Where we left off, the reliability was unacceptably low for our measure to assess students knowledge of sad iconmultiplication, division and other third and fourth grade math standards. We were sad.

One person, whose picture I have replaced with the mother from our game, Spirit Lake, so she can remain anonymous, said to me:

But there is nothing we can do about it, right?I mean, how can you stop kids from guessing?

mother from game

This was the wrong question. What we know about the measure could be summarized as this:

  1. Students in many low-performing schools were even further below grade level than we or the staff in their districts had anticipated. This is known as new and useful knowledge, because it helps to develop appropriate educational technology for these students. (Thanks to USDA Small Business Innovation Research funds for enabling this research.) 
  2. Because students did not know many of the answers, they often guessed at the correct answer.
  3. Because the questions were multiple choice, usually A-D, the students had a 25% probability of getting the correct answer just by chance, interjecting a significant amount of error when nearly all of the students were just guessing on the more difficult items.
  4. Three-fourths of the test items were below the fifth-grade level. In other words, if you had only gotten correct the answers three years below your grade level, the average seventh-grader should have scored 75% – generally, a C.

There are actually two ways to address this and we did both of them. The first is to give the test to students who are more likely to know the answers so less guessing occurs. We did this, administering the test to an additional 376 students in low-performing schools in grades four through eight. While the test scores were significantly higher (Mean of 53% as opposed to mean of 37% for the younger students) they were still low. The larger sample had a much higher reliability of 87. Hopefully, you remember from your basic statistics that restriction of range attenuates  the correlation. By increasing the range of scores, we increased our reliability.

The second thing we did was remove the probability of guessing correctly by changing almost all of the multiple choice questions into open-ended ones. There were a few where this was not possible, such as which of four graphs shows students liked eggs more than bacon . We administered this test to 140 seventh-graders. The reliability, again was much higher: .86

However, did we really solve the problem? After all, these students also were more likely to know (or at least, think they knew, but that’s another blog) the answer. The mean went up from 37% to 46%. 

To see whether the change in item type was effective for lower performing students, we selected out a sub-sample of third and fourth-graders from the second wave of testing. With this sample, we were able to see that reliability did improve substantially from .57 to. 71 . However, when we removed four outliers (students who received a score of 0), reliability dropped back down to .47.

What does this tell us? Depressingly, and this is a subject for a whole bunch of posts, that a test at or near their stated ‘grade level’ is going to have a floor effect for the average student in a low-performing school. That is, most of the students are going to score near the bottom.

It also tells us that curriculum needs to start AT LEAST two or three years below the students’ ostensible grade level so that they can be taught the prerequisite math skills they don’t know. This, too, is the subject for a lot of blog posts. 

If you’re a teacher (or parent) and you’d like students to take the test for practice, you can see it here

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For schools who use our games, we provide automated scoring and data analysis. If you are one of those schools and you’d like a report generated for your school, just let us know. There is no additional charge.

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