One Week Down

As I mentioned before I am started a new job this school year. The Sycamore School is a pre-school through eighh gradet gifted and talented school. I am teaching the fifth and sixth grade pre-algebra and the seventh and eighth grade Geometry classes. It was an amazing first week. I was told that the kids would constantly surprise me with what they know and the question's the ask. I must say they were entirely accurate. Here are some highlights:

• A 7th grade Geometry student was able to prove the square root of two is irrational. I didn't learn this until graduate school and I would imagine many of you have never done it.
• A 5th grader aced the pre-algebra pretest.
• A great dialogue in my 7th grade Geometry class about the definition of skew lines. In general skew lines are not very interesting, but, through their questions we were able to learn a lot about the importance of rigorousness in our definitions.

Professionally it has really challenged me. In my previous teaching assignments I have been able to, how shall I say it...fly by the seat of my pants? Not always, or even most of the time, but if I chose not to spend the time preparing, I could usually come up with very effective lessons on the fly. I am not able to do this at Sycamore. I have to have all my i's dotted and t's crossed as well as spending time considering ways to deepen the discussion beyond what is usually presented in a math class. I love it and am anxious to continue to pursue this challenge.

One of the issues with my new position is it is a long commute and a considerable amount of work. This will make it more difficult to continue to web activities, but I plan on building time into my schedule to continue them as I really enjoy it.

I hope all of you have had a great start to the school year!!!!

Grade Systems Part 4 - Testing

There were many things that bothered me about the structure of my undergraduate education program. One of those was that I was given no information on best practices in testing. Evaluating student performance is a vital component of every classroom. This happens in many ways and has many different names. Formative and summative assessments are two of the more recent names that have been applied to evaluating student learning. There are many things to consider when evaluating students.

• What types of questions should I write?
• Is it OK to use multiple choice? If so, when and how many?
• Should students be asked to explain their answers in a math class?
• How much should each question be worth?
• Should I give partial credit or not?
• How much of the test should be basic skills and how much should require higher order thinking skills?
• Should my tests be summative or formative?

The chair of the board of directors at my new school told a story that I think is important for educators and for this discussion. His son was reading a book that had a genie and the ensuing wishes in it. The son asked, "Dad, what would you ask for if you were given one wish?" The dad said he didn't know and turned the question back on his son. The son responded, " at first I thought I would ask what the meaning of life is, but then I thought maybe that is not the right question. So instead I thought I would wish to know the right questions to ask."

I think a big part of writing tests is about asking the right questions(not just the ones on the test). What are some of the questions that you think need to be answered by someone writing a test?

Intermission: An Lament On Teaching Math

I recently read Paul Lockhart's essay "A Mathematician's Lament" that was published at The Mathematical Association of America Online. It is the best description of the issues that many see in math education that I have come across. On the surface I agree with much of what he discusses. I absolutely agree that discovering math is better than being told it. I believe that the current "ladder" curriculum is weird and disjointed and I agree that most math teachers(me included) are not really qualified to teach math.

But here is the rub and there is really no way to get around this. This essay is idealistic to a point that it is never going to be applicable in any mass educational system. There is one question I have for the author. Why, when I was actually taught by mathematicians, did they teach their class exactly opposite to what you are describing? I understand that I couldn't expect this type of teaching in my K-12 classes and maybe not even in undergraduate, but when I entered graduate school the teaching and lecturing was worse than anything I had experienced up to that point.

With that in mind, I still think it is an excellent read for any math teacher/aspiring math teacher. Found within the idealism are some very good points about teaching math. The most important, though not explicitly mentioned, is that the goal of a math teacher should be to teach students how to learn math, not to teach the math itself.

I will continue my grading systems series this weekend. I wanted to comment on the essay while it was still fresh in my mind.

Grading Systems Part 3a - Homework

This is part three to a series of posts on grading. Part one dealt with percentages and part two dealt with grade weighting. As I have mentioned before, I know that I do not have all the answers on these topics. My goal is to present some of my ideas and then to hear some thoughts of other teachers. So please feel free to let me know what you think in the comments.

I have actually used five different methods of dealing with homework. Let me give a quick recap of each of them.

• During my student teaching I taught Pre-calculus. The teacher I worked with assigned homework everyday. The interesting thing is he never picked it up or even checked to see if it was completed. We went over it and by the questions the students asked the clearly did it. The students entire grade came from tests.
• Also during student teaching I worked with a different teacher who taught Pre-algebra. He also assigned homework everyday and never checked the assignments. What he did was give a homework quiz everyday. These quizzes usually involved problems on the homework as well as problems not on the homework.
• During my first two years of teaching I generally checked the homework for completion. I would occasionally give homework quizzes as well. I usually allowed students to turn in homework late for half credit.
• While in graduate school I taught a class that was comparable to Algebra 1/Algebra 2. We were asked to pick up and grade all of their homework assignments(we met everyday). I always tried to have them graded before the next class and I picked up the homework after going over it. The grade was out of 10 points. I would give them 5 points for completion and randomly pick 5 questions to grade.
• Last year I used a combination of grading the homework and giving homework quizzes. I had more trouble grading the assignments in a timely manner because I had a 100+ students versus 20.

In general I think all of these systems had value. My goal with homework is very clear and two-fold.

1. It gives the students to practice problems on their own. Practicing is an essential part of learning math.
2. It is used as a catalyst for reteaching the material the next day. Every homework system needs to foster discussion of the problems the next day. This gives a chance to answer questions, review the material and occasionally teach to students who missed the previous day.

Which of the systems best accomplishes the afore mentioned goals? I am not sure...I want to think about it a little more and talk with the other teachers about my school before I decide what I am going to use in my class this year. I will revisit this post next week. Until then I would love to hear how you deal with homework in you class.

Grading Systems Part 2 - Weighting

From my first year of teaching I have always placed weights on the different categories of graded work in my classroom. For example this year, though not by choice, my weights looked like this:

70% - Tests

20% - Quizzes

10% - Everything else

I was not a fan of this weighting system because I thought it devalued responsibility (we also allowed retests). But I believe a system that weights the grade categories is the most appropriate. As I was going through school I was always amazed at how "fly by the seat of the their pants" teachers were with their grading system. What I mean is they seemed to randomly assign points and then they would add up the points and divide by the total to see what the grade was. The problem with this method is that from grading period to grading period the grade represents something different. Also it is much more likely that one category will dominate the grade. Often this leads to homework being overvalued, which I think is a problem.

Here is a few things I believe:

• The majority of the grade should be knowledge/skill based. The grade should be an accurate representation of what a student knows.
• Homework and responsibility should play a minor roll in a students grade. The grade should also represent a student's probability of success at higher levels. Hard work and responsibility are key to success(especially in math classes) as students reach harder classes.
• Behavior should play no role in a student's grade.

So the question is, what is the appropriate percentages?

Grading Systems Part 1 - Logic and Percentages

This is part one of a series of posts on grading students. Last year during a professional development seminar my former principal starting discussing perceived inequities in grading systems. He rambled on about an F being worth 50% and 5 point grading scales. I attempted to follow what he was talking about, but failed to understand its relevance to my(or any) classroom. Recently, I ran into an article describing exactly what he was talking about. I finally am starting to grasp the issue that lead to the faulty conclusions discussed in that article and by my principal.


The general problem is when teachers arbitrarily assign a letter grade to an assignment and then try to convert it to a percentage. Thus what happens is a D is worth 60% and an F a 0%. The article is correct, this does not make sense. The problem is the use of a letter grade as the initial grading system and then trying to convert this into a number. This problem does not include the more common practice of converting a numerical grading system to a letter grade. Thus for most math classrooms this article should not apply. Math lends itself to figure all grades in terms of percentages. Then when grades are reported letter grades are assigned to those percentages. Here is the statement I am referencing from the article.

Their argument: Other letter grades — A, B, C and D — are broken down in increments of 10 from 60 to 100, but there is a 59-point spread between D and F, a gap that can often make it mathematically impossible for some failing students to ever catch up.

The problem with this is they are incorrectly viewing the problem. There are two sets, passing and failing. Failing is from 0-60 and passing is from 60-100. Now the other letter grades give the student, parent, school and college exactly how well they are passing. Now if they want to make an argument that failing should be 0-50 and passing from 50-100 that is fine, but the argument that 50% should be a minimum failing number is weird and doesn't make sense. If you want to do that then work off of a 4 point grading system.


However, I am not sure I logically agree with a 0 to 4 scale. My problem is that it doesn't distinguish well between a student that is almost passing and one that isn't close. This is an important distinction to make. Not because it matters on their report card, but from a teaching perspective. When I grade something I need to be able to quickly determine the skill level of each student. I am digressing though because, as I said before, this doesn't apply to a math classroom. Math lends itself to total points and percentages.


As you can tell I disagree with the ideas put forth in this article. They are born out of a desire to pass more students and are disguised as a self esteem booster. It always amuses me when schools attempt to dictate grading systems to their teachers. In a classroom it is always possible to manipulate the system so the grades look like you think they should. I think in general schools spend way to much time looking a the grading and numbers involved with failing students. At my last school our failure numbers were monitored. If they were too high then you were going to here about it. Accordingly many teachers lowered standards.

In my mind the best way to grade a student is using point totals and percentages. Letter grades are only useful as communication tools to parents, students and colleges. All assignments should have number values associated with them. A much more difficult question is, how do I determine what number represents a minimum competency in my classroom? This question is not asked nearly often enough.

Eighteen Days and Counting!

As I mentioned earlier I am starting a new school this fall. The first day for students is August 18th. This will be a completely new experience for me as I will be teaching middle school instead of high school. Also my new gig is at a gifted and talented school private school, which I suspect will be a much different teaching environment from the public schools I have taught at in the past.

Anyway, it is time for me to start considering the norms that I want to establish in my classroom. There are many different things that I need to consider.

• Discipline
• Homework
• Presentation Style
• Organization of Students Work
• Group work
• Seating Chart and Desk Arrangement
• Communication with Parents
• Website
• Grading Structure
• Retesting Policy

I am sure there are others but those are the ones that immediately came to mind. I am going to spend some time the next couple of weeks discussing these topics. Some of them (Discipline, Grading, Retesting) I will delay until I learn more about how the other teachers at my school handle them. I have always thought it was important to try and follow the norms at my school as much as possible.

Per usual I am very interested in what others think of these topics. Check back the next couple of weeks and let me know how you handle these in your classroom. Most of what I do in my room has been stolen from those around me.