Content Versus Formal Equivalence and SMARTResponse XE

I remember getting my Response XE’s for the first time and not even looking at the user manual that came with it. Big Mistake!

There is one page that anyone with Response XE needs to be familiar with and that is the page on Exact match, Formal Equivalence and Content Equivalence.

What sets SMARTResponseXE apart from the other response units, is not just the fact that students can enter formal mathematical language, but that teachers can set math equations to be graded with what is called Intelligent Grading, meaning that you can choose how SMARTResponse reacts to various ways that students may interpret and enter data.

The options available are…

  • Exact Match – Students must enter exactly what the teacher enters
  • Formal Equivalence – Students may enter same terms and operators in any order
  • Content Equivalence – Response will accept “all” mathematically equivalent answers

I wrote “all” in bold italics because ResponseXE does not accept fractions and decimals as mathematically equivalent which used to be a problem. To counter that, I basically tell students ahead of time which format I will accept and they tend to comply so it’s technically a non-issue. However, that is something that I would like to see TPTB @ SMART address =)

The biggest quetion that I have gotten is when to use formal and when to use content equivalence. The photo below is a look at how Response interprets the same problem both ways.

What you don’t see is what I entered as the answer. I told the software that the answer should be 6(x-1).

The instructions were to simplify and content equivalence will accept ANY response as long as it is mathematically correct. So in essence, students can still have a correct answer even though they didn’t simplify. Honestly, I tend to never use content equivalence unless simplification is not an issue.

With formal equivalence, students only receive credit if their answer is in simplified form as I have entered into the software. With that said, this will only work IF you make it clear to students what you are looking for in an answer.  Notice that 75% of my students would have had a correct answer had I entered 6x-6 as the answer versus 6(x-1)…which I have seen written both ways on state assessments.

So, If you have SMARTResponseXE or are planning to make a purchase, the moral of this story is to read the manual and make sure that you have a pretty good understanding of what is accepted as possible student responses before you set your answers and allow students to enter.


Leave a Reply

Your email address will not be published. Required fields are marked *