Tag Archives: highschool math

My Classroom Culture Is Shifting

Well, it looks like the past six weeks of having students sit in groups and emphasizing that they work together is possibly paying off. Today, instead of hearing, “I have a question…” I heard “We have a question…”

That was beautiful to me. I had just rearranged the seating chart. At our school, we have moved into our second of three grading periods for the semester. These kids knew to work together with their new partners, and they were doing it. They knew I was pretty much only answering questions no one in the group could answer. They are learning to check in with the other students in the group before asking me for individual help.

I highly recommend this type of group seating and emphasis on student-to-student communication. It’s been so helpful to have students talking to each other about math. This should happen during warm-ups, work times, activities, and class discussions. To get them to start talking to each other, I sometimes ask why something works a certain way and ask them to discuss it with each other. Then, I might walk from group to group to check in with the group. Then I might summarize for the class what I learned from the groups.

Full disclosure: I used to be afraid to have them “Discuss at your tables…” because I was afraid they would talk about other things. And, that was often true because I was letting them sit with their friends. Better to mix them up. I first made a seating chart that was alphabetical. That was helpful to get to know their names and faces and to check off homework and take attendance quickly. Now that I know them better, I mix up the seating thinking about male/female, test scores, personalities, etc. I plan to change the seating every grading period. We have six throughout the year.

Groups are working better than two partners. I think it’s because students have more people to talk to who might know the answer. It’s important for me as the teacher to circulate to each group several times during the class period. I ask if the table has any questions. If there are questions, I ask if anyone at the table can answer. Then, if so, I’ll listen to that discussion and help if needed. Or, I’ll walk to the next group and repeat. I try to only answer what students can’t answer.

Students learn that I’m available and want to help, but can’t take the time to answer every single question from every single student. It’s like an economic situation where the teacher’s time is the scarce resource. Students are learning to make their questions be worthwhile to their group.

 

Attitude Matters, Everyday…

Attitude – sometimes mine’s not as good as I’d like it to be. What’s my attitude towards my students, towards teaching math, towards my colleagues, my administration, etc? My attitude may change throughout my day, week, year, and over the life of my teaching career. Or, maybe I just lose touch with why I got into teaching and why I decided to teach math, thanks to all the hurdles that seem to toss themselves in front of you.

I actually really like my students and I think my job, teaching math, is really important. But, things get in the way sometimes and my attitude can suffer.

Luckily, attitude isn’t a fixed frame of mind. It’s a changing and evolving beast and while it can get bent out of shape by other things, such as fatigue, illness, tough teaching assignments, difficult colleagues, etc. it can also be straightened back out. We really have control over our attitude. I’ve decided to focus on it for the rest of the month, and see what happens. For a better breakdown of the impact of life’s events on our attitudes, check out this article by Micheal Graham Richard, Growth vs. Fixed Mindset. It asks which one are you, but my theory is that will very likely evolve and shift.

Staying in touch with your good attitude towards your students and teaching is probably the most important thing to do everyday. In fact, I’ll argue the most important thing to prepare each day, before lessons and tests, homework, etc., is our attitude about our students. It will define our approach to problems that arise during the day. It will allow for open mindedness and acceptance when our lesson doesn’t go as planned (especially when it is way below expectations).

My plan is to think of my students as the multi-faceted creatures that they are. They have interests and math may or may not be one of them. My goal is to try to inspire students to enjoy math, feel challenged, but not overwhelmed. Sometimes, this attitude really drives the activities and sometimes I lose touch and get caught up in the ‘listen, take notes, here’s your 20-25 problem homework assignment.’ this is usually when I get concerned about how much I’m supposed to teach them in a year and how little time I feel that I have to do it. I also realize that there’s nothing wrong with notes, lecture and lots of problems. However, that can be a drag for a lot of kids, so I don’t do it everyday, and when I do I try to give lots of class time to work the problems together. Even better, I love it when I can engage them in open questions. I think that’s one of the best times I have with them.

For the rest of March, I’m challenging myself to adjust and refocus my attitude each day, before the kids arrive, and to have some good open questions ready. My hope is, by giving attention to my attitude and this one teaching tool for the next few weeks, these two things will become second nature. I’m hoping my attitude will not only be positive, but will evolve and become better as I open up to outcomes with my students. And, as I open up my questioning. I’m hoping to open my mind enough that I transform my classroom and kids experience for the better.

I think our attitudes are really important and I know I don’t give mine enough attention. I want that to change. I think attitude may be like a muscle and for it to be strong, it needs attention and proper feeding. Otherwise, it feels like I’m sometimes being swayed by the event in front of me, or the person in front of me. I want my attitude to be really strong and drive my response to that event, or that person. Teaching math isn’t easy. So, I need to tend to my thoughts, my views, my attitude towards my students, towards teaching, towards my school, my colleagues, etc.

 

 

It all starts to gel…

I’ve been reading books, articles and blogs. I go to training meetings and conferences and see presentations from experts with great ides. I am always inspired to try new things. So, I do. But, they don’t stick. Finally, I’ve found the right combo, the right approach, the right attitude.

I am exploding with ideas. But, I’ve finally found a formula – that I don’t intent to stick to all of the time, because that will cause problems too, in terms of engagement.

I am starting the day with an open question. To get kids to enter where they are. For example, yesterday’s question was “How many solutions are there to the equation  x+1 = x^2-1  ?” They worked in pairs and also had to answer, “How do you know?”

These questions allowed for multiple entry points, and was an effective and engaging differentiation strategy. Some students used guess and check and found one or two solutions. Some students combined like terms across the equation and either factored or analyzed the discriminant, much to my delight. No one graphed. I knew what everyone had done because I had time to circulate, discuss methods and ask questions that moved kids into engaging more deeply with the problem.

For the students who analyzed the discriminant, I asked them if they could then find the solutions. This was puzzling for them at first. For those using guess and check, I asked, “how do you know when you have them all?” They went back to the drawing board and asked other students what they did. It was great to watch.

Using a “You, We, I” strategy, thanks to CMC-North conference and Steve Leinwald’s presentation, I then brought the class together and tell them I saw three great strategies used. We discussed the merits of each. Then decided which might be best for that particular problem. This was the ‘We’ part. We started with the ‘You’ part, where they generated their own ideas and tried to articulate their reasoning.

Then came the ‘I’ part. I asked them what they would do if the functions were higher degree. I asked them which of the strategies would still work. I also asked them what they would do if the expressions weren’t factorable. I asked them if they’d like to learn a method that would work every time, for any two expressions, from an isolated constant term to a higher degree polynomial or other more complicated function. Of course, they were hooked and interested.

Thank you, Desmos! I graphed and displayed the functions on the overhead. They could easily see the intersection of the linear expression, x+1, and the quadratic expression, x^2-1.

Here’s the handout to students, Desmos Intro and Parabolas.

From there we went into the lesson. More You, We, I. Then into a short homework assignment. This is the 2-4-2 idea (not perfectly executed by me) that I learned about from the same Steve Leinwald presentation. I also asked for feedback. Today, when the kids came in and had to  turn in the sheet, one student let me know she really appreciated it. I can wait to read their feedback. I would have done it then and there, but, y’know, lots going on in a room of 28 Algebra 2 students.

The lesson itself was really a summary of the structure of both the standard and vertex forms of the equation of a parabola. It was meant to introduce them to Desmos and better demonstrated what a, b, c, h and k, do in the equations. I wish I had known about teacher.desmos.com and the calculator with so many pre-existing awesome tools. If you are not aware of Desmos and it’s many wonderful capabilities, you have got to yourself educated on Desmos. It’s easy to learn. The team there seems to be a great group of people, thinking up wonderful activities. Next week, the kids will use Marbleslides for rational functions to review graphs of rationals. I can’t wait.