## Posts filed under ‘technology’

### ICTCM & What’s On The Way

I just got back from the 24th ICTCM, and, as usual, I am full of great ideas that I picked up. There were two trends that I saw – Pencasts and Simulations.

There were several talks on using smart pens. I recently received one as a gift, and I think that it is becoming a very important tool for me as an educator. They can be used to communicate to students who email questions, post supplementary materials online, or even as a note taking tool. I will share my approach in future blogs.

There were also several talks that incorporated the use of simulations in introductory statistics. This is a BIG idea that will one day revolutionize the way we teach inferential statistics. Resampling and bootstrapping are effective ways to show our visual students what is really going on. I usually use StatCrunch for this purpose.

Matt Davis (Chabot College) did a great job, and he has some fantastic simulations. You can find him through a quick Google search for “Matt Davis Chabot”, and he seems pretty willing to share. (Tell him I sent you.)

I gave a talk on my new mastery based learning approach using MyMathLab, which incorporates elements of game design. I think that my students have changed their focus from doing homework to earn points to doing homework to learn and understand mathematics. I will be putting together a blog series on this new approach that will share last semester’s results, explain exactly how I set my class up, and share the elements of game design that I have incorporated, as well as some commentary from my son.

One other blog series that I will put together is one on my MyMathLab top 10-ish features. Now that most classes have gone to the new design of MyMathLab, it’s time to go over these features.

I’m looking forward to getting this blog rolling again. I hope you have all been well.

-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.

### Hypothesis Test – Single Proportion (p-value)

In this blog I will go over the steps for performing a hypothesis test for a single population proportion. I will use the p-value approach, and give directions for using StatCrunch.

Example: A physician claims that more than 10% of pregnant women smoke while pregnant. A survey of 400 randomly selected pregnant women revealed that 60 of them smoked while pregnant. Test the physician’s claim at the 0.05 level of significance.

This is a one-proportion test because the claim compares a single population proportion (the proportion of all pregnant women who smoke) to a certain number (10%). In addition we have one set of sample information of the form x out of n (60 out of 400).

Step 1

Since the claim is that the proportion of all pregnant women who smoke is above 10%, this tells us that the hypotheses for this test are:
$H_0: p=0.10\\ H_1: p>0.10$

Step 2

The level of significance stated in the problem is $\alpha=0.05$. If the p-value is less that 0.05, this is sufficient sample evidence to reject the null hypothesis.

Step 3

The appropriate test statistic for the one-proportion hypothesis test is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$. This formula is used to calculate a z-value associated with the sample data, which is in turn used to determine the p-value for the test.

Step 4

The decision rule for this test is to reject $H_0$ if the p-value is less than 0.05. When using the p-value approach, the decision rule is always to reject $H_0$ is &latex p-value<\alpha}$. Step 5 In StatCrunch, begin by following Stat > Proportions > One sample > with summary. Enter the sample information for the number of successes (60) and the number of observations (400). Click the “Next” button. The hypothesis testing option should be active. In the box for the null hypothesis, change the proportion to 0.10, and change the option for the alternate hypothesis to “>”. Click the “Calculate” button. Here is the output from StatCrunch: The value of the test statistic is $z=3.33$. (You could calculate this with a calculator using the formula in step 3.) The p-value for this test is 0.0004. (You could determine this by finding the area under the normal curve to the right of $z=3.33$.) Since the p-value is less than 0.05, we reject $H_0$. This supports the physician’s claim that more than 10% of all pregnant women smoke. Summary I hope that you find this useful. In future blogs I will explain how to use StatCrunch to perform other hypothesis tests. If you have any StatCrunch or statistical questions, you can reach me through the contact page on my website . -George I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday I often blog about technology (including StatCrunch), inside and outside of the classroom. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website: georgewoodbury.com. ### StatCrunch – Hypothesis Tests For A Population Mean In today’s blog I will go over the steps for performing a hypothesis test for a single population mean using StatCrunch. Although I will be explaining the p-value approach to these tests, you could also use StatCrunch for a classical hypothesis test. I will be focusing on both the z-test and the t-test for a single population mean. Consult your instructor, class notes, and/or textbook for the conditions for determining when to use a z-test and when to use a t-test. z-test if you have summary data … If you want to perform a z-test and already know the sample mean, sample standard deviation, and sample size, click the “Stat” button in StatCrunch and select “Z statistics” > “One sample” > “with summary” from the menu list. When the dialog box opens, input the sample mean, sample standard deviation, and sample size in the appropriate boxes. Click the “Next” button to go to the second screen. Here you need to determine the inequality sign for the alternate hypothesis as well as the claimed value of $\mu$. Click on the “Calculate” button to display the results. Here is the output box showing the results for testing $H_0: \mu = 55.8$ versus $H_1: \mu > 55.8$ with a sample mean of 57, a sample standard deviation of 6.2, and a sample size of 123. In addition to calculating the Z-Statistic, StatCrunch provides you with the p-value for the test. Here the p-value is 0.0159. Here is how the hypothesis test would be written at $\alpha = 0.05$. Step 1 $H_0: \mu = 55.8 \\ H_1: \mu > 55.8$ Step 2 $\alpha = 0.05$ Step 3 One mean, z-test $\frac {\bar {x} - \mu}{s/ \sqrt {n}}$ Step 4 Reject $H_0$ if p-value < 0.05. Step 5 p-value = 0.0159 Reject $H_0$. There is significant evidence to support $H_1$. z-test if you have sample data … If you have sample data to work with, begin by typing it in one column in the StatCrunch spreadsheet. (Sample data can be copied and pasted into StatCrunch from other programs.) To perform the test, start with the “Stat” button and select “Z statistics” > “One sample” > “with data” from the menu list. On the first screen of the dialog box you bill be prompted for the column containing the data, as well as the population standard deviation. On the second screen, enter the inequality for the alternate hypothesis as well as the claimed value of $\mu$ and click the “Calculate” button. The output is displayed in the same fashion as the test “with summary” as shown above. t-tests If you need to perform a t-test, use the “T statistics” button. The test “with summary” is exactly as it is described above for the z-test. The test “with data” is the same as the z-test above, except you will not need to enter the (unknown) population standard deviation. Summary I hope that you find this useful. In future blogs I will explain how to use StatCrunch to perform proportion tests, 2-sample tests, chi-square tests, ANOVA, and paired sample tests. If you have any StatCrunch or statistical questions, you can reach me through the contact page on my website . -George I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday I will blog about technology, inside and outside of the classroom. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website: georgewoodbury.com. ### Geogebra OK, I’ve been a little busy on a few projects and I’ve had a little trouble getting to some of the things on my “To Do When I Get A Chance” list. At the top of my list is learning to use Geogebra. Geogebra is an interactive algebra/geometry program that can be used to help students develop an understanding of mathematics. Geogebra can be downloaded for free, but you can also run it on their web site. Go to www.geogebra.org to get started. There are so many tutorials available online that it is almost overwhelming. I’d recommend looking at the various video tutorials that are available on YouTube. It took me 10 minutes to make an applet to help my students learn how to shift exponential functions. If you want to check it out, here is the page: http://georgewoodbury.com/exponential_function_1.html . It needs some improvement (I want to show more of quadrants 3 & 4), but it is easy to edit the geogebra file and create a new html page with those changes.Here’s a quick snapshot of the screen. It seems like the possibilities are endless – shifting graphs in trigonometry, a demo that explains the mean value theorem conceptually, an exploration of slope in algebra, … Have you used Geogebra to help teach your classes? What topics have you worked with? Do you have any pointers to share with a newcomer? Please share your experience and leave a comment, or you can reach me through the contact page on my website . -George I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday I will blog about technology, inside and outside of the classroom. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website: georgewoodbury.com. ### Using Camtasia in Your Math Class A couple of weeks ago I blogged about Using Jing in Your Math Class. Some of the pros included it being free and having the ability to easily share screen shots or short videos with people of your choice. Today I will be blogging about Camtasia, which is also produced by TechSmith. (The Camtasia Studio is not free, but there is a 30 day free trial available on their web site.) I have used Camtasia to record several videos that I have posted on my YouTube channel. Camtasia videos can also be shared using Screencast.com. One huge advantage with Camtasia is the ability to edit your videos before sharing. You can fix audio errors, splice videos together, add title screens, … I particularly like the PowerPoint plug-in which makes it really easy to record from a PowerPoint presentation. Camtasia can automatically transcribe your video’s audio file into 508-compliant open or closed captions. You can type your own captions as well. Camtasia allows you to insert Flash quizzes at any point in your Screencast. I have not used this feature yet, but it seems like that would be a great way to make “demo” videos more interactive. You could ask your students to think about what step comes next, and provide them with a series of options. The videos I have created are mostly from PowerPoint presentations. I type up problems and their solutions using MathType. I set up the PowerPoint presentation to show one line at a time, and I voice over the solution as I click my way through. (By the way, I use this sort of PowerPoint presentation in class on review days as well. They are very powerful!) I have also created some videos to show my students how to type particular expressions in MyMathLab, how to graph lines and parabolas in MyMathLab, and even solve particular problems presented to students in MyMathLab. I purchased the Camtasia Studio (as well as Snag It) after picking up a discount code at an AMATYC conference. I found it to be well worth the money. Camtasia Studio currently sells for$179 (educator pricing), and I received an additional percentage discount on top of the educator price at the time.

Have you used Camtasia to help teach your classes? Do you want to share your experience? Perhaps you have used a free/less expensive alternative to Camtasia that you would like to share. Please leave a comment, or you can reach me through the contact page on my website .

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday I will blog about technology, inside and outside of the classroom. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website: georgewoodbury.com.

### Online Graphing Site – WebGraphing.com

I recently stumbled across an online graphing site – WebGraphing.com. It is a free site, although you will need to register in order to access many of the features.

It can graph any function you would run into in an algebra or trigonometry course, including piecewise functions. You can also graph multiple functions on the same graph.

One tool I have been searching for has been a number line generator, and WebGraphing.com really nails it. For instance, if you type $|x-2| \ge 5$, it produces the following graph, and lists the solution $x \le -3$ OR $x \ge 7$.

It also handles inequalities in two variables, including systems of inequalities.

The interface is easy enough to use, and there are plenty of examples to view. Give it a try and let me know what you think.

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday I will blog about technology, inside and outside of the classroom. Let me know if there are other topics you’d like me to cover by leaving a comment or by reaching me through the contact page on my website.

It’s funny – lately I have had several conversations with instructors about using Facebook and Twitter in the classroom. I have been asked which I prefer, and my answer depends on the level of the class and the computer skills of the students in the class.

This is definitely the easier way to go. Many students already have Facebook accounts, so it is convenient. They are familiar with the interface, they know how to find new posts, they know how to make a post, and they most likely know how to attach a photo to a post. Being able to attach a photo allows students to attach their work on a problem if they are looking to get some help from their classmates.

Facebook also works well as a replacement for the traditional discussion board. I have my students, in groups, answer writing/discussion questions in my Facebook group. Other students can look through the posts of other students and critique them.

By the way, I have a Facebook account that is set up for professional activities – I use it for my friends across the country that are instructors and my publishing contacts. I use this account to create Facebook groups for my classes. My students can join the groups without becoming my Facebook friend, which is a line I have chosen not to cross.

In the Facebook groups I post summaries of class sessions, homework assignments, etc. I also use it to post links to videos I have created for my students.

Twitter can accomplish the same tasks, but it is not as easy to get started. First, very few of my students have Twitter accounts, so getting them up and running takes some time and effort. Second, for students to be able to share photos of their work requires the use of a secondary program such as Jing/Screencast. Third, students have to be able to track down information through a search as oposed to finding it all on one page in Facebook.

As the level of the class & the computer abilities of the students rise, the easier these problems are to overcome. At that point they can use the power of Twitter to connect with others outside of the class, which is one of the major strengths of Twitter. I use Twitter all of the time to connect with my PLN – a group of teachers from all over the world. They keep me up with new technologies, instructional strategies, ..

Summary

I prefer Facebook to Twitter, but either web site can be used to improve student understanding and learning.