One of my goals is to be an agile teacher. I also want that for my students. Often students arrive in my class preferring to work with one method that works for every problem of a certain type. I want them to flexible and use the most efficient solution depending on the particular problem. Case in point – quadratic equations. Students who have seen this material before want to use only the quadratic formula, as they know it can be…
One of the biggest complaints I hear about MyMathLab homework is that students rely too heavily on the learning aids. (I know the name is now MyLab Math – but it sounds wrong to me!) In particular, many students use the “View An Example” in an attempt to mimic their way to a correct answer by replacing the “5” in the example for a “7” in the problem. I think we can all agree that this is not an effective way to learn,…
In my Intermediate Algebra course, we finished our work with rational equations and their applications this Wednesday. On Monday I plan to get through solving quadratic equations by factoring, by extracting square roots, by completing the square, and by the quadratic formula. I thought I’d walk you through my thoughts for setting up the Flip assignment for that day. Flip Topic 1: Factoring Trinomials and Differences of Squares These are review topics from Elementary Algebra, and students have been factoring…
In my experience, the printed word is not the most efficient way to learn mathematics. When a student looks through an example problem that has already been worked out, they are robbed of the time to stop, think, evaluate, reflect, or create because they can already see the next line of the solution. When the math is presented in real time it is more effective, and that’s why video of some type is so effective. My primary recording tool is…
Today I led a highly structured class that made effective use of technology, and finally got some skeptical students on board. Several students told me when they got to class that they were having a hard time with rationalizing denominators, and fortunately I had my lesson set up to begin there. We started by rationalizing a one-term denominator and then a two-term denominator by hand. I explained how and why we began rationalizing denominators in the first place, and although…
Lately I have been thinking about how great a job we have done in modernizing our intro stats courses, and how we have not done that in our algebra courses. In statistics we have embraced technological changes, such as transitioning from the binomial formula to binomial tables to using technology like StatCrunch/TI to compute probabilities. In algebra, that sort of transition is far from wide spread. When students have more ownership and control, they are more motivated to learn. In…
It’s Flipped Friday, where I update how my flipped classes are going. If you want to see how my Intro Stats course is going, check out the day-by-day posts on my StatBlog. This week I had planned to cover two sections in my intermediate algebra class – multiplication and division of radical expressions, and solving radical equations. I decided to devote half of the two-hour block to the first section, and the rest of the class to the second section….
The Bootstrap Method The bootstrap method is a very useful tool to have an introductory statistics class. The bootstrap method begins with a sample of size n. Then a large number (I use 10,000 in my classes) of samples of size n are drawn with replacement from that sample. A sample statistic is computed for each sample. A typical use of bootstrapping involves the mean, but this procedure can be applied to the median, quartiles, variance, … Percentiles can be…
Last week I came across a Wired article: Wolfram|Alpha (& AI) Is Making It Easier To Cheat, and reading the article brought so many thoughts to mind about teaching mathematics in today’s world. Here goes … 1) We need to make sure that students understand that HW is a learning tool, not just something that earns points. — George Woodbury (@georgewoodbury) August 25, 2017 I feel that we often assume that students know why they do homework and that they…
The cycle of learning that I use with my students is one of Discover – Engage – Reflect, and today I want to focus on Reflect. It is hard to imagine that true learning can happen without some sort of reflection. What have we done? How is it similar to what we have done before? How is it different? What are my key takeaways? What concepts are not as clear as they need to be? On Monday I revisited using…