This semester has been a little different for me. I haven’t had too much grading to do. Why not? Well, I’ve been focused on helping students in class and seeing how they are doing.

Our building has also been using Study Island this school year. I have enjoyed using it because it is aligned to our standards . . . sort of. There are a few topics that either go a little further than what we need for testing (which isn’t a problem) or it is asking for the wrong information that we don’t need. Again, this is ok, I just have to teach a little more to help with the understanding.

What I really like about Study Island is that it is broken down by standard. So I can teach, then have students jump on there and take an assessment. I can tell the students how many questions to do, ask them to try for a certain percentage, and strive to better themselves. If students don’t get the percentage they like (I have a few who want 90% on every topic), they can go back in and try again.

That leads me to allowing standards based grading in my grade book. I can look and see how students are doing and then post that grade. I can also see what problems students have missed and know how to help them out.

Now, this past week I did the old fashioned paper quiz. But I didn’t just give them percentages . . .

My Pre-Algebra classes are working on graphing lines. Last week we worked on finding choosing x values and placing them into an equation, finding the value of y, then plotting the points and drawing the line. (For those of you who don’t understand what I’m talking about, bare with me.)

Here’s an example:

Suppose the equation is y = 2x – 4

First the student had to choose four x values. For my example I’m going to choose 3, 5, 0, and -3. Now, let’s substitute each of them into the equation and solve.

y = 2(3) – 4 –> y = 6 – 4 –> y = 2

y = 2(5) – 4 –> y = 10 – 4 –> y = 6

y = 2(0) – 4 –> y = 0 – 4 –> y = -4

y = 2(-3) – 4 –> y = -6 – 4 –> y = -10

That now gives us the points of (3,2), (5,6), (0,-4), and (-3,-10) to plot on the graph. After plotting the four points, the student takes a straight edge (ruler) and connects the points to create a line. I ask students to take the line all the way through the grid (easier to see) and draw arrows at both ends (which helps with the understanding that lines never end).

In my younger days of teaching, I would look at the line and grade it. 1 point if they tried and 1 point if they were correct. Thus making the problem worth 2 points.

WAIT! WHAT?!?!??! All that work for 2 points?!?!?!?!

This time each of the y values was worth a point (4 total), plotting each ordered pair was a point (4 total) and drawing the line with my criteria was worth 2 points (1 for going through grid, 1 for arrows), which gives the problem a total value of 10 points.

But wait, there’s more!

Again, in my younger days, if a student didn’t solve correct (example below):

y = 2(-3) – 4 –> y = 6 – 4 –> y = 2 (the error is dropping the negative sign in front of the 6)

So when they go to plot this point, they plot it at (-3,2) instead of (-3,-10). Many math teachers would count the student wrong for miscalculating AND count them wrong for plotting the wrong point AND count them wrong because then there isn’t a straight line to be drawn. THAT’S NOT FAIR! They would fail because of ONE error.

How I grade now is that this student lost a point for the miscalculation, but I look and see that they plotted THEIR point correctly (even though it isn’t correct for the equation) so they only lost the one point.

Now, in a perfect world, a student would notice that the point isn’t in line with the other points, so they would go back and try to find their error and fix it. However, that is a taught skill that I now realize I need to help the student with this week. However, for this quiz the student would receive a 9/10 points along with notes on their paper about what was wrong and what was correct. The younger me would have given a 7/10 (if they only made the one mistake) without notes of how to improve.

Another example of what I’m grading . . . .

Other classes were looking at central tendencies (mean, median, mode) and range this past week. On the state assessment students are not allowed to use calculators. Ok, on the median (rearrange the numbers from least to greatest and find the number in the middle) and mode (occurs most often) is easy to do without a calculator. Actually, how would you do those on a calculator? Well, I guess you could put them in a spreadsheet and then order them . . . . . sorry for the tangent.

However, when dealing with the mean (average) of data, there is some work to be done. Again, let’s look at the following:

Find the mean of the high temperature of the last 7 days.

46, 59, 51, 49, 39, 51, 36

So the first thing you have to do is add these numbers up. 46+59+51+49+39+51+36 = 331, then we have to divide by 7 because there are 7 numbers. 331/7 = 47.29.

Now I allowed students to use a calculator on the quiz. Why? Because I know my students can add and divide. That’s not what I was testing them over. I was testing to see if they knew what the word “mean” meant and then if they understood that they need to add all the numbers and divide by how many they have. Btw, some students still struggled with what to do and some still miscalculated (sometimes they miss a number or hit the wrong number). However, I am able to know the difference and know how to help them out.

I’m not grading to know if they can add or divide (their previous teachers did that and I can see in daily work that they can do that), I’m grading on understanding of concepts.

I get frustrated with state assessments because they feel that students should be able to do everything without a calculator. How do “real people” in the “real world” solve these problems? WITH A CALCULATOR OR IN A SPREADSHEET!!!!

In fact, the standards state that students need to find the central tendencies of data with up to 30 numbers in the data. THIRTY NUMBERS?!?!??!?!

Find the mean, median, and mode of the following numbers.

3, 54, 72, 4, 85, 12, 53, 95, 6, 3, 5, 54, 74, 83, 83, 6, 21, 43, 96, 65, 32, 5, 2, 74, 83, 54, 12, 43, 54, 5

How many of you just freaked about because now you have to order these numbers to find the median.

2, 3, 3, 4, 5, 5, 5, 6, 6, 12, 12, 21, 32, 43, 53, 54, 54, 54, 54, 65, 72, 74, 74, 83, 83, 83, 85, 95, 96

the median is 53

And then I have to find the mode, which is kind of easy because they are all put together.

the mode is 54

But now I have to add all of these numbers and divide by 30! Yea, that’s not happening. I think I’ll just choose answer D.

That’s what kids do.

Now, how many of you noticed that I forget one of the 43s when looking for the median? Yea, so my median is actually 48, not 53. (I did that on purpose)

What are we testing and grading?

How do you grade and give assessments?

What can we do to help encourage change?