Math Class With Less Direct Instruction

In response to @lmhenry9's post...

I've realized that with my smaller class sizes this year, it seems like I am doing less activities than usual. For one reason, direct instruction is a lot easier with 10 students compared to 28. Last year, I knew 100% that lecturing would not hold the attention of my 28 students and so I desperately searched for anything that I could turn into an activity. I was always looking to free myself up to wander the room and put out fires.

This year, that thought hasn't even crossed my mind. Whatever activities I've used in the past I have used again but I can't really think of one new activity that I've created this year. Sad. :(

But I think there are small things that I do that make me feel like I'm not all direct instruction. I guess it depends on how you define direct instruction. I think of it more like a traditional college setting- a professor writes and talks a lot and students write a lot and don't talk. Some people probably define direct instruction as anytime the students are looking at the board or teacher.

If you peeked in my classroom window, it would probably look boring and just like direct instruction. I think it's more the way you arrange, present, scaffold, and question things.

If the paper my students are working on asks them to analyze graphs, write the data in a table, make comparisons, and find a relationship between two categories, is that direct instruction?

If the paper my students are working on asks them to look at two columns of expressions and asks them to explain why the column of expressions on the right can't go in the left column, is that direct instruction?

If the paper my students are working on asks them to write proofs or cut and paste statements and reasons into coherent proofs, is that direct instruction?

If the paper my students are working on asks them to work out various pattern and look for a common end result, is that direct instruction?

Just because I'm at the board and my students are working at their seats, writing on paper, is that direct instruction?

If I am questioning, asking students to try hard problems on their own, asking students what is different about this problem than the last, asking students how they think we should start, asking students what could we do next, asking students to explain another method, asking students to work problems, compare, and discuss with their group; if I am giving students individual think time, asking more questions than I answer, redirecting questions from me to the whole class, and students are writing and talking more than I am, is that direct instruction?

To me, direct instruction is when I am directly instructing students every step of the way; when I say this is the only way to do this, you must copy exactly what I've written; when there is more writing than thinking and more listening than talking; when students have no input; when there is no puzzle, no pattern finding, no analyzing, no comparing, no questions, no discussion.

And to that effect, math class with less direct instruction does not ONLY mean activities, projects, students out of their seats or on the computer, or peeking in my classroom and seeing chaos.

It means my students ask each other for the correct answer before they ask me. It means that they find different patterns and question whose is correct. It means that they can write without listening to me talk. It means they have to look at things, they have to analyze, compare, observe, sort, organize, write definitions, create examples, explain counterexamples. They have to THINK.

I feel that I can accomplish the majority of these things with the way I design and scaffold my guided notes. I have a lot of good activities. I'm not good at projects. I haven't flipped my classroom. I haven't found anything computer based that I like. But I've found a way to present things, to question my students, to scaffold my concepts, that allows my students to do the skills I think real mathematicians need.

I don't feel like a lecturer. I don't feel like a college professor. I don't feel like a public speaker.

I feel like a highlighter. A pointer outer. An offerer. An observer. A questioner.

And I hope my students feel the same.

Geometry Constructions

Normally I skip right over constructions in geometry because I've just never found them to be that important.

I hope that I am teaching more authentically, in a way that involves doing math like (what I think) a mathematician does. I also hope that I am teaching more with kids in mind, in a way that realizes different students think differently and can be successful at different parts of math.

So, I'm doing them.

I found step-by-step demos of tons of constructions over at Math Open Reference. They have printable step-by-step instructions that go along with them but I took a different approach.

As a class, we watched the demo and did one step at a time. Then we tried to do another drawing from memory. We stopped and wrote out own directions (hey hey another writing across the curriculum moment!) and then completed two more drawings.

Here's what the demo for perpendicular bisector looks like.

Here's what my worksheet looked like (also included angle bisector):



I used this method for several constructions and I was pretty happy with the results.

I also like the alternative circle method for drawing an equilateral triangle. Definitely doable without a demo. Especially since I didn't find one.



Demo: Incircle/Circumcircle
(Worksheet)

Demo: Centroid/Median and Altitude/Orthocenter
(Worksheet)

Semester Reflection

I'm always looking for a way to incorporate writing into my math lessons. Most of the time it is just a sentence or two here or there as an explanation or a definition.

A semester reflection is one way I thought of to focus on writing in a way that naturally fit into my classroom. I think it was interesting for them because it was opinion based but also interesting for me because I received feedback on my students, my instruction, and my classroom.



At the end of the first semester we give our end of course exam for the second time as a way to show growth from August to December. I did this early enough so that I could give students class time in the computer lab since once of my requirements was to type their paper.

I broke it down very specifically for each paragraph to avoid students saying they didn't know what to write. I thought it went over very well. I didn't give a page requirement since I gave a paragraph requirement and there really was very little complaining.

For Algebra II, I substituted graphing calculator for compass and ruler.

I graded these over Christmas break which was actually a fun way to get back into my teaching groove. I was so amused that I made a 'reflection reflection' based on "trends" I noticed in their papers.

I laughed. They laughed.



P.S. I despise Times New Roman with all of my heart. Almost as much as Comic Sans.

Completing the Square

This was my first time teaching completing the square and I was nervous about it.

Luckily for me, I bookmarked this post by Mimi.

I used the area model to teach polynomial multiplication in Algebra I so I really liked this connection into quadratics. It worked out soooo well! The students even said it was easy and this included ones with fractions too. There is something about having boxes to fill in that just makes things seem simple. Or at the least, doable.



I took Mimi's worksheet and made it my own, using her methods of scaffolding. We first practiced rewriting equations in vertex form and then solving all the way.

Teacher Evaluation Binder {A Teacher Evaluation Series}

I can't believe I haven't posted anything since August!

Short summary: this is my best year yet! My biggest class size is 13, I have less preps, I've been decorating the crap out of my brand new house, and I just generally feel like I actually know what I'm doing and I'm doing a pretty good job!

I feel guilty for not posting but I also feel like a lot of my posts were complaints anyway....so it's actually GOOD that I haven't posted.

But to make up for it, I want to write a few posts and share some resources!

For those of you being evaluated under the Charlotte Danielson model, this is a set of binder dividers labeled with each domain and component. It gives a checklist of possible documents to include such as: lesson plans, pacing guides, parent contact logs, end of course exams, final exams, etc.

It also includes a customizable binder cover and spine cover for a three ring binder.

Even if you're not being evaluated under Charlotte Danielson, it is still a great resource for evaluation. It keeps you neat and organized and looks very impressive to administrators.

We had to create this for one of our classes in our master's cohort and it spread to other teacher's in our school.