## Posts filed under ‘General Teaching’

### Start of the Semester

This semester I have been assigning reading homework. Students have to answer vocabulary questions and outline procedures that will be covered in the next class period. Essentially, I am having them read ahead. I also include a handful of warm-up problems that focus on the prerequisites for that section. (I get mine from a publisher workbook that goes with the textbook. On MyMathLab it is available under Instructor Resources. I am sure other textbooks/publishers provide similar material.)

I give my students the first 5 minutes of class to discuss their answers with their groups. I then take attendance, one group at a time, and ask for one of the answers. It is working out to be a great way to get students to warm up for class, and my classes seem to be more participatory this semester.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

### Geogebra – Graphing Absolute Value Functions

I added two new pages for graphing absolute value functions, complete with sliders for h & k.

You can find them here: http://georgewoodbury.com/geogebra.html

– George

### Doing Homework

Sorry for the lack of blogging – this has been a busy semester. One project I have been working on is incorporating elements of game design into the grading policy for my intermediate algebra class. Students earn points on each exam based upon their exam score and their homework/quiz status.

Students who have scores of at least 90% on each homework assignment and at least 70% on each quiz are said to have satisfactory scores. (I probably need a better name for that than “satisfactory”.) Students in this category have done pretty well when it comes to passing the exams.

• Test 1: 33 out of 38 (87%)
• Test 2: 24 out of 28 (86%)
• Test 3: 19 out of 25 (76%)

Students who do not have satisfactory scores have not performed as well on the exams.

• Test 1: 7 out of 9 (78%)
• Test 2: 13 out of 19 (68%)
• Test 3: 11 out of 21 (52%)

So, students doing the homework are doing better on exams. Now I understand that I cannot go on to claim that doing the homework leads to better performance, but there is an association here. One thing I am concerned about is that the number of students earning satisfactory scores is dropping as the semester progresses. However, the fourth exam is today and it appears that there will be 32 students with satisfactory scores and 14 without – a good sign.

In upcoming blogs I will try to explain the game design dynamics, and include student thoughts on the policies of the class.

– George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

### What I Learned About Teaching Math – At Starbucks

Last night I dropped my daughter off at her dance class, and as is sometimes the case I went to Starbucks to work on the new Statistics project I am involved with. I sat down next to a 9th or 10th grade kid and his college aged tutor. They were working on Algebra I.

Over the 5 minutes that they stayed, I found myself getting more and more frustrated. Here are words that came directly from the tutor’s mouth, followed by my thoughts.

• “Just do it like the one I did a minute ago.”
Having students mimic your work will definitely not lead to understanding. I need to keep this in mind every day during class. “I’m the expert. Just do what I do.” is not an effective way to get students to understand. Students can watch me work one hundred problems in a row and not be able to work problem 101 without me helping them to find some level of understanding first. I’ve watched Tim Wakefield throw thousands of knuckle balls, but that doesn’t mean that I can do that too.
• What’s wrong with you? Don’t you get it?
I’m pretty sure that making the student feel inferior doesn’t help at all. If you want to help a student to understand mathematics, you need that student to be motivated and inspired. You cannot motivate and inspire a student by making the student feel bad. I think the tutor might want to pick up a copy of Daniel Pink’s Drive.
• You know those 20 problems you did on that worksheet earlier? Just do it like those.
This just screams to how ineffective “drill & kill” can be when there is no understanding tied to it. Mindlessly going through those 20 problems did not increase the student’s level one bit. I need to remember that fewer, well-chosen problems can definitely make for a better assignment that 1-157 odd. When students view homework assignments as a tedious, meaningless task that must be accomplished, then I am afraid we have lost that student.
• Any number times 1 is … one. Followed shortly thereafter by  Any number divided by 1 is … one.
Yes, both statements were wrong. I know the tutor probably meant to finish both sentences with “the number itself”, but he didn’t. We have to be careful with what we say, because a confused student will just get more confused when we misspeak.

The night didn’t end as badly as it started. Two older women came in and sat next to me – a 40-ish woman with her 60-ish French tutor The tutor was warm and positive. When her student made a mistake, she was supportive and tried to help her student understand why what she said was incorrect. I was fascinated as I listened to them. That’s the type of teacher we all need to be. One more point – the student was trying to learn French so she could travel to Paris. When students understand why the material they are trying to learn is important, they will be more motivated to learn.

Have any lessons that math teachers should learn? I’d love to hear them.

– George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

### Solve This #1 – Wrap Up

This was pretty interesting. I posted a blog asking for solutions to a problem, and got a lot of feedback.

Colleen Young (@ColleenYoung on Twitter) in the comments & Colin Graham (@ColinTGraham on Twitter) on Twitter used a graphical approach. They graphed $y=|x^2-9|$ and noted where the function was between 2 & 9.

David Radcliffe (@daveinstpaul on Twitter) and Liz Durkin (@LizDK on Twitter) both used an algebraic approach that was right on the money.

Shawn Urban (@stefras on Twitter) used a unique algebraic approach as shown in the blog post Algebra 2: Solving Absolute Value Equations by Kate Nowak (@k8nowak on Twitter). I hadn’t really seen that before, and liked it a great deal. I may work it in next semester when solving absolute value equations/inequalities.

My Solution

What jumped out to me was a graphical approach as well. I thought about graphing the parabola $y=x^2-9$, and then determining where the function was between 2 & 9 and between -9 & -2.

All that remains at that point is finding the endpoints of the interval algebraically.

• $x^2-9=9$
• $x^2-9=2$
• $x^2-9=-2$
• $x^2-9=-9$

Of course, I imagine many students might initially miss the problem at x = 0.

Second Solution

Another approach that came to me was to initially solve the inequality $|x^2-9|<9$, and then taking out the solutions to $|x^2-9|<2$. These two inequalities are quite easy to solve algebraically as they are intersections as opposed to unions.

In other words, I’d start with $(-\sqrt {18},0) U (0, \sqrt{18})$ and then delete the intervals $(-\sqrt{11},-\sqrt{7})$ and $(\sqrt{7},\sqrt{11})$.

Summary

I think this can be a fun feature of the blog. I will try to work it in on a regular basis. If you have any ideas for problems to include, let me know. I also welcome comments on my two approaches to this problem.

– George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

### Using Tokens in Math Class

As I go through the process of attempting to gamify my class, I came up with an idea that I am pretty happy with. After the first test, I announced that students who earned all 3 points on the first test have earned a “magic token”. (To see how grading works in this class, see my previous blog entry here: https://georgewoodbury.wordpress.com/2011/08/16/tests-in-my-mastery-based-class/ .)

What is a token worth?

A student can cash in his or her token for a 1-day extension on a single homework assignment or quiz.

What if I don’t use the token this test?

If the student does not use the token, they can be saved up for a bigger reward. I didn’t mention what the reward would be to keep their interest and wonder, but I’m thinking it will be something like skipping a problem.

Impact on Students

I know that this has motivated many of the students who scored below 3 points on the first test. The students who already have tokens are looking forward to a chance to use them for something bigger and better.

Currently tokens are a digital currency, but I am planning on heading down to the local party store and getting real tokens to hand out. Should be fun!

– George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.

### Intermediate Algebra New Approach – Test 1

The results from the first test are in, and things seem to be going pretty well.

Of the 46 students (I also have one out with strep throat), 37 of them had satisfactory homework and quiz scores. (Satisfactory scores are 90% or above for each MyMathLab homework assignment and at least 70% on each MyMathLab quiz.)

Of those 37 students, 25 earned 3 points on the exam (they scored 80% or higher on the exam), 8 earned 2 points on the exam (they scored between 70% & 79%), and 4 failed the exam.

Those 4 students who failed the exam will be allowed to retake the test, provided they complete 2 assignments that I give. The first assignment is to correct their exam – reworking any problem they lost points on and explaining their errors in their own words. The second assignment is a review assignment.

Of the 9 students with unsatisfactory homework or quiz scores, 7 passed the test and earned 1 point. 5 of those students scored above 80% (and would have had 3 points if they had satisfactory homework and quiz scores), and the other scores in the 70s (and would have earned 2 points). Two of the 9 students did not pass the test and are not eligible to retake the test.

Here’s what I am hoping for:

• The students who had unsatisfactory homework and quiz scores will come through and do the work for the second exam.
• The students who failed the first test after performing well on the homework and quizzes will improve their performance on the second test.
• The students who earned 2 or 3 points on the first test will continue their hard work and do just as well on the second test, which covers more difficult material.

– George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.