Month: September 2017

A Quick Question about Test Questions

One of the classes I teach is a non – AP Calculus class. Many of my students are showing a reasonably firm grasp of the ideas of Calculus that we are studying, but they are plagued by algebraic struggles and fears at times. I was thinking about the following two ways that I could ask them the same question:

I asked this class today how they would feel about these two forms of the question. Most of them quickly agreed that they would feel more comfortable answering question B than question A. I followed up by asking whether success on question A might feel more like success and a handful agreed that this probably was true. I am not sure what to make of this informal poll and I am bouncing this idea around in my head. I’d love to hear what you think and push back with some questions about my motivations/hopes in (possibly) restructuring my assessment in this direction.

P.S.

I have been urging them to have GeoGebra open nearby when they do their work so that they can look at graphs and ask for derivatives to verify their own work.

Checking in on a new Policy

I recently blogged about a commitment made by our math department. As a reminder to you, dear reader, here is the statement from one of my course syllabi:

Beginning in the 2017 – 2018 academic year, our math department is adopting a policy of expecting test corrections on all in-class tests. The policy is described below.

  • When grading tests initially each question will get one of three point assignments
    • Full credit for reasonable support work and correct answer.
    • Half-credit for minor mistakes as long as some reasoning is shown.
    • Zero credit (in very rare cases) when there is no reasonable support shown or if the question is simply left blank.
  • When grading tests, I will not put comments, I will simply mark one of these three ways.
  • You will be allowed to turn in corrections. Corrections will be on separate paper and will have written explanations of errors made in addition to the correct work and answer. This work is to be in the student’s words but can be the result of consultation/help. These corrections will always be due at the beginning of the second class meeting day after the assessment is returned. You will return your original test along with your correction notes. I will remind you of this every time I return a graded test to you.
  • It is not required that you turn in test corrections.
  • The student can earn up to half of the points they missed on each individual problem.
  • This policy does not apply to quizzes, only to in-class tests.

There are  a couple of items in the learning curve to report on here. I will lead with the positives –

  • We have an after school conference time that many students take advantage of for extra help. My room has been more crowded this year than it has been for years. I take this as a plus sign that students are committed to seeking help and investing in their math studies. Many of them are there talking with me and with their classmates about test corrections.
  • I have had a number of students turn in their corrections the same day that they received their tests. It is a rare thing for students to turn in work days early, it is happening regularly right now.
  • I walked out of my classroom today with a new student who was talking excitedly about how she is really thinking carefully about her work and she is sure that she’ll remember material better because of this.
  • It is faster to return tests since I am simply marking them 100%, 50%, or 0% for each problem.

Now a few negatives, followed by some philosophical pondering about this whole endeavor.

  • I anticipated that there would be very few zero scores on problems. There have been more than I thought but I hope that is a factor of students learning to show some work. This may be a positive as a zero stings a bit and they may be more inclined to be careful in their explications.
  • Some students feel stung by relatively minor mistakes that initially result in a 50% on an individual problem. These minor mistakes turn into 75%. I am trying to point out that relatively major mistakes can also end up at the 75% level but some students feel a bit cheated.
  • Early in the year averages fluctuate quite a bit anyway, but the fluctuations are exaggerated in this system. I see already that overall averages are a bit higher than normal and there is much less variance in scores. However, some students are scared since they have a hard time seeing the long game as clearly.
  • Explaining this to folks outside the department has been a bit of a challenge.

 

When I was working on my doctorate I had a professor (my thesis advisor) who had a policy that every paper will be rewritten, not just every paper can be rewritten. The way he did this was to return our first drafts with no comments, just hash marks in the margin at certain points of the paper. These hash marks might be there to point out a flaw in our argument or our paper’s structure. They might also indicate a highlight. They might indicate a misspelling or a simple grammar problem. He was willing to discuss these hash marks in his office hours as long as it was clear that we had sound questions about them, in other words we had to prove to him that we had reflected on our writing. I have never thought so much about my own writing as I did in that class. I do not expect my 14 year olds to do this kind of self analysis, but I know that they ARE capable of careful reflection if they are given the time, space, and motivation to do so. What I am seeing when they come to me is that they have looked over their test, they have referenced notes and their HW. They have done careful thinking and they can usually explain their mistake on their own. This is not universal, but it is happening more often than not. Many students who come to my room to work on corrections have almost no question for me. They are berating themselves for ‘stupid mistakes’, they are laughing at silly things they wrote, they are even saying ‘I have no idea what this work means’ I am pretty convinced that this can be a huge growth opportunity for my students. They are being responsible for their own error analysis here and they are writing thoughtful reflections in the form of ‘On problem 4 I made this mistake, I should have done this instead’

We have midterm grade comments looming and as department chair I know I will have some questions coming my way about our reasoning and the long-term impact on grades. I will try to steer the conversations to long-term impact on learning and self-sufficiency. So far the policy has exceeded my hopes in my classes. I will be checking in with my department to get other points of view soon and I plan on sharing some of those conversations as well.

 

Should My Preferences be my Students’ Preferences?

At the beginning of every year I am reminded that there are little quirks I have about how I would like to see answers presented and I have this silly assumption that my brand new students should just know what I want. I wish that I remembered this in August and prepped myself and my students with some conversations. I am writing this brief post this morning while one of my classes is taking a test. I would love some feedback here in the comments or over on twitter where I am @mrdardy

I just graded my first problem set from my AP Calculus BC wizards. One of the questions asked for the point on the curve y = x^(1/2) that was closest to the point (4,0). Everyone correctly identified x = 3.5 as the critical x value and about half of them identified (3.5)^(1/2) or sqrt(3.5) [my LaTex skills are weak and I am in a bit of a hurry…] as their y-coordinate. However, about half of them gave me a three decimal approximation. For reasons I cannot completely justify it makes me nutty to see a less exact answer written as an extra step in their work. I know that their science teacher is not interested in radicals in their answers. I know that carpenters do not have radicals on their measuring tapes. I also know that all of my Calc BC kiddos had the exact value for y written at one point in their solutions and many chose to do a little extra writing to make their answer less exact. Am I being a crank if I make this a point of conversation? Along the same lines, I urge them not to rationalize but many cannot help themselves. I urge them to leave a line equation in point-slope form when that is one of the steps in their problem-solving process. I ask them to write x < 3 rather that 3 > x, especially in a piecewise function where I want to read through their domain in order.

These are tiny, tiny problems to focus on. I recognize this. But I also know that I will spend many months with this group of students and I want them to understand my thoughts since I am asking them to routinely explain theirs on paper to me. I would love to hear points of view about how important any of these habits are for kids of this caliber. I am completely open to recognizing that these are just weird little quirks of mine, but I also hope that there is some mathematical logic underlying all of this. Please drop a line to let me know what you think and how you have responded to students in your efforts to help them develop a clear and consistent strategy for communicating their mathematical ideas.

Test Corrections, Round One

I mentioned in an earlier post that our school’s math department has adopted a new policy this year. After our spring workshop with Henri Picciotto (@hpicciotto) one of the decisions we arrived at was to allow (almost require) test corrections from students. The goal was to encourage and reward reflection and communication on the part of our students. When I wrote about it originally Brian Miller (@The MillerMath) told me he would hold me to my vow to report back on this. Here is round one’s report.

First, I should remind everyone reading this what our new policy statement is. Here is what my students read on their syllabus this year.

Beginning in the 2017 – 2018 academic year, the math department is adopting a policy of expecting test corrections on all in-class tests. The policy is described below.

  • When grading tests initially each question will get one of three point assignments
    • Full credit for reasonable support work and correct answer.
    • Half-credit for minor mistakes as long as some reasoning is shown.
    • Zero credit (in very rare cases) when there is no reasonable support shown or if the question is simply left blank.
  • When grading tests, I will not put comments, I will simply mark one of these three ways.
  • You will be allowed to turn in corrections. Corrections will be on separate paper and will have written explanations of errors made in addition to the correct work and answer. This work is to be in the student’s words but can be the result of consultation/help. These corrections will always be due at the beginning of the second class meeting day after the assessment is returned. You will return your original test along with your correction notes. I will remind you of this every time I return a graded test to you.
  • It is not required that you turn in test corrections.
  • The student can earn up to half of the points they missed on each individual problem.
  • This policy does not apply to quizzes, only to in-class tests.

The first class to have a test this year was my AP Calculus BC class. This class has sixteen students of the highest math caliber at our school. They had a test in class on Tuesday and on Tuesday night I marked those tests. On a number of occasions I had to restrain myself from circling something or writing a note to a student. I went through and only marked each question as a 0, a 5 or a 10. There were six questions, so I graded 96 questions overall. Only one 0 out of all these 96 questions. Thirty four questions earned half credit and the other sixty one questions earned full credit. Of those thirty four, most mistakes were minor and in the past they would certainly not have suffered a five point penalty, but in the past they would not have had the ability to earn back points and they would not have had the motivation to think clearly about what happened. Due to quirks in our rotating schedule, the second class day after yesterday is not until Monday. However, I have six of my students in my room after school yesterday working on corrections. All of them spoke to me about problems and three of them were working with each other. Four of the six students there completed their corrections and turned them in already. This feels like success. I know that it is early in the year and students have a little more energy right now. I know that this is my most motivated (by knowledge, by interest level, and by grades) group of my four different class preps I have this year so I will not expect quite this level of engagement right away. Oh yeah, two of the students there yesterday only missed points on one of the six questions. The could have happily taken their 92% and gone home to worry about other work instead. I expect that I will see another one or two folks today and then get a slew of corrections in on Monday. The initial grading was a little bit faster and I could get them their tests back right away. Looking at the corrections will take a little time, but this is time I want to take and it is encouraging the kids to think about what mistakes they have made and (hopefully) not make those same mistakes again. I’ll keep updating on this experiment.