I first formalize the hypothesis testing language and procedure with a test for the linear correlation coefficient. Students were already doing this “test” anyway by comparing their correlation coefficient to a table of critical values to determine if a linear relation existed. I use StatCrunch to generate a P-value, so the test is more consistent with the tests that will follow.

Today, in week 7 of the course, we covered the one proportion test. We use the binomial distribution to compute P-values. (Later on, when I cover the one proportion Z-test, we will refer back to this binomial test when conditions for the Z-test are not satisfied.) Students are definitely developing an understanding of the null and alternative hypotheses, what the level of significance represents, what a P-value is, how to make a decision about the null hypothesis, and how to make a conclusion about the alternative hypothesis.

This test is accessible to students, and a great application of binomial probabilities. Introducing it this early in the course keeps students focused on the big picture in this course, which most assuredly is not to compute means or draw pie charts. It is a great midpoint on our journey from simulation (coin-flipping) to the Z-test. After we make it to the Z-test we will come back and reexamine these two techniques.

If you’d like copies of the documents I used, or you want to see how the class progressed, check out this post on my StatBlog.

Questions/comments are always welcome – George

]]>- My students are more active and engaged in class.
- I am able to cover much more material than I ever covered before – including simulations, bootstrapping, and non parametric tests.
- My students level of understanding when it comes to inferential statistics and the “big picture” is higher than ever.

I am currently blogging each day, documenting my progress this semester.

You can check out my progress on this web site: http://georgewoodbury.com/statblog/

There are three portions to consider when flipping your class: pre-class, in-class, and post-class. Today I will write about what my students do before class. (I’ll come back to the other two as the semester progresses.)

In my class we are using the Interactive Statistics online text that I wrote with Mike Sullivan. My students complete an Interactive Reading Assignment (IRA) before they come to class. In the IRAs students read a little, watch a little, and do a little. They read standard text, which is supplemented with concept videos, example videos (including StatCrunch videos), applets, and activities. Along the way, students answer conceptual questions and solve problems and these are recorded into their MyLab gradebook. If you worry about students actually doing the work before class, having some sort of assignment that is submitted before class definitely increases completion.

Students complete an IRA before class on days that we cover a section, but I do not have pre-class assignments for days that we work on projects.

If you have any questions about these interactive reading assignments, please leave a comment or reach out to me on Twitter. I love to share!

]]>First, students need to dispel that myth that there is only one way to solve a problem. This week I was introducing the general addition formula for finding the probability of *A* or *B* occurring. I asked students for the probability of drawing a king from a deck of cards, and they got 4/52 pretty quickly. Then I asked for the probability of drawing a heart. Again, a quick reply of 13/52 followed. When I asked for the probability of drawing a king or a heart, the initial response was 17/52, obtained by totaling the 4 kings and the 13 hearts. A student pointed out that simply counting those cards produced only 16 that were kings or hearts.

I asked them to come up with a strategy for solving these problems. Some suggested taking one group, like hearts (13), and adding the extra kings (3) to the total. Others suggested adding the kings (4) and hearts (13), then subtracting away their overlap (1). We all agreed that there was more than one way to get there, and that was OK.

Fast forward to today. I gave my students the probabilities that a student was taking math, taking English, and taking math and English. They applied the general addition rule with little difficulty. Then I proposed using a Venn diagram, and some students understood the addition rule much better after that. I then added that they could begin with the probability that a student is taking math, then add on the probability that a student is taking English but not math.

I made a big deal about how there is usually more than one way to solve problems in math, and that the best approach is to try to find your own way. I shared some of Jo Boaler’s research and they seemed more at ease with the idea of trying to find their own way to solve problems. Hopefully they continue to be creative.

]]>When I first started my homework assignments had somewhere between 15 and 20 questions. My chapter quizzes, which became semi-chapter quizzes, also had between 15 and 20 questions.

As I have aged, I apparently have become a minimalist! I have drastically cut down the length of my assignments, and I have done so with my students’ success in mind. I start each section with a media assignment that is a mix of concept and example videos accompanied by 5 or 6 problems. (I blogged about this type of assignment here.) When students are working on a smaller number of problems they are more likely to take them seriously and less likely to just use the learning aids to slosh their way though them all. This assignment should be enough to get students prepared for my section quiz.

Students next take a 5-problem quiz. (Read more about quizzes here.) I select 5 problems that I think are the most important for that section. With only 5 questions, students are more likely to try the quiz a second (or third) time, which is a plus. The quiz loads a personalized homework assignment that focuses on the areas that each student needs to work on. (Read more about personalized homework here.) Although the personalized homework could be at most 15 problems long, it is often shorter than that. Also, because students know they need to improve on these topics, it has less of a drill-and-kill feel to it.

Since I have adopted this approach, I rarely hear complaints about how long the assignments are. Instead, I hear students tell me how the assignments are helping them to learn and understand. Isn’t that refreshing!

I encourage you to look at your assignments and see if you can streamline them.

]]>Last Spring I flipped my elementary algebra class. For each section I used a cycle of three assignments in MyMathLab to make it all work.

**FLIP Assignment**

This was a media assignment that incorporated concept videos, example videos, and homework exercises.

Students completed these assignments before class.**Reflect Quiz**

This was a 5-question quiz, focused on the problem types I felt were the most important in that section.

The first attempt loaded a personalized homework, and students could take the quiz as many times as they would like.

Only the highest score counted.

Students completed the quiz after the material was covered is class.**Personalized Homework**

This assignment began as a 15-question homework assignment, with 3 problems for each objective covered in the Reflect Quiz.

For each objective mastered in the first attempt of the Reflect Quiz, students received instant credit for the three related problems in the personalized homework.

Students then worked over only the problems they struggled with on the quiz.

This assignment was also done after the material was covered in class.

This semester I am teaching Elementary Algebra online, and I have recycled these assignments for my online class. The FLIP assignment has many of the features of a traditional classroom – the concept videos are similar to what would be delivered in a lecture, the example videos are similar to examples an instructor would do in class, and the homework exercises are similar to problems an instructor would have students try on their own. The videos are quite short, which I know learners prefer. Students can work through one objective at a time, or they can finish an entire section in one sitting.

My students are telling me that they love the format, and their written homework (submitted to the document sharing folder or by photo) looks like they are doing well. I’m looking forward to the midterm to see how they do compared to previous online sections I have taught.

I’d be happy to share my Course ID if you’d like to take a look at the assignments. Reach out to me by leaving a comment, through Twitter, or through the contact page on my website – georgewoodbury.com.

]]>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 applied to any quadratic equation. However, it is not always the most efficient approach.

- I encourage my students to begin with the 10-second rule: If they can factor in 10 seconds or less, they should factor.
- Some equations, such as (3x-7)^2 + 21 = -11, are easier to solve by extracting square roots than they are by squaring 3x-7/rewriting the equation in standard form/using the quadratic formula.
- For certain equations (leading coefficient of 1, b is even) completing the square can be more efficient than using the quadratic formula. It will always be easier to simplify the solutions.

After finishing with the quadratic formula this week, my class will take a quiz where they have to solve four equations using the four techniques (factoring, extracting square roots, completing the square, and quadratic formula). But here’s the catch – they can only use each technique once. They will have to think about the most efficient strategy for each equation. Hopefully it will help them to develop some intuition about when to use techniques other than the quadratic formula.

The same strategy can be used for graphing lines (intercepts vs slope), solving systems of equations (substitution vs addition), and many more problem types. I’d encourage you to try an assessment like this, and I’d love to hear back from you about how it goes.

*TeachBetterTuesday (TBT) is a weekly blog series I am writing this semester. If you have a topic you want me to cover or a strategy you want to share, reach out to me on Twitter or leave a comment below. – George*

I think we can all agree that this is not an effective way to learn, but it might fit with the student’s perspective of homework as something to do in order to get points rather than something to do in order to learn. As instructors we need to do more to change that mindset, but that will have to wait for a future post.

Back to that learning aid – if you don’t want your students to use “View An Example” then you should consider disabling it. (My friend Michael Sullivan has disabled that learning aid by default in one of his newer books.) It’s not that hard to do. If you follow the link to “Manage Course” in the left side menu, you can then click on “Edit MML Settings”. Click on Edit next to “Learning Aids and Test Options”. Now you can disable any learning aid you desire. In the picture you can see that I have disabled View an Example.

You can also do this for a particular assignment, or even for a particular problem on an assignment. Those can both be done in the assignment manager. If you’d like to see how that is done, just leave a comment and I can put together a short video on that.

If you don’t like a particular learning aid, or how your students are using it, then please consider disabling that aid.

George

]]>These are review topics from Elementary Algebra, and students have been factoring trinomials while solving radical equations. I feel comfortable that students can handle this before class. I included two short concept videos on (1) factoring trinomials and (2) factoring a difference of squares. I included two example videos as well. After watching those videos students will work through a few exercises that get submitted through MyLab Math.

Again, this is a review topic from Elementary Algebra and my students have been solving quadratic equations by factoring while solving radical equations. There are a few short concept/example videos to watch and a few exercises to submit.

By the way, even though this is review, my main message in the next class meeting will be that solving by factoring will be option 1 for us when solving quadratic equations.

This is a brand new topic, and I thought for a while about whether students can introduce themselves to the topic. I finally decided that it is similar enough to simplifying square roots and students should be able to handle it with proper guidance. There are a few short concept and example videos, and a few exercises for students to work through and submit. I imagine this topic might take some discussing when we meet in class.

This topic is also new, but is made up of several ideas that have already been addressed while working with radicals (simplifying radicals, solving radical equations, …). Again, there are a few short videos followed by a few exercises to turn in.

On the Flip assignment, the combined running time of the videos is just under 14 minutes, and there are 13 exercises to submit.

I’ll begin by having students solve a few quadratic equations by factoring, perhaps at the board.

We’ll then have a brief discussion of imaginary numbers, allowing me to clear up any misconceptions and get students to offer their advice to their classmates. Students will then work through a few of these problems.

Extracting square roots will be handled the same way – a brief discussion followed by a handful of problems to work on in groups. There will be more problems to solve for this type than the previous types.

I’m shooting for approximately 30 minutes total devoted to the above. I do teach a 2-hour block class.

Since students will then have solving by extracting square roots under control, solving by completing the square will focus on getting the equation into the correct form by completing the square. I plan to debrief this topic by discussing when this technique should be used.

Finally, we will finish up with a mini-lecture on the quadratic formula. After 2-3 examples together, students will work in groups to solve a few equations using this technique.

I plan to finish with a short group quiz where students will use the various techniques to solve quadratic equations. I will limit them to only using each technique one time, forcing them to think about when it is most efficient to use each technique.

]]>My primary recording tool is Camtasia Studio in conjunction with Power Point. Camtasia makes an add-in for Power Point that allows you to record directly from a slide show. I type the problems into a Power Point presentation, then solve the problems by writing on a Wacom tablet connected to my laptop PC. One of the things I love about Camtasia is the ability to edit the video, add callouts/text, and add in audio. It also produces the videos in a variety of formats, allowing you to control the quality of the video.

In my opinion, it is crucial to invest in a high quality microphone. This is the one I use, Amazon link. It costs about $150, but it is a great microphone and students are distracted by poor audio quality and respond poorly to poor microphones. A pop filter really helps with sound quality.

I upload most of the videos to my YouTube channel. It’s a convenient place to house videos that can be referred to semester after semester by my students. Some instructors make their videos private, but I like to share my videos with everyone – you never know who you could be helping.

**OTHER OPTIONS**: I have used a Livescribe smart pen, Snag-It, Jing, a few apps for my iPad, and other resources. There are so many great options available today to incorporate screencasts/videos into your bag of tricks. You can start small by recording videos for certain problems that students ask for help with, then work your way up to making your own content videos to aid all of your students.

Have a tool that you love? Perhaps a question? Please leave a comment below.

Thanks – George

]]>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 this can be a useful tool in trigonometry (trig ratios) and calculus (limits) it would not be a major topic of focus for us. I then showed them how to rationalize a denominator using Wolfram|Alpha by simply typing “rationalize 12/sqrt(75)”. The focus shifted to determining which of the results seemed best suited as an answer for us.

We moved on to graphing square root functions by hand using transformations. After 4 by-hand examples, we opened up Desmos and learned to speed the process up. They felt graphing by hand wasn’t too difficult, but did appreciate the speed and precision of Desmos.

We then pivoted to solving radical equations in Desmos by graphing two functions and looking for the point(s) of intersection. We first solved two equations by hand before turning to Desmos, and it was fun watching them try to figure out what happened with the extraneous solution. They then moved on to solve 7 more difficult equations, including one where a square root was equal to an absolute value. (That would have been challenging to solve by hand – definitely more of a college algebra level problem!)

We finished with some applications of pendulums and skid mark analysis, and we used Desmos to solve the equations by graphing after we solved them by hand.

I think students left feeling that these two sites are quite powerful and can really help them to focus on conceptual understanding. A good day!

Here is a PDF copy of the worksheet I used.

George

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