Study Skills – Test Analysis

I remember handing an exam back to an algebra student. He looked at the score, crumpled the exam into a ball, and dropped it into the trash. I was quite surprised and asked him, “Don’t you need to keep that?” He replied, “Why?” I laughed a little on the inside, but then I realized he was serious – he had no idea that he could benefit from looking over his test. He just wanted to know the result, and was wondering why I didn’t just hand him an index card with his score on it.

Many students view an exam as the end of the learning process, but it is simply not true. A student that does not analyze their errors will carry their misconceptions to the material in the next unit. The student may also repeat the same mistakes on a cumulative final exam.

Test Analysis Assignment

Here is an assignment that I like to give after I hand back the first exam:

For any problem you have lost points on,

• Explain the error in your own words.

• Rework the problem correctly.

• Cite a page number and example number where this type of problem can be found in the book.

• Make up a similar problem of your own and solve it.

By having the students explain their error, I am asking them to begin by identifying what went wrong. When they choose the words necessary to explain their error they are more likely to retain this information.

By asking them to rework their problem, I am giving them a chance to prove to themselves that they can do it. Students who struggle on an exam often suffer a blow to their confidence and this is one way to get them back on track.

By having them find a page number and example number I am trying to give a subtle hint that they need to use their book as a learning tool. (As opposed to thinking of their book some device that simply holds their homework problems.) Hopefully the next time they are stuck on a homework problem they will remember to look to their book for help.

If a student is able to make up a similar problem and solve it, they are showing that they truly understand the concept involved in that problem.

In addition to the immediate analysis of their exam, they are also creating a study guide for the final exam. This guide is filled with common errors to avoid, 2 correctly worked out problems per topic, and a reference location for further help. Students are creating a study guide tailored to their individual needs, something that would be impossible for me to do for each of my 200 students.

Grading the Assignment

For me, this really depends on the class. When I have a highly motivated class I treat this like a homework assignment. For other classes I offer them a chance to earn back some of their test points (as a rule, Test 1 only) or to earn some other special reward like the ability to earn points at our tutorial center. In some classes I deduct 10 points from their exam and return them when they turn the assignment in. (I suppose this is the “Tough Love” approach?)

If you have any questions about this assignment, or questions about math study skills, you can always reach me through the Contact page on my website.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. Each Tuesday I put out an article related to math study skills.

Creating MyMathLab Homework (for Beginners)

I’m going back to the beginning with this article on creating homework assignments in MyMathLab.

Nuts & Bolts

To begin to create an assignment, open the MyMathLab Homework/Test Manager – go to your Control Panel and click on the MyMathLab Homework/Test Manager link.  Under “Create Assignment” select Create Homework. (You can also create a quiz or test this way.)

• On screen 1, name your assignment and click next.
• On screen 2, select the chapter and/or section you want to work on. For beginners I recommend using the Preview & Add button. This allows you to look at each problem as the student would see it. You can decide to add a problem or skip to the next problem. You can also use Preview & Remove to look through and delete problems. Once you are satisfied with your assignment, click next to advance to screen 3.
• On screen 3 you can enter due dates, add a prerequisite to your assignment, limit the number of attempts for each question, and adjust other settings. When you are finished, click on the Save & Assign button.

You’re done!

Strategy From Experience

Selecting Exercises Although I usually create my assignments using the Preview and Add feature, but there are times I go a different route.  Our algebra text has roughly 30 available questions per section and I feel that I can get through those questions pretty efficiently with Preview & Add. However, our prealgebra text has about 80 available problems per section, which is a lot to go through. In this case I print out the listing of available exercises and select problems while looking at the available problems in the textbook. To find this listing of online exercises, click on Instructor Resources in the Control Panel.

How Many Problems? I find that in elementary and intermediate algebra, approximately 20 exercises per section works well. In prealgebra I raise it to approximately 30 exercises per section. It really depends on how much practice, and how much repetition, your students need.

How Much Should Homework Be Worth? This is a tricky question. I feel that you must make it worth it for the student, but I’m cautious about weighting it too heavily. I typically make all MyMathLab work worth 20-25% of the overall grade, including quizzes. (This semester the homework is worth 0% and serves as a prerequisite for section quizzes – see this blog post for more information.)

Deadlines I set firm deadlines, and I think they are vital for getting students involved. I open homework the day before I cover the section in class, and it is due on the 3rd night after I cover it. For example, if I am going to cover section 3.4 on Tuesday, I open the assignment on Monday and it is due Thursday night.

Summary

I hope that you found this helpful. If you have any MyMathLab questions, please send them to me. I’m working on a future “MyMathLab Q&A” blog.

-George

I am a math instructor at College of the Sequoias in Visalia, CA. I can be reached through the contact page on my web site.

Things I’ve Learned – Tell Them Why

I hear instructors talking about how their students lack motivation and display little to no effort. They can’t figure out why, so there’s usually a shrug of the shoulders followed by a sigh. In the last few years I’ve made a concentrated effort to tell my students “why” – why they should take notes in class, why they should try to solve the problem instead of waiting for the instructor to do it, why they should do homework, etc.

Students will do the work if they know why they are doing it. This is especially crucial for developmental students. Based on their high school experience homework is just a task – it’s our job to let them know that the purpose of doing homework is to increase their understanding and that it’s not just some task that will be checked off. They need to know that we take notes in class not just to keep busy, but instead to keep a transcript that they can use outside of class. So I tell them why.

A perfect example is my new MyMathLab homework/quizzing policy. Can you imagine developmental math students doing homework that is worth 0% of their grade? My students do. (In my class homework is worth 0%, and serves as a prerequisite for the quizzes in MyMathLab.) On the first day of class I explained to them that the homework is there for them to gain understanding while using any resources available to them, and that the homework is intended to prepare them for the quizzes. That made so much sense that they were willing to accept this, and they have been doing their homework faithfully.

“Tell Them Why” does not just apply to getting students to work, but also to helping students understand mathematics. Telling them why we use a certain procedure, rather than just saying “Here are the steps”, will help your students to gain conceptual understanding and be more likely to buy in.

Tell them why.

I am a math instructor at College of the Sequoias in Visalia, CA. If there are topics you’d like me to address in future articles, or if there’s something you would like to share, send in your requests through the contact page on my web site. Be sure to check out next Wednesday’s article.  – George

General Teaching – New Statistics Approach

Last semester was a difficult one for me in my statistics class, so I have decided to change some things up. Here’s a summary of my plan.

Get the students more involved during class.

I think that students learn and understand best through participation. Last week, while covering different sampling techniques, I had my students participate in examples of the different techniques. This activity helped them to understand the differences between the techniques in a way that my carefully crafted lecture could not. (This was especially true for cluster sampling versus stratified sampling.)

Incorporate more technology & focus on conceptual understanding.

Stats has always been a tough course to teach because the students have different technological tools. Some have a scientific calculator, others have the TI 83/84. Some have spreadsheet access on their laptop, others do not. We use MyStatLab in our course, and StatCrunch is part of the package. So far StatCrunch has been outstanding for me. It’s very intuitive for the students to use. Now I can take the grunt work out of their hands and focus on conceptual understanding. For instance, it’s easier for me to test hypotheses using p-values because students can easily generate p-values with this tool. Currently I am giving weekly StatCrunch assignments that are task oriented, but future assignments will be 50% task oriented and 50% conceptual.

Look at more student work.

I am collecting a weekly assignment of homework problems, as well as using in class assessments on a regular basis. It helps me to diagnose student issues in a more timely fashion. My students would rather find out their approach is wrong on one of these assessments than on one of the exams. It does create more work for me, but I am OK with that.

Conclusion

Two weeks into the course I find that my students seem to be doing much better, and are more connected to the material. I will post results after exam 1, which should be late next week. I can say that it is nice to feel excited about my students performance and interest to date.

I am a math instructor at College of the Sequoias in Visalia, CA. If there are topics you’d like me to address in future General Teaching articles, whether they are related to statistics, developmental math, or other topics, send in your requests through the contact page on my web site. Be sure to check out next Wednesday’s article.  – George

Study Skills – Focus on Math Anxiety (Day One Activities)

At the developmental level it should be no surprise that many of the students have feelings of anxiety related to math. Here are a few of the things I do on the first day of class to help students deal with these feelings.

“Heads Down, Hands Up”

After I take roll on the first day of class, I ask the students to put their heads on their desk with their eyes closed. I then ask students to raise their hands if they feel that they struggle with math or if math is their worst subject. Most students raise their hands, and the students can tell this by all the rustling associated with that many hands being raised. I then ask them to put their hands down and open their eyes.

We talk about how many students feel this way. It’s odd, but so many students feel that they are the only one who struggles with math and that there must be something wrong with them. I tell them about all the hands that went up, and that it’s pretty common to feel that way. I ask them to consider this as their chance to start over, to wipe the slate clean, to develop a positive attitude. Honestly, it does not matter what series of events led to a student being in a developmental class, it’s what happens from there that matters.

Positive outcomes: Students realize they are not alone and that they can start over now.

“A Picture Is Worth 1000 Words”

One fun activity that I enjoy is asking my students to draw a picture of a mathematician. I see lots of pictures of little bodies and big heads, some glasses, some pocket protectors, and some crazy Einstein hair. (I have an ex-colleague that does this activity, and once he had a couple of students draw wizards – mat is so “magical”!) The pictures rarely look like any of the students in the room.

Students feel that anyone who understands math is some sort of super-genius. There is a giant wall in front of them that leaves math inaccessible to them. I explain that any student who is willing to devote the time, effort, and thought to learning mathematics can do it. And I’m here to help them. I tell them that if they want to see what a mathematician looks like then they should check out the mirror when they get home.

Positive outcomes: Students realize that math can be accessible to them.

“Tell Me Your Strengths And Weaknesses”

On Day One I give my students a survey that helps me to understand them a little bit better, as well as showing them that I am interested in my students and their success. Near the end of the survey I ask my students to give me 3 reasons why they will pass this class. Basically I am asking my students to list their strengths because I want them to acknowledge that they have student and/or personality traits that can help them be successful regardless of the arena. Even in math class.

I also prompt my students to finish the following statement “If somehow I do not pass this class, it will most likely be because …” Here I am asking my students to identify what they feel is their greatest weakness as a math student. The thought is that the best way to overcome a weakness is to begin by identifying that weakness. I read over the surveys that night, and on the second day of class I go over coping strategies for overcoming these weaknesses. Students at the developmental level have little experience with developing coping strategies, but once this is modeled for them they are more likely to be able to do this for themselves.

Positive Outcomes: Students realize that they have their own strengths, as well as plans to overcome any perceived shortcomings.

Conclusion

Day one is a great opportunity to break down student misconceptions about math and mathematicians, for students to realize that they are not alone in their struggles, and that there is a path to success if they choose to take it. The activities I have shared are great ways to alleviate some of the anxiety our students feel. Give them a try, and let me know how it goes. If you have any activities of your own, please share them with me by leaving a comment or reaching me through the contact page on my website.

George

This Semester’s New Elementary Algebra Approach With MyMathLab

This semester I’ve taken a new approach with MyMathLab in my Elementary Algebra class. I was really happy with how things were going with my student contracts, but I got to attend many MyMathLab sessions in the last year and heard many great ideas that excited me. I’m hoping that this approach shows just how powerful MyMathLab is, and maybe wins over a skeptic or two.

MyMathLab HW – Now worth 0%!

I still assign MML HW for each section, but I have cut the number of problems in half. The HW counts for 0% of their overall grade, but the students must score at least 85% to access a MML Quiz for that section. Even though there are some instructors who feel that MML does too much to help students with the different learning aids, I feel that students can truly understand the material through the use of MML. On day one I explained to my students that the purpose of the homework was to increase their understanding, not their grades. I told them that the HW gives them a chance to practice, using the learning aids, without impacting their grade. I told them that these homework assignments were to prepare them for the section quizzes. I told my students that if they got a problem correct after employing one of the learning aids, they should see “Similar Exercise” to rework the problem and make sure they truly understand.

So, students are using to MyMathLab homework and its learning aids to increase their understanding but the homework is not (directly) impacting their grade.

MyMathLab Quizzes – Worth 20%

I use 3 types of quizzes – section quizzes, chapter quizzes, and Student Learning Outcome (SLO) Checkpoint quizzes.

Section Quizzes

The section quizzes are new for me, as well as the use of prerequisites in MyMathLab. To access a section quiz, students must score at least 85% on the corresponding section HW assignment. The quizzes are roughly the same length as the HW assignments, and the learning aids are turned off. Students can take the quizzes as many times as they like before the deadline, which falls on the 3rd night after the material is covered. (Halfway through the semester that will change to the 2nd night.) I like the section quizzes because students have to work through all the problems and topics before getting their feedback. At that point they can self-remediate, going over the problems they struggled with, before attempting the entire quiz. I do count only the highest score.

Chapter Quizzes

I do give chapter quizzes halfway through the chapter and again at the end of the chapter. These quizzes help the students to determine which topics they have under control and which topics require further study. I have always given these chapter quizzes, this is not new. In my experience, these quizzes have the highest correlation with exam scores. The chapter quizzes are being weighted as 3 times the weight of a section quiz.

SLO Checkpoint Quizzes

In our Elem. Alg. course we currently have 10 SLO’s. I have made up 10 comprehensive quizzes covering these SLO’s, and I release them during the last 3 weeks of the semester. The ulterior motive is to get students to start preparing for the final exam, but it also gives me good data for measuring SLO performance. These SLO quizzes are weighted as 4 times a section quiz.

Written Assignments – Weekly Assignments & In-Class Assessments 10%

I give out a written assignment each Thursday that I collect the following Thursday. As the week progresses, students are able to attempt more problems. This encourages them to keep up with the material. At the end (or beginning) of most classes, I give a brief 2-3 question assessment. Sometimes they are solo, sometimes my students work with partners. Both of these assignments allow me to see student work, to make sure that there are no gaps in their understanding. I can also alert my students to typical errors that they should avoid. As I mentioned, these assignments also help me to ensure that my students keep up with the material. Also, since paper & pencil exams make up a majority of the grade, it gives my students a chance to practice in the format they will be tested.

Paper & Pencil Exams – 50%

I essentially give 1 paper & pencil exam per chapter. They get 1 hour to take the exam.

Final Exam – 20%

I give a comprehensive final exam. Lately I’ve been part of a group of 4-6 instructors giving a common final that we grade collaboratively. (For what it’s worth, my online Elem. Alg. class performed outstandingly on last semester’s final.)

So Far, So Good!

I was expecting a minor revolt on day one. “You mean we HAVE to homework, AND we don’t get any points for it!?!?” As I’ve learned, if students understand why they seem to be willing to go along. I explained that the homework was their chance to practice and develop the understanding that prepared them for their quizzes. The look on their faces – “That makes sense.” The first exam is still a little more than a week away, and I know that things can always unravel in a hurry, but I’ve got a real good feeling. I’ll come back and post results as the semester progresses.

I look forward to reading your comments and answering any questions you might have.

George

Blog Hiatus Over

Hi Everyone – Getting back on track after a hard drive crash derailed me.

Tomorrow’s post: Algebra Course Redesign using MyMathLab.

George

Study Skills – The “Half Test” (Tuesday November 24)

Note – A series of Study Skills related articles appears here each Tuesday. I now shift my focus to practice tests and helping students prepare for an exam.

If you typically spend a day reviewing prior to an exam, consider the following activity instead.

For my developmental level math classes I will often bring in a “half test” on the day before the first exam. I figure that they’ve seen me work enough problems, and watching me go through problems one more time might not be so helpful. Here’s how it goes.

• Write a varied practice test that will take half of a class period.
• After the students have finished, give out a sheet with solutions.
• Have students determine whether they are working quickly enough.
• Have students determine which subjects/problems will require further study and spend the remainder of the time answering questions.

The main idea is to put students in a test-like situation prior to the test. You can never tell how you will respond until you experience the feeling of walking the tightrope without a net. For a student with anxiety, it gives them a chance to experience that feeling, then focus on techniques to overcome it. This also clearly helps students to determine where their weeknesses are while they still have time to study and prepare for the exam.

I only use this activity once a semester. After that students can do this on their own prior to all subsequent exams. 

Although I usually only do this in developmental math classes, I tried it this week in my trig class. I’ll update you on how it worked tomorrow, after I have finished grading.

I am a math instructor at College of the Sequoias in Visalia, CA. If there are topics you’d like me to address in future Study Skills articles, send in your requests through the contact page on my web site. Be sure to check out next Tuesday’s article.  – George

MyMathLab – Homework Grades (Monday 11/23/09)

This week I’ve decided to focus on MyMathLab homework and the grades we assign to it. (Sorry for the delay – exams, exams, exams …)

How I’ve Always Done It

For the last few years I have made MyMathLab 25% of my students’ grade. I divide the 25% equally among the following 3 categories: homework, chapter quizzes, SLO quizzes. I have always felt comfortable assigning a little over 8% of my total grade to homework. I know some instructors get a little worried about students getting high homework grades without actually learning, and therefore setting themselves up for failure on exams.

I spend a significant amount of time at the beginning of the semester talking about how to do the homework to maximize understanding. I explain each of the learning aids and how to incorporate them in an effective plan to learn, while also explaining some of the pitfalls associated with the learning aids. (See my article on “Student Pointers” on my web site for more information.) With this approach I have a very small number of students who do well on the homework but do not learn.

Here are a few other strategies you can use if you worry about the homework.

Option 1 – Limit the number of attempts per question.

MyMathLab now allows the instructor to limit the number of attempts per question. I have a colleague who currently uses this strategy, limiting his students to 3 attempts, and has found it to be successful. First, he says, this is actually 9 attempts – 3 chances to answer each of the 3 questions. Second, he feels that his students take each question more seriously due to the limited number of attempts, rather than just going through the motions.

Another benefit to this approach is that the use of the “Help Me Solve This” learning aid uses up one of their attempts. This makes students less reliant on the learning aids, which should improve their exam scores.

(Keep up the good work, JB.)

Option 2- Turn off the learning aids.

MyMathLab now allows you to turn of some or all of the learning aids for an assignment. So, if you don’t want your students to abuse the learning aids, turn them off. You could create one assignment that leaves them on, and another that leaves them off. You could turn them off in homework assignments, and direct students to Study Plan problems for help.

Option 3 – Make the homework worth 0%.

What?!?!?! If the homework is worth 0%, the students won’t do it. Not so fast, my friend.

At Pioneer VI in Kentucky, I got a great idea from two instructors (one from Hazzard County) that I plan to implement next semester. For each section, create a homework assignment and a quiz. Leave the learning aids on for the homework, but not for the quiz. Make the homework a prerequisite for the quiz; for example, set the prerequisite to 90% for access to the quiz.

Students still need to do the homework to learn, because they will need to be able to solve the problems on the quiz. This way, they use the learning aids as they were intended – to increase understanding.

This is a win-win situation. We can get students to do the homework and demonstrate proficiency on the quizzes, without inflating their grades.

Summary

MyMathLab homework is not the “magic bullet”. It needs to be one part of a comprehensive plan to help students understand. Using quizzes, without learning aids, is one way to make sure students understand and are not simply clicking through problems until they get one they have seen before. Also, if you want to make sure your students are understanding the material, find a way to check out their written work. I give quick quizzes at the beginning of class and group assignments at the end of class so I can take a look at their work.

If you have any questions, leave a comment or drop me a line through the contact page on my web site. – George

Note – MyMathLab related articles appear every Monday.

I am a math instructor at College of the Sequoias in Visalia, CA. If there are topics you’d like me to address in future MyMathLab articles, send in your requests through the contact page on my web site. – George

Potpourri – Student Success Story (Thursday 11/19/09)

About 10 years ago, I switched to teaching mostly developmental mathematics classes. It wasn’t that I didn’t like the material in Calculus (my family tree does contain Newton, after all), I found that teaching developmental mathematics can be more personally fulfilling. Here’s a story to illustrate this.

On the first day of each class, I collect a survey from my students. It contains the standard information (name, email address, math background, …). I also give the students a space to share any information that they feel I should know. One student, who I will call Laura, wrote down that math was her worst subject and would like to talk to me about it during office hours.

When Laura came to my office I asked her when her problems with math began. (It’s funny, but in my experience students can answer this question in about 0.3 seconds. We always seem to know the cause of our troubles, even if we don’t know how to fix them.) Laura told me that she remembered a time in the third grade – that’s right, the third grade -  when her teacher held up her math paper and told the class “Take a good look at this paper. This is a bad paper. Don’t do it this way.” Naturally, Laura was crushed. It was so bad that she still hadn’t recovered over 10 years later.

I asked her how she did in the rest of her classes, and she told me that she was a great student except in math. I told her that I had a deal for her. If she would put aside her negative math feelings and give her fullest effort, I would work as hard as I could to help her. I felt that if she could experience one success, she could lose all of that old baggage and move on. I promised her that if she passed the first test, I would hold her test up in front of the class and tell them “This is a good test! This is how you do it! Well done!”

So, we worked really hard, and Laura passed the first test. I held up my end of the bargain, held up her test, and said my piece. As I glanced over at Laura, I saw her eyes starting to well up. My eyes started as well. That’s why I love teaching developmental mathematics.

Laura went on to pass elementary and intermediate algebra, eventually transferred, and got a bachelor’s degree.

“Laura” – If you are reading this, thank you.

I am a math instructor at College of the Sequoias in Visalia, CA. If there are topics you’d like me to address in future Potpourri articles, send in your requests through the contact page on my web site. Be sure to check out next Thursday’s article.  – George