a very exciting, albeit hectic, first term!

Wordle as a Tool to Respond to Feedback

This year, particularly after reading Thanks for the Feedback, I am making a conscious effort to gather on-going feedback from my students, in order to address them in real time and to engage my students in a two-way communication. But, let's be honest, the thing that takes the time in class is not to gather feedback, but to go over it. It always feels tedious to go over kids' concerns and appreciation bullet point by bullet point, so this year I am going to try using Wordle (or one of the alternatives) to make the discussion take up less time.

Here is an example of my Algebra 2 wordle, based on feedback for what is working well in the class thus far. I couldn't get the Java interface for Wordle creation to work either on my laptop or on the school's laptop, so I used TagXedo to make this in the end. I like TagXedo, because you have choice over both font and orientation of text. If I wanted to, I could have orthogonally-oriented text. As you can see, kids mostly thought that group work and their classmates were very helpful, as well as handouts that had some basic examples on them. Lots of kids mentioned fixing their errors as being very helpful as well, and the idea of growth mindset being weaved into that. With this picture, I can hopefully whittle down this part of the discussion into a couple of minutes, and then focus on discussing what isn't working well yet. (It didn't make sense for me to create a wordle for what isn't working well in this class, because they are only individual concerns and no real repeats.)




Incidentally, we had a great open house this week, which also weighs in as a source of feedback for me. I tried out an exercise where I asked my students' parents to write down on an index card one hope or excitement they have towards their child's math class this year, and one anxiety that they have towards the class this year. My student parents blew me away on this task! Their responses continue to reinforce my belief that our approach to teaching mathematics needs to consider, in every step, how we are impacting our students' mindset and attitude towards math.

Here are their hopes or excitement. Believe me, their concerns are equally insightful!!

I would love it if [my child] developed a sense of the Beauty of Mathematics.

I am hopeful that [my child] can regain [their] confidence and enthusiasm for math.

Feel like a mathematician and enjoy math.

Hoping that [my child] sees the beauty of method and that it becomes a great mix of method, understanding, and simplicity as a meditative experience/tool.

[My child] continues to love learning.

I hope [my child] grows [their] confidence in Math and is able to solve problems with numbers.

Confident enough to not fear mistakes and attempts and iteration.

Learn algebra

I hope for [my child] not to hate Math.

To gain confidence by asking questions and talking more in class.
 
Excited that [my child] is taking Calculus in high school.

Hope [my child] continues to enjoy math.

Deeply interested in math/Calculus both as theory and application.

I want [my child] to enjoy Calculus and math and to want to do more of it in college, to embrace quantitative theory and analysis.

Excited for [my child] to learn Calculus!!

[My child] is totally turned on by math. [They have] not expressed any anxiety.

Understanding the basics of differential equations and still keeping [their] interest/love/self-confidence in math.

Understanding the basics of Calculus.

I never took Calculus so I am excited for [my child] to learn something beyond what I took.

Glad [my child] has got classes and teachers that [they like].

I am excited that my student is in Calculus and I'm looking forward to [their] development of understanding derivatives.

Excited about [my child] building confidence with Calculus to ease the college course experience.

[My child] seems to love it.

My hope is for [my child] to appreciate that Calculus will be applied to Sciences, and necessary for [them] to succeed in.

Excited for [my child] about [their] continued exploration of new math concepts.

[My child] LOVES math and I'm excited that [they are] able to do 2 classes this year.

I am excited that no matter what [my child] learns, [they] will know more than me.

[My child] is taking charge of [their] work and meeting with you regularly.

Excited for [my child] to continue advancing in math as it is one of [their] favorite subjects.

That [they] can apply [their] learning to real life situations.

Thinking about incorporating some of this parental input into my discussion with the students about how class is going, where we are headed, and why.

How do you manage gathering and addressing feedback in your classes, on an on-going basis?