To those who have submitted some variation on the theme of, “C’mon, it’s isn’t that bad” or “I’m not distracted by the uselessness of the jerseys,” I say, yeah, I’m in total agreement, except it isn’t about us. Our tolerance is ever so much higher than theirs. And nothing is neutral. If it doesn’t add to the problem, it subtracts.

I’d like to highlight the line Matt McCrea has been repeating throughout this thread: that the jerseys are an implicit admission that numbers are not fun or interesting on their own.

Matt: Number patterns are a beautiful mathematical topic on their own, and if they are to be assessed, then it’s best to just leave them on their own instead of trying to force a context.

and later:

Matt: Why bother with a context? Just test the concept on its own, and don’t kid the kids out of the chance to realize that sometimes, math for math’s sake isn’t a bad thing.

That you can’t enjoy math for its own sake is one of the two sad, false signals pseudocontext sends our students.

In all honesty, are you able to find a genuine context for “factors?” In my thoughts, I’ve only been able to come up using factors in the context of making division easier to compute and prime factors, but of which are abstract concepts. In that case, why bother with a context? Just test the concept on its own, and don’t kid the kids out of the chance to realize that sometimes, math for math’s sake isn’t a bad thing.

1) my guess on the “what were they thinking” line is that they wanted to separate the numbers from one another visually. This can actually be helpful with certain learning differences. The shirts put a contextual “box” around each number, thereby physically and visually separating it from its neighbors. Why the shirt instead of an actual box…? I have no idea.

2) a lame attempt at giving the problem a context in which shirts with numbers on them makes sense: The math club at Anywhere Middle School made shirts for each team member. If these are the shirts pictured below, what is the name of the team? a. “The Odd Numbers”, b. “Greater Than 20”, and so on…

It’s still completely lame, but the shirts now make sense in terms of the question being asked. It’s not a retribution though, as there really is no reason why this problem needs to have shirts in the first place. This is why test and textbook designers should not have unrestricted access to clip art.

The inch problem assesses the ability to convert measurements more than testing and understanding of factors/multiples.

Neither of the questions proposed uses the term “factor” or “multiple”. I think it is understanding these terms (along with even/odd, greater than/less than) that the question was trying to assess. I see the question assessing the ability to choose an accurate description of a set of numbers using mathematical terms.

“You have 90 tickets to give out to your friends. You want each friend to receive the same amount of tickets, and you don’t want to have any left over. Which could be the number of tickets you give each friend? 12, 24, 30, 60”

I know it’s subtle, but the information and setting is half the battle in setting up problems.

Which of these measurements is equal to an integer number of feet: 40 inches, 50 inches, 60 inches, 70 inches?

You gave 90 raffle tickets to some friends. Each friend received the same number of tickets, with none left over. Which of these could be the number of tickets each friend received: 12, 24, 30, 60?

I’m sure others could do better. The first requires kids to additionally know there are 12 inches in a foot, and the second is maybe pseudocontext-ish, but they assess the right skills.

I actually like the shirt problem’s question and choices, but the potential for student error and confusion needs to go. If the shirts weren’t there, and it was just the numbers, it would be fine.

Is it not possible for a team to have jerseys with numbers that happen to be able to be described as a factor or multiple of another number? When I look at winning lottery numbers, I look for these types of relationships all of the time. No, it doesn’t always happen, but it is interesting to me to see if there is a relationship at all.

Honestly, I don’t see the jerseys as distracting. While they may not be the best context, they make the question look less threatening while allowing the numbers to be larger and to be separated by more space. This gives students the opportunity to consider each number separately, rather than gloss over them in a list. If they were just shown in a list, how should they be shown–from greatest to least, least to greatest, random order? If random, wouldn’t that be distracting?

I’m curious, how would you assess student understanding of factor and multiple in a real context in a multiple-choice format? (This question was taken from a state test and, unless you want to see money available for schools drop even more, state tests will have to stay in multiple-choice format.)

The context here is derinitly unnecessary and offputting and may introduce bias into the resposnes, depending on the students’ particular feelings about sport. Some anxiety may be induced by the clearly nonesensical selection of numbers – what sport has this sort of number?

The original comment I have to agree with – we should assume and encourage a fascination with numbers in and for themselves, not dress them up in odd contexts in order to moitivate.