Learning Notebooks for Online Math Homework

May 28, 2012 by

After teaching math at a community college for 10 years (and using online homework for at least 7 of those), I have noticed that my online math students don’t seem to have the same grasp on notation and the steps to “prove” the solution to a problem as when they did old-fashioned paper & pencil homework.  I have also found that the students who use online homework have become much more unorganized, and are unable to find the work for the problems they have questions on.

 

Example of student work in a Learning Notebook

This last year, I’ve been experimenting with what I call a “Learning Notebook” – where students keep an organized notebook of the handwritten work for selected problems from the online homework system. In these Learning Notebooks, the students have to show the steps required to complete the required problems (including all necessary graphs and proper notation).  They don’t have to keep a record of every problem, since some questions can be answered by inspection alone. For the Learning Notebook, I typically choose problems that would require me to show steps in order to complete it with a reasonable confidence in my answer.   The online homework, graded on accuracy, is worth 20 points per unit.  The Learning Notebook, showing sound mathematical thinking and notation for required problems, is worth an equal weight of 20 points.

The student is responsible for keeping the notebook organized, including a Table of Contents and page numbers (these help me to find assignments when I go to grade the notebooks).  While this may seem like busywork, keeping a notebook has several benefits to the student:

  • When studying for an exam, the student can find the work associated with each problem quickly.
  • When there’s a question on a specific problem, the student can quickly find their version of the problem and what they tried.
  • Repetition of the use of proper notation leads to better outcomes on the exams (since they don’t “forget” to include the notation there when they are required to have it in their notebooks).
  • Thoughtful reflection on the problem steps may be more likely when they slow down to write the steps down instead of trying to do too much in their head.
  • Students get points for showing their work, which can act as a slight padding of their grade when the tests are hard (which they inevitably are).
One of the additional benefits of the Learning Notebooks is that it gives me a “place” to collect additional assignments that can’t easily be covered by online homework.  For example:
  • Sketching the graph of a function given a list of properties
  • Explaining the transformations of a graph in multiple steps
  • Proving that a series converges or diverges
  • Explaining all the properties of a rational function

A collection of Learning Notebooks on exam day.

For my traditional classes (that include an in-person meeting) I grade the Learning Notebooks while the students give the exam. I select ten problems at random to check for completion, notation, and supporting steps.  I typically give a 2-hour exam, and I can grade the notebooks for 15-25 students by the end of that time.  This is when it becomes vitally important to me that the students include a Table of Contents and numbered pages.  Without those, I would spend a lot of extra time searching for assignments.  I use a 0-1-2 point scale for each of the ten problems.

  • 0 points = the problem cannot be found, there was only a problem and answer,  or there was no reasonable attempt to solve the problem
  • 1 point = some reasonable attempt to solve the problem, but details missing or problem is incomplete
  • 2 points = problem is completely solved, with all appropriate details included
After I have worked through all 10 problems, I give the student a score out of 20.
To help you understand the process a little better, I asked a few students to let me share their notebooks and the grading process.  They agreed, so here’s a little video explanation of how the process works.

Video: Learning Notebooks for Online Math Homework

Here is a Sample Table of Contents and Sample Notebook Check for the Learning Notebooks.

Because they have to keep a Learning Notebook, students know that they shouldn’t cut corners when they work through problems.  At first, many will try, rushing through the online homework (probably with the aid of calculators and WolframAlpha) with the belief that they will just “take a few minutes to go back and write up the steps.”  For this reason, you shouldn’t be surprised if the grades for the first set of Notebooks are pretty bipolar (half will be great, half will be awful).  It turns out that to actually think through and write the math takes time, time that some of these students have been cutting corners on ever since online homework was first introduced.

I’ve been using these notebooks in Math for Elementary Teachers, College Algebra, Calculus I, and Calculus II over the last year, and have seen an improvement in mathematical thinking, use of notation, and study habits for those students that keep good notebooks.  I don’t have any scientific evidence, but overall, I feel like these Learning Notebooks are helping improve my students’ success.

NOTE: In about a week, I will share how I’m using the same strategy in my online classes.  I want to get all the way through the process of collection once before I write about it.  Hint: It involves webcams and cell phone cameras.

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Help Students Pay Attention to Test Details

Oct 7, 2010 by

Students lose SO many exam points because they just don’t read the directions and pay attention to details.  On the first exam, they usually discover this … but they don’t REMEMBER it for the other exams.

This is a very simple exercise that takes about 1 minute at the beginning of the test.

Just have the students repeat after you:

I promise … to read all the directions … for all the problems on the exam …

And if I finish early, … I promise … to RE-read all the directions … to make sure I haven’t missed some detail … or forgotten to come back to some question I skipped.

I understand that … it is not important to finish quickly … it IS important to demonstrate what I know … and once the points have been lost … the points cannot be regained.

Believe it or not, this results in a remarkable number of students that stay until the bitter end, making sure that they have been careful and answered every question completely.

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Can we Teach Students to Understand Math Tests?

Nov 22, 2009 by

A few weeks ago, I gave a test where the grades were less than stellar. Whenever this happens, I try to sit down and reflect on whether the poor test grades were a result of something I did differently in class, a poorly written test, or a result of poor studying habits. After careful reflection and analysis of my own, I was pretty sure that this was the result of lack of studying (a theory which was verified … later in this blog post).

I was dreading the task of passing back these tests and prepared myself for an onslaught of questions aimed at trying to discredit the test (or the teaching).  Then I got one of those great last-minute ideas that come to you right before you walk in to face the students.  Maybe I should let them “pick apart” the test BEFORE they see their own tests.  The class in question is Math for Elementary Teachers (MathET) and I figured that a detailed test analysis would not be an inappropriate topic for us to spend class time on.

First, I made some blank copies of the test (enough for each group to have one).  I also created a handout with every single learning objective and assignment that I had given the students for each of the sections on the test (these are all available in their Blackboard shell, but  I compiled these in a paper-based handout that was 3 pages single-spaced). Here is what one section looked like:

5.1 Integers
• Describe operations on signed numbers using number line models.
• Demonstrate operations on signed numbers using colored counter models.
• Explain why a negative times a negative is a positive.
• Add, subtract, multiply, and divide signed numbers (integers).
• Know the mathematical properties of integers (closure, identity, inverse, etc.)
• Complete #1, 3, 7, 9, 15, 17, 19, 21, 23, 25, 37
• Be able to model addition, subtraction, and multiplication of signed numbers using a number-line model
• Be able to model addition, multiplication, and division of signed numbers using a colored counter model (why not subtraction? because subtraction is really the addition of a negative – treat it so)
• Read the blog posts about why a negative times a negative is a positive and be able to paraphrase at least two arguments in your own words.
• Study for your Gateway on Signed Numbers (be able to add, subtract, multiply, or divide signed numbers)
• Play with Manipulative: NLVM Color Chips Addition
• Play with Manipulative: NLVM Circle Game

When we met in class, I counted the class into groups of 3 students each. Each group received a copy of the learning objectives & assignments (by section) and a blank copy of the test. All of these were un-stapled so that the group could share and divide up the pages as they wanted.

Task #1: Look at all the objectives and assigned tasks/problems. Determine where these objectives, tasks, and problems showed up on the exam. (20-30 min)

Objective: Make the connection between what I tell them they need to learn/do and what shows up on the test.

Task #2: What didn’t show up on the exam? We discussed why these objectives might have been left off (for example, maybe it was not something that I emphasized in class) (5 min)

Objective: Make the connection between what is likely to show up on an exam and what is not likely to show up (with the caveat that any of the learning objectives are really fair game).

Task #3: Make a chart that shows how the points for each test question were distributed between the sections that were covered on the exam. We then compared the results from each group and compared these results to my analysis of the point-distribution for the test. (5-10 min)

Objective: Clearly see that it is necessary to study ALL sections, not just a couple of them.

Task #4: I passed back the individual tests. Each student was given three questions to answer as they looked through their tests. 1. Where were the gaps in your knowledge? 2. What mistakes should you have caught before turning in your test? (read directions more carefully, do all the problems, etc.) 3. What can you do to better prepare for the NEXT test?  I collected these, made copies, and passed them back to the students the next class. (10 minutes)

Objective: Take responsibility for your own studying.

It was here that students surprised me by being honest on Question #3. Most of them confessed that they had not studied at all, but now realized that they needed to start studying. I cannot help but wonder whether I would have gotten the same result if I had simply passed back the tests with no analysis.

Task #5: At the same time the students were looking over their own exam, I passed around one more blank copy of the test and asked students to write their score  for each problem (no names) on that problem so that we could see what the score distributions looked like.  When this was done, I placed the pages on the document camera one-by-one so that they could see the scores problem by problem.

Objective: To show the students that for many questions, students either get the question almost completely right, or completely wrong (you know it or you don’t).

Task #6: We had already covered the first section of the next unit, so I had the students begin a set of “How to start the problem” flashcards. On the front of the flash card, they wrote a “test question” for the new unit. On the back of the card, they wrote some tips for starting the problem and details they might otherwise forget.

Objective: To begin to see tests from the perspective of a test-writer instead of a test-taker.

Take-home assignment: I told each student that they must come to the next test with at least 5 flash cards per section (35+ flash cards). I suggested that a great way to study would be to swap cards with each other and practice with someone else’s questions. I checked to see if they carried through (although I assigned no consequences if they didn’t). All but two carried through. Anyone want to guess how those two fared?

Results: I just finished grading the latest test (signed numbers, fractions, and decimals – not easy topics), and the test results were almost all A’s and B’s (instead of C’s and D’s on the previous test). Most students left the test with a smile on their face, and several finally got the “A” they had been trying for all semester.

Three questions for you, my busy and wise readers:
1. Will the students persist in better study habits now? For example, will they study like this for the next exam?
2. Would this detailed test analysis have had the same effect if the class hadn’t just crashed & burned on a test?  (i.e. is it necessary to “fail” first)
3. Was this a good use of class time? Would it be good use of class time in a different math course, like Calculus?

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How to Study for a Math Test

Nov 3, 2009 by

The Fall 2009 Calculus class at Muskegon Community College was tasked (by me) with learning how to study for a math test and then making presentations or videos to help other students.

how_to_study_for_a_math_test_thumbnails

The students started by doing their own Internet research, and then were placed in groups of 3 to focus on a particular topic. Each student was asked to interview a math instructor as part of the project to find out the details of the particular study strategy they were assigned.

Their projects generally fall into three categories:

  • General Organization, Note-taking, and Time Managment
  • Specific Study Strategies that can be used
  • Managing Stress so that you have a good test-taking experience

All of the projects can be found on their website: How to Study for a Math Test.

how_to_study_for_a_math_test

It’s a nice resource written by students for students, and I hope that many of you will pass it on to your classes.

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Math Study Skills Evaluation

Mar 10, 2009 by

Last week I was in Denver for a 1-day math conference and one of the speakers was Paul Nolting (who has written several books about math study skills).

One of the resources that he passed along to us was an online Math Study Skills Evaluation.  Paul suggested that rather than discussing a bad test during office hours, you have the students take the survey and bring the printout with them for discussion during office hours.

Although the survey printout refers to specific pages in Paul’s book, Winning at Math, it also tells the students a bit about why this particular behavior might be causing problems.  Here is an example of the results:

Winning At Math Survey Results

Especially for those of us that teach developmental math courses (although good for any student that is struggling), this survey would be a great activity to do right after the first exam.  Our students often focus on not being “smart enough” to do math, and this should bring the focus to the student not having the appropriate study skills.

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