New MyMathLab Site For My 3E – Available To Copy

I have put together a MyMathLab course for the new edition of my Elementary & Intermediate Algebra textbook. I have set it up so you can copy it. Inside the course are 14 Chapter quizzes, 14 Chapter midpoint quizzes, 22 Student Learning Outcome (SLO) quizzes, 83 homework assignments, and announcements that can be posted/emailed to your students for Chapters 1-8. (The remaining announcements will be posted in the next week or so.)

The Course ID, and all important information can be found on this page on my web site.



If you do copy the course, please drop me a line through the Contact page on my website  so that I can keep you apprised of changes I make and new features that become available. You can also reach me through that page if you’d like me to customize a course for you – cut out certain chapters, delete certain assignments, …

-George

I am a math instructor at College of the Sequoias in Visalia, CA. You can reach me through the contact page on my website – http://georgewoodbury.com.

So, I was at ICTCM this weekend … Help Wanted?

During the week I will be posting a series of blogs inspired by sessions I attended at ICTCM – including Wolfram|Alpha, Discussion Boards, Redesign, Inverting the Classroom, and Resampling in Statistics. I will also blog about things that happened outside of sessions, I came back with several ideas and projects. (Maybe this will take a couple of weeks.)

The most exciting topic to come up was introduced by my friend Susan McCourt from Bristol CC. She has an idea to create a blog site where we can have a pool of college math instructors blogging at a certain schedule (once a week, every 2 weeks, …) or have guest blogs as they fit. Blogging is a great way to share ideas and to learn, but it is difficult to blog on a daily basis. If you’d like to get involved, or if you know someone else that you’d like to nominate, leave a comment on this blog or reach me through the contact page at my web site – georgewoodbury.com. I’ll be helping Susan to get this off the ground.

-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.

Guest Blog: Using Game Mechanics to Fix the Grading System and Motivate Students

NOTE: This guest blog was written by my 17-year-old son, who is a high school junior. He plans on majoring in game design in college, and we are constantly talking about how education can be improved by incorporating elements of game design. He wrote a guest blog for me last year on video games in education.  Please leave feedback by commenting on the post – we’d both love to hear what you have to say. Enjoy!

Using Game Mechanics to Fix the Grading System and Motivate Students

                There are two halves to a good education: one is learning, but equally important is the motivation one needs to learn. Boards have been reforming schools, teachers have been changing the way they teach, and technology is playing a more important role in the classroom in hopes of creating a better learning experience. I have seen little to no effort put forth to reform how students can be motivated to take advantage of these improvements. We currently use the standard A B C D F grading system, which, when examined with the eye of a game designer (masters of motivation), fails the students whom it is literally failing.

                The current grading system thrives on fear of failure, on punishment. Throughout a class, students do all that they can to stay afloat in the upper levels of the grading chart (A B C). But once you fall into the water, it is nearly impossible to get back to the surface. The students above water take note as these students completely give up all motivation, letting themselves sink to the bottom without a struggle. This is how a majority of our students think. They do the minimal effort required to not fail, when the system should motivate students to do all that they can to learn the material and do the work required to learn the material. But to do that, we need to look at the classroom differently.

                We need to look at the classroom as a metagame, which is pretty much a game we throw on top of something that may or not be a game in order to motivate people to do something. We see metagames everywhere. If you have ever played Farmville or Foursquare, been involved in scouts or karate, or taken part in the reward systems run by stores, airlines, or hotel chains, than you have played a metagame. The formula for a metagame: Actions = Feedback + Rewards. Buying ten lattes gets you one free latte. Flying fifty thousand miles gets you a free plane trip. Completing certain tasks in scouts gets you badges, and getting certain badges gets you a new ranking, which comes with its own rewards. This is a great system for motivating people, but why does it work? All games, including these metagames, use game mechanics, or strategies game designers use to manipulate human behavior (fundamental list of game mechanics: http://gamification.org/wiki/Game_Mechanics). We need to use these game mechanics to transform our grading system into a reward system.

                A basic rule of game design: the user should always know exactly what will come about in reaction to his/her actions. For example: if I buy fifteen  drinks at Starbucks, I get one free – with this rule, there is no doubt in my mind as to what will happen if I buy fifteen drinks at Starbucks. Students should always know what rewards lie in store for completing homework, doing well on a test, etc. For this reason (among many), curves destroy the motivation of most students. Students being graded by a curve are unsure about how much they need to study in order to get their desired reward.

                The point/reward system found in games such as Farmville works very well as a grading system. Students would be given a packet at the beginning of each unit, outlining due dates for all homework assignments and projects, as well as test and quiz dates. In addition to these dates, the packet would detail exactly how many points could be rewarded for each assignment, for each action.

Students would spend the year doing assignments and taking tests, collecting points. After every unit, each student sees the number of points he/she has collected so far in the year. The teacher should know exactly how many points he/she will offer in the year. The percentage of points the student has out of the total number of possible points for the year yields the student’s level. If a student has 246 points, and the class is going to be out of 1000 points, that is 24.6%, or level 24 (out of 100 possible levels). Instead of the student minimally rising or drastically falling throughout the year, he/she is continually improving, increasing his/her points the entire year (the students cannot go down). After every unit, when the students are given their stats, a set of minimum levels should be announced, projecting what scores are on track for which grades. At the end of the year, the students will be given a standard letter grade depending on their level (or percent of points).

This system is based solely off reward, and will not demotivate students by punishing them. A student in this system will do more homework assignments and spend more time preparing for tests because of the points mechanic and levels mechanic. And this is not the end. Teachers can go as far as they are willing with this system, adding more game mechanics to motivate students as much as possible.

Rewarding achievements (achievements mechanic) can also motivate students. If you give students badges for completing certain things beyond the usual, like completing every possible homework assignment, or for improving his/her test score from one chapter to the next by ten percent, or for getting an A on every quiz in a chapter, they will be even more motivated to work hard. These can come in the form of badges or stickers and usually motivate a younger audience, but for older students, bonuses can be more effective.

Bonuses (see bonuses mechanic) can be awarded for certain situations when students go beyond the usual to positively impact their behavior. Rewarding bonuses (no matter how small/big) every time someone asks a deep question based on the material leads to more alert, thinking students. Rewarding bonuses to students who find an alternate way of solving a problem leads to more critical thinking. Bonuses are another powerful way to motivate students. Teachers can use bonuses like these and tailor them specifically to improve certain aspects that certain classes lack.

There are many more game mechanics. Another game mechanic used frequently in the classroom is the Community Collaboration mechanic, in which a group works to solve a problem or do something together. Quests (see quest mechanic), or a series of tasks, also motivate students. A quest could force students to solve a riddle or a problem, giving them a clue and leading them somewhere if they use what they have learned (great for history classes). Leaderboards of the top 10 students (or of the whole class, if showing it would not demotivate students who are way behind) motivate students to work harder, rather than motivating them to work less, a result of the curve, as they do not know what will result of their studying and they may not have a chance of doing well compared to others.

Teachers need to step out of their traditional roles of formal educators and into a new role of a game designer. Teachers should carefully design their class, not just their lessons, to motivate students using game mechanics. By morphing the grading system into a reward system incorporating many other game mechanics in the classroom, students can and will perform better without any change in regards to how you teach them.

So, what do you think? Please leave your feedback as a comment, or drop me a line through the contact page on my website. If you have any questions, or if you have ideas for topics that you would like to hear about from the perspective of a high school student, just let us know.

-George

Flipping the Class & Khan, Part 2

So, I went back and watched several videos at the Khan Academy last night. To be fair, there is more conceptual presentation than I thought. This makes me feel even better about sending my students to watch these videos. Yesterday’s blog shows the power of Web 2.0, blogging, & Twitter. I asked if I was missing something, and got lots of great feedback including from Jason with the Khan Academy team.

Where am I today?

I still feel that flipping the classroom is a worthy pursuit. There are lots of ways to get this done. The easiest way would be to flip the class in such a way that all of the students were working at the same pace on the same material. A motivating conceptual lecture could be given at the end of the class session, students could visit web sites for conceptual enrichment & how-to practice, with collaborative work in class the following day. There are variations that could work – written assignments for students to develop conceptual understanding at home, computerized assignments for drill practice, conceptual portions of the collaborative work. The Khan Academy videos could definitely be a tool utilized in this approach.

But is keeping everyone on the same pace the best way to flip the class? Isn’t there something to be said for allowing students to learn at their own pace? This is much harder to pull off, because it would then be impossible to give mini-lectures that conceptually motivated the topics. (Imagine 30 students in 30 different places – even if you could give all the mini-lectures there would be no time left for coaching/mentoring). So, we’re reliant on using the work of others to deliver the conceptual understanding or we must create all of the material ourselves. The best option is often the most difficult option.

Even after looking at the Khan Academy videos again, I don’t think that there is sufficient conceptual development there. It will be hard to find a one-stop shop that couples solid conceptual explanations of mathematical ideas along with practical how-to videos (which Khan does quite well) along with an arena for interactive student practice.

For me, I think the opportunity is there with MyMathLab. Depending on the book, there are videos that explain concepts & demonstrate how to solve problems. The homework & study plan, with all of its learning aids, can provide students with the quality practice they need. I’m going to try it in the fall, using the “all on the same pace” approach. I may need to supplement with more how-to videos, either from other sources online or by creating my own. I may need to develop some conceptual videos & materials. But I’ve got all summer, right? I wonder if I’m stumbling into one of those a-ha moments?

Let’s keep the conversation going. Please leave your opinion as a comment, or you can reach me through the contact page at my web site – georgewoodbury.com. I’d still like to hear from those of you who have experience in flipping the classroom.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. Each Wednesday I post an article related to General Teaching on my blog. 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.

Can the Khan Academy flip a classroom?

Salman Khan’s recent TED talk has generated a lot of buzz. (You can check out the video here.)

At one point he mentioned how the Khan Academy videos are being used to “flip” the classroom, and that’s when I got a little worried. I like the idea of flipping the classroom – having students learn concepts via video outside of class and using class time to work on problems, turning the teacher into a mentor or coach. My friend Mike Sullivan has done this with great success at his college. In this environment, there is more time for collaborative learning and one-on-one instruction. I feel that this can really help students to learn and understand mathematics.

My problem with the Khan Academy videos is that they are “how-to” videos, and conceptually barren. I recently watched a video on dividing fractions, and the video began with the problem on the screen. He started by saying “Whenever you are dividing any fractions, you just have to remember that dividing by a fraction is the same thing as multiplying by its reciprocal. So this thing is the same thing as three-fifths times … two over one.” This video does not explain why we multiply by the reciprocal when dividing by a fraction, it’s just what we do. There is no development of the topic. I think that students that are told “Do this. Do this. Do this.” will not understand what they are doing, but instead will be able to mimic the video’s work. I don’t think they will retain the knowledge, and we cannot build world-class math students on such a shaky foundation.

Now, don’t get me wrong, I love the Khan Academy videos. But I love them for what they are – how-to videos that students can refer to as they are learning a topic. I send my students to these videos all the time. I love that they are available online for free. I love the story of how he started doing the videos. I especially love how he left his job as a hedge fund analyst to do these videos, there’s something admirable and Escallante-ish in that. I feel badly saying anything negative. It’s just that in their current form they cannot teach students, they can only reinforce what has been already covered in the classroom. They cannot be used to truly teach mathematics.

Am I missing something?

Please leave your opinion as a comment, or you can reach me through the contact page at my web site – georgewoodbury.com. I’d especially like to hear from those of you who have experience in flipping the classroom.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. Each Wednesday I post an article related to General Teaching on my blog. 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.

Solving Systems of Linear Equations by Substitution

The first algebraic technique for solving systems of two linear equations in two unknowns is the substitution method. I teach my students to look for one of two scenarios for using substitution:

• One of the equations already has an isolated variable, like or
• One of the equations can be easily manipulated in order to isolate a variable. What we are really looking for here is an equation that has a “plain” x term or a “plain” y term. That is, there is an equation in which the x term or y term has a coefficient of 1 or -1.

(Later I amend this approach to only using substitution when one of the equations already has x or y isolated.)

Example 1

Solve:

Note the second equation: . This equation has isolated on the left side of the equation, and tells us that is the same as , so we can replace in the equation by the expression .

     (Substitute for .)
       (Distribute.)
              (Combine like terms.)
                      (Subtract 18 from both sides.)
                         (Divide both sides by -1.)

Now that we have “half” of our solution, we need to find the y-coordinate of the ordered pair by back-substituting 5 for x in either of the original equations. It will usually be more efficient to substitute into the equation that had the other variable isolated.

        (Substitute 5 for x.)
                  (Simplify.)

The solution to this system is .

We can check our solution by substituting 5 for x and 1 for y in the other equation, .

              (Substitute 5 for x and 1 for y.)
                       (Multiply.)
                          (Subtract.)

The solution checks.

Example 2

Solve:

Note the first equation, has isolated on the left side of the equation, and tells us that can be replaced by  in the equation .

     (Substitute for .)
       (Distribute.)
              (Combine like terms.)
                      (Subtract 30 from both sides.)
                             (Divide both sides by 11.)

To find the x-coordinate of the ordered pair, substitute 6 for y.

        (Substitute 6 for y.)
                                   (Multiply .)
                                        (Simplify.)

The solution to this system is .

We can check our solution by substituting 9 for x and 6 for y in the other equation, .

              (Substitute 9 for x and 6 for y.)
                       (Multiply.)
                               (Subtract.)

The solution checks.

Summary

I hope that you find this helpful. If you have any questions, or if you have any other topics you are interested in, you can reach me through the contact page at my web site – georgewoodbury.com.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. Each Wednesday I post an article related to General Teaching on my blog. 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.

Systems of Linear Equations in Two Variables – Graphing

There are 3 methods for solving systems of two linear equations in two variables: by graphing, the substitution method, and the addition (or elimination) method. Without using technology, the least efficient technique is solving by graphing. Even if a student scales their graph perfectly, if the intersection of the two lines does not occur at a point whose coordinates are integers we cannot determine the exact solution. (Never mind if the student’s graphs are not perfect.) So, why even teach students to solve systems by graphing?

I start to teach systems by graphing because it helps students develop a conceptual understanding of what a solution represents. Suppose we had the following system of equations:

When we graph the line , we are displaying the ordered pairs that are solutions to that equation. When we graph the line , we are displaying the ordered pairs that are solutions to that equation. So, what does the point of intersection represent? This is the one ordered pair that is a solution to both equations. This helps students to understand what the solution of a system of equations represents.

Once we understand how to find the solution of an independent system of equations by graphing, I ask my students if all systems of linear equations will always have one solution. Someone will always ask “What happens if the two lines are parallel?” Since distinct parallel lines do not intersect, my students understand that some systems will have no solution. (We call this type of system an inconsistent system.)

I then ask if there are any other options besides one solution and no solution. Can two lines have more than one point in common? We then figure out that this could happen only if the two lines are identical. Now my students understand the type of system we call a dependent system. By the way, since graphing lines is so fresh in their minds, along with the slope-intercept form of a line, my students have an easier time understanding how to present solutions to a dependent system as an ordered pair of the form (x, mx+b).

Once I am sure that students understand the graphical interpretations associated with these types of systems, I then move on to the substitution method and later to the addition method. But this discussion on solving by graphing is invaluable to student understanding.

By the way, I do not ask students to solve systems by graphing on their exam. I do ask questions like the following:

• Draw two lines that would form an inconsistent system of equations.
• Draw two lines that would form a system whose only solution is (3,8).
• Draw two lines that would form a dependent system of equations.
  [Yes, essentially I’m finding out if they can trace a line 🙂 ]

How do you introduce this topic? Do you ignore it? Do you incorporate technology? Please leave a comment, or reach me through the contact page at my web site – georgewoodbury.com.

-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.

Assessing Student Learning Outcomes (SLOs) with MyMathLab

Last Friday I had the chance to sit with some high-quality math instructors at Taft College, discussing how to use MyMathLab to assess Student Learning Outcomes (SLOs) and to generate data. The basis of the discussion was how to use something similar to my SLO Checkpoint Quizzes on a department wide basis.

One way to begin is to create a quiz for each SLO in the course outline. Since MyMathLab will mark each question as correct or incorrect without partial credit, each quiz should be long enough and varied enough so that students who make a “careless error” on one particular problem can still prove mastery on the remaining problems.

One option would be for one instructor to create a series of SLO quizzes and have the rest of the department import those quizzes. Another option would be to create a new MyMathLab course that all of the students can enroll in. (MyMathLab allows students to sign up for other courses that use the same textbook.) The advantage of this new course would be that all of the data would be in one place (no exporting and emailing results by individual faculty). A potential drawback is that the results will not be broken down by individual instructors, but if you are looking for department-wide information that is OK.

When to give the quizzes? I give mine at the end of the semester, but you could give them as the semester progresses.

How many attempts should each student get? I allow my students to take them as many times as they’d like, but you can limit them to as few attempts as you’d like. (In my experience, leaving no limit for attempts encourages students to pursue mastery.)

Data to report? There a lot of ways to go. You can report the average score for each quiz. You can report the percentage of students who achieved a benchmark score. Both of these are quite easy to do in the MyMathLab gradebook, or you could use Item Analysis to drill deeper for results on particular questions/objectives.

If you have any questions about how I use SLO quizzes, or if you’d like to run ideas for your school by me, drop me a line. You can leave a comment, or reach me through the contact page at my web site – georgewoodbury.com.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. Each Monday (during the semester) I post an article related to MyMathLab on my blog. 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.

Creating a Community of Learners – TCCTA (1/2011)

This year I gave a talk entitled “Creating a Community of Learners”. Here’s the presentation synced up to the audio:

http://connect.txpod.org/l38077493/

(Thanks to Marcos Molina for setting this up!)

You have to register at the web site in order to see it, it’s free:

http://connect.txpod.org/thenetworkcontentevent/event/registration.html

Let me know what you think. Please leave a comment here, or reach me through the contact page at my web site – georgewoodbury.com.

-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.

Teaching Linear Inequalities in Two Variables

In Elementary Algebra, I love teaching linear inequalities in two variables at the end of the chapter on graphing lines because it gives me one last chance to go over how to efficiently graph a line. Use the intercepts or use the slope? Is it vertical or horizontal?

It can be a frustrating section for me as well. Some students really have a hard time grasping which half-plane to shade. The way I have always done it:

• Determine if the line is dashed or solid.
• Graph the line using an efficient technique.
• Pick a test point not on the line, preferably the origin (0,0).
• Substitute the coordinates into the original inequality for x and y.
  If the inequality is true, then the ordered pair is a solution. Shade the half-plane containing the test point.
  If the inequality is false, then the ordered pair is not a solution. Shade the half-plane that does not contain the test point.

Each semester there will be a group that can do everything except figure out which side to shade. It’s frustrating because I think it is pretty clear and straightforward.

Next semester I am changing my approach. Suppose the example is .

• I will have them graph the line, using the intercepts of (6,0) & (0,-4).
• We will then label the line and we will go over the idea that this line represents all of the ordered pairs for which is equal to 12.
• I will explain that this line divides the rectangular plane into two half-planes. One of the half-planes contains points for which and .
• I’ll pick a point below the line to the right, like (6,-5) and substitute the coordinates into the expression , which will result in 27. Since , we will then label that half-plane as .
• I’ll pick the origin, which is above the line to the left, and substitute the coordinates into the expression , which will result in 0. Since , we will then label that half-plane as .
• We will finish by shading the side labeled .

After 2 or 3 examples done this way, I think the students will understand what each half-plane represents and have an easier time determining which half-plane to shade.

How do you introduce this topic? How do you feel about this approach? Please leave a comment, or reach me through the contact page at my web site – georgewoodbury.com.

-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.