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.

 

Demonstrating the Structure of Quadratic Functions with Desmos

I am a big fan of empowering students to look for and make use of structure in Algebra 2. This is most true for me as we work with functions, parabolas, and quadratics.  I’m writing this post about what I’m finding to be an indispensable tool for helping students quickly learn about the structure of the equations of quadratic functions. This tool is easy to use. Simply project the Desmos calculator (use the links below) and activate the sliders.

One of the many great things about Desmos is some of their built in functions on the calculator. Like this one, using vertex form of a parabola:

Link 1: Vertex Form of a Quadratic Function

In this window, you can activate the sliders* individually to demonstrate to students (and share with your math team)  how a, h, and k affect the parabola. You may want to stop the slider and manually slide a to values you want to emphasize with the class (a = 2, 1, 1/2, 1/3, 0, -1/3, -1/2, -1, -2 for instance).

*To activate the sliders, click on the arrow buttons in rows 2, 3 and 4. To stop them, click again, or manually move the slider to any spot.

Next, move to standard form, which is really interesting.

Link 2: Standard Form of a Quadratic Function

I suggest you first let c slide and have students watch as the parabola moves up and down. Ask them whether the shape is changing. Some will think it is, but it’s just an optical illusion. Tell them to look again.

Then, stop c and let a slide. Kids can see how the parabola stretches, shrinks and reflects just as it did with vertex form.

Last, the fun one. Ask them to predict and then tell their partner/group what they think will happen when b slides. Will the shape change? Will it move up, down, left, right? Then, activate the slider.

This is where the math just gets cool. Ask them, as they watch the motion, “What is the path of the vertex?” (it travels along a parabolic path); “What is happening to shape of the graph?” (nothing, it stays the same); and, “What is happening to the y-intercept?’ (the parabola travels through the point (0, c) and the intercept doesn’t change).

I found this to be so helpful to me as a teacher and to students to see quickly what the structure of these equations do. To get to them and many others, just click on the bars at the top left corner of the window for the desmos calculator. There are all kinds of great functions to work with. Here’s a picture I made in paint – screen shot, save in paint, edit with brush – to help you find the drop down menu.

desmos-menu-location-for-blog

P.S. I need to create a note sheet for this where they summarize these structures and the impact of the key components. Next week. Yep, next week. 🙂

 

Tough grading moments….

One of the toughest things about grading is when the students with 79% or 89% ask/plead/argue for the B- or the A-. I do round an 89.5% or higher, to the 90%. I think that’s just doing proper rounding, as I like to teach in my classes, as opposed to truncating the grades. [Don’t know what truncating is? You can find out here] . But then, the 89.2% kid asks for the A-, too. I would be inclined if their test scores were in the A range, but they weren’t completing all the assignments, and so homework was dragging the grade down. But, if the test scores are in the B range, and homework completion is bringing the grade up to B+, I think that’s good enough.

I have several students who’ve missed a lot of school, or have ADHD and just don’t complete every assignment, or just never are there or aren’t organized enough to present the assignments for credit. If they have high test scores, I’m inclined to round their grades towards those test scores. However, high homework scores with lower test scores are not a compelling argument for me to round the grades higher, even though that’s the request I get a lot.

We just had final exams, another tough grading challenge. I think it’s normal for students to score about one grade lower on the final exam than their unit test scores. And, when that happens, I usually let them keep the grade they earned prior to the exam. An example would be a student who had a B in the course, earned a C on the final, bringing their grade to a B-. I would be inclined to let them keep the B. But, if they score low on the final (a D or an F), I do let the grade drop, but not by more that a half a grade. And, if that same student with the B earned a D on the final, they would end up with a B-. They see the B part and are still feeling content, I think. However, if a student had a B- to begin with, scored a D on the final, and ended up with a C+, they will see the C and possibly (probably) be upset about the outcome. The difference in the GPA would be the same (0.3 points) but, suddenly, the letter B to the letter C is very noticeable. That’s when I get the email with the ask/plead/argue message. Sometimes the parents get involved, too. But, I have to stick with my convictions on the grading in these situations.

My grading policies and decisions around tests versus homework and semester grade versus final exam grade are pretty generous in my opinion. Many teachers let the computer calculate the grade based on the settings for the weights they decided at the start of the semester. Many others make exceptions, too.

In addition to the above rules of thumb around my grading decisions at the end of the semester, during the semester I’ve been known to drop some low scores when the class doesn’t do well on a quiz. I think that I didn’t teach them very well when that happens, and we revisit the material.

Algebra 2 is a hard class and not everyone will get an A, even if they usually get As in other classes or in prior math classes. This is one of the tougher lessons for high school students to learn. They are hitting a level of math that really requires studying, critical thinking and perseverance for the longer, more involved problems. They aren’t all ready for that level of problem solving. Even if they are, the course is content rich, meaning there is a lot to learn and a set amount of time in which to learn it.

Students are busy with tough course loads, sports, hobbies or jobs, and social and family activities. Many students don’t have adequate time outside of school to study as much as they need to in order to get the grade they want. Others make sacrifices and get every assignment done every day. They come in and ask questions after they’ve tried to figure things out on their own. Some ask questions immediately without giving themselves time to try a solution, because they are used to the quick answer or they feel pressed to get the questions answered quickly, without a deeper understanding for when the next question comes. In learning math, you learn so much from making mistakes and trying new approaches. Especially at this level. But, I think that requires a level of calm and concentration that many teens aren’t used to. Trial and error are involved. I try to talk abut this to my students when I can.

Some people may wonder about the purpose of the final. Well, I think it’s important to review what they learned over the year. I think it’s important to have a idea of what they’ve retained and to remind students what they need to know for the next course. I think it’s good for them to have an idea of what they remember and what they may need to re-study. And, I don’t let the final exam kill their grade. I think that’s the bad part about finals, which is why I have some of the policies listed above. A final exam can bring a student’s semester grade down much more than it can raise it.

I plan to include these grading philosophies and practices, and study tips and techniques for retention and deeper understanding in my beginning of the year mini-unit next year. I introduced the idea in my blog post  Summer reading, relaxing and revamping…. and will post it when it’s done.

Comments, experiences, input welcome…