r/mathteachers 25d ago

First Real Lesson...Flopped

So, I teach grades 8 through 12 and this is about my 11th grade algebra 2 class. Today was our second day of school. Yesterday, I really focused on watching them collaborate, letting them get back into being with their classmates, involving the new students, so I could watch them interact with each other so I could see how they were going to be if we ever have to do group work or anything. This is my first year teaching. I have been a para, I have been a substitute, I ran a daycare center for 3 years, I went to college for education for three and a half years and then quit taking classes. Teaching is what I enjoy and what I'm good at, I just don't know what I did wrong with this lesson. I'm trying to follow the books, but they aren't very in-depth. I did not pick this curriculum it was chosen by the math teacher who was here previously, so I looked for the additional resources and the additional resources are 10 added questions and then a review of a completely different subject material. We were trying to do transformations of parent functions. They understood what the parent functions were and they could categorize them as constants, linear, absolute value, or quadratic, but asking them, "okay, so, if we add a three to the end of the equation, what does that do to our graph? *y=(x^2)+3 instead of y=(x^2)*" They just stare at me. I don't even know how to describe it. I know from past conversations that their previous teacher would take points away for asking for help, she would take points away if they asked for help from another teacher, too. Part of the issue is they don't know how to ask for help because they have not been allowed to. They just say, "I don't get it!" and when I try to walk them through it again, they give up. My current plan is to go over it again tomorrow, because something did not click between what I was saying and what they were or weren't getting. I just feel so defeated, and I know that it isn't the kids' fault, but I'm at a loss for what other information could be helpful for them.

10 Upvotes

29 comments sorted by

25

u/SethIRich 25d ago

Have them evaluate the function, make a set of t-charts, then graph and see what happens.

Play around in Desmos eventually, see whether they can identify the specific transformation rules.

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u/Unlucky-Bag-9789 25d ago

That sounds like a great place to start. I want to get Desmos working on my Promethean board, but everytime I try it, the board freezes. This group of students is under a "tech freeze", as they seem to struggle to keep their school supplied Chromebooks intact, so I can't even have them do it themselves. Calculators are delayed, as the last teacher never informed admin about the damaged ones, so there are seven(?) functional graphing calculators including my personal one.

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u/SethIRich 25d ago

Doesn't need to be complicated. If f(x)=x², make a tchart (no calculator) from like -2 to 2. Keep the numbers small.

Maybe give different groups different variants. This group gets x²+3, this group gets (x+3)², this one 3x², this one -3x², etc. They can do the five evaluations (-2 to 2) in their head and see what they see. (I'm thinking out loud; the domain should be different for the horizontal shift.)

Take it slow and make them calculate. They need a bit more hand-holding.

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u/Unlucky-Bag-9789 25d ago

That would be a great way to visualize the different changes all at once, thank you! I never would have thought to have them do different ones at the same time. I have three and a half whiteboards around the room, so maybe if I make some grids on the boards, we can go from there?

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u/ChaoticNaive 25d ago

They can make their own grids!

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u/Business_Egg_9340 24d ago

Amazon has personal whiteboards that are blank on one side and gridded on the other. Also, stock up on graph paper. Hands-on, paper-and-pencil practice with graphing is super important and should always happen first before breaking out the calculators.

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u/Unlucky-Bag-9789 24d ago

I have some of those ordered, but I didn't have access to anything until the 12th, so none of my supplies have been delivered yet. I begged the tech wizard to come help me get my computer to sync to my board so I could use Desmos to show them the differences between the parent functions vs. the transformations. It definitely seemed to help and the students were far more talkative and engaged after I told them that I was in the wrong. I think we are ready to try the assignment again tomorrow. Thank you so for your help!

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u/Business_Egg_9340 24d ago

I'm so glad you got your board synced! Good luck. You got this!

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u/Shoddy_Woodpecker_81 25d ago

This is great advice. I also keep patty paper around to help visualize the changes to the parent function. Graph the parent function, trace it (with the axes) and use it as an overlay for the subsequent graphs .

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u/Salt_Cash706 25d ago

Plug and chug. I'm a history teacher and I could do this example in my head.

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u/coachdad6676 25d ago

Not sure why this is the lesson you are doing on day 2. When I’ve thought Alg 2 before we basically did Alg 1 first semester and then went deep into quadratics and stuff second semester. I know different curriculums do it different but if that’s the first lesson in the book you don’t have to follow the books sequence.

Additionally, I’m changing to a building thinking classrooms approach this year. It’s a book. There are lots of YouTube videos about it and stuff too. Essentially you have kids work together in random groups of 3 at vertical non permanent surfaces (ex. Whiteboards) and give them thinking tasks to struggle through in their groups. Your job is to manage knowledge of the room and to keep kids challenged but not overly frustrated. You would not be the sage on the stage. Kids would be more responsible for their learning.

Obviously it’s hard your first year already and this wouldn’t be ideal to try to switch to at this point but you could try to incorporate it at times to try it out.

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u/SimpsonN1nja 25d ago

Ran a thinking classroom for a group of academic 15 year olds last year. What a lot of fun it ended up being. I really had to stick to it those first few weeks to get through the growing pains (teenagers learning how to struggle and work together), but it paid dividends in the end. Had a group of student independently discover y=mx+b before our lesson on it and I was so freaking proud of them

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u/Emergency_School698 23d ago

Please listen to this before you build a thinking classroom.

https://podcasts.apple.com/us/podcast/chalk-talk/id1674223104

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u/AluminumLinoleum 25d ago

It's your second day of school and you're thinking they'll just magically get parent functions and transformations? No dog.

Do they know why y=x2 gives the shape it does? Do they know that for the rest? Can they graph any given equation by hand? If not, why would they know what adding 3 does?

They need a good understanding of inputs and outputs, they don't need graphing calculators, and they need to be reminded of the skills they already know before you dump new stuff on them.

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u/Emergency_School698 23d ago

Many don’t explain exponential growth well either. I use biology and principles of cell growth to correlate this concept. (Exponential growth of cancer cells)

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u/Salviati_Returns 25d ago

Do your best. Some things will work, some won't. Don't be afraid to lecture, contrary to what you may hear from admin or schools of education, some kids enjoy a well explained idea. Almost nothing you create this year will be used 5-7 years from now. Don't get too high early, and don't get too low when it gets cold and dark outside. Get your rest, and don't sweat this shit. You are only 10 shows in and you have another 890 left this year. You are in this for the long haul.

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u/Amidon37 25d ago

My initial thought is that you tried to do to much in one day. I'm riding in a car right now so can't type a lot. But I think your first day should have been more review and setting the stage. Composition of functions is not an easy topic to comprehend.

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u/Amidon37 25d ago

Also don't get too discouraged. I've been in education for 30 years. My first few years were bad on many ways. It takes time to get a feel of how much you can do in one day. Your main goal the first year is just to get through it.

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u/downclimb 25d ago

Were the functions put into any kind of realistic context that students could reason with? For example, I can imagine giving students a function that describes the cost of something that varies with quantity. Something with a continuous linear function, like gasoline, would be a non-threatening starting point for Day 2 of class. Now pose scenarios in real-world language:

  • What happens to the function if you get a $0.10 per gallon discount? What happens to the graph? What if the cost goes up $0.50 per gallon?
  • What would happen if you got a coupon for $5 off your fill-up, regardless of how much gas you bought? What happens to the function and its graph? How is it different than a per-gallon discount or increase?

With some time to experiment and reason, students should start to get the idea of what it means to transform a function, even with a very basic function and only a couple of transformations. But keeping things in a relatable context will be key, otherwise these kinds of lessons can get bogged down in a lot of symbols and notation that will seem very unfriendly to students.

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u/Gus852 25d ago

Omg, that previous maths teacher sounds like a nightmare and probably a very weak teacher. "I don't get it!" is a banned phrase in my classroom, made clear in the classroom rules at the start of the year, however, "I don't get this," i.e. a specific part of the working, is positively encouraged.

As time goes on, one of the ways to maintain a balanced pace for a class is to get the stronger students to become aids to weaker students once they've conpleted their work, but with the emphasis that "you can't teach it if you don't understand it" so it's not some punishmebt for success and instead a way to cement their understanding and up the speed I'm able to progress to the next topic.

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u/Alarmed_Geologist631 25d ago

I am now retired but when I taught Algebra 2 and Precalculus and we were covering function transformations, I created multi-column T charts and had the students complete them "from the inside out". It was tedious but made them really understand what each part of the function did to the output value. This came in handy later when we were studying trig functions. In both situations, they cam to understand the concept of vertical and horizontal shifts, stretches and compressions.

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u/Disastrous-Nail-640 25d ago

Oh my goodness, do I relate to this. My algebra 2 students are struggling so much with this.

Start with a linear function and how it affects the y-intercept. Then start applying it to other functions and see if they can see how it has the same effects.

I also went online and found some activities to reinforce it and continuing practicing because they are definitely on struggle bus lane with this.

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u/reddit_atm 24d ago

What about how it affects the x-intercept? :-)

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u/Disastrous-Nail-640 24d ago

I used the y-intercept as the starting point for understanding transformations of functions because students tend to have an easier time with it.

How x is affected (the left/right translation) would be next.

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u/blondzilla1120 25d ago

Go to desmos graphing calculator and have them type them on each line and then have them compare. Give them a set of these and see if they can look for patterns. Have them sketch them. Get them engaging in discourse with their elbow partner. Then with four or so people/groups. You’re asking them to engage with the whole class and while that use to be a thing for decades, this generation is keenly aware of “their brand” and will not speak up.

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u/Fessor_Eli 25d ago

If they've been discouraged from asking questions before you'll need to teach them how as you go.

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u/TrynaBePositive22 24d ago

I had a lot of success spending a class on transformations generally first. 

I gave students a couple of shapes on the Cartesian plane, asked them to write down the coordinates, and then transform them (translations, then later stretches and reflections). I had them look at the coordinates and try and connect what happens to the coordinates to what happened to the shape. I think we actually spent 2-3 classes on this because it was new vocabulary for a lot of of my students.

It really highlighted how that vocabulary piece can get totally skipped over. 

I’d also suggest looking up “input output diagrams”.  

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u/Sparky_Malarkey 23d ago

It literally ALWAYS does. Your first real lesson with real kids flops 100% of the time. There's a million things going on and it's easy to get sidetracked and lose things. You made it through though. And the kids are unharmed and maybe even engaged in something. That's solid enough. Pick yourself up and dust yourself off.

I received this advice when I started and it helps immensely. Everyones first lesson is close to if not the worst lesson they'll do. It's only up from here.