The main problem was how hard it was to make these tests. He could not just toss off a new one each semester, and they did get purloined/passed around.

]]>For example, a question like

*Two lines either intersect once or are parallel*

is a great argument starter in a classroom. Are two conincident lines really just one line? Are we in the plane or in space? Are we assuming the Euclidean axioms? This grey area is great for a classroom, but terrible on a test.

And asking for examples and counterexamples takes great mathematical sophistication, in both posing and evaluating. I think a fitting summary of my 50 or so posts evaluating the NYS Math Regents exams over the past several years is that this mathematical sophistication is terribly lacking in this process.

]]>It is during active class discussions that our students learn to use acceptable mathematical language and develop an understanding of mathematics. Thoughtfully crafted T/F, or “always true, sometimes true, never true” statements with or without prompts like “give an example, a counter example, justify, or explain” have helped me gauge students’ understanding on written assessments.

If well written, these types of questions could offer an alternative to the often unnecessary “Explain” that appear in some sample Common Core questions. ]]>

Nor do I feel compelled to somehow protect the promise of assessment. If these tests can’t deliver on the promises test-makers are making, then students shouldn’t be taking them and my employment shouldn’t be contingent upon them.

]]>My direct experience with open-ended questions on state assessments is that often vague ambiguous questions are developed by some testing company and students struggle to answer it even if they know the concept/skill. In the scoring and item review process, considerable time is spent determining how to evaluate unanticipated student responses. Of course open-ended should lead to a variety of student approaches. The problem is when students are unable to demonstrate their knowledge because the semantics are too confusing. Programmers all know what this phenomenon is called – “garbage in, garbage out!” Teachers need numerous high-quality model problems to use as a basis for implementing the Core. But many released items are not of this caliber. The rewrite of the question which I offered could be criticized for being multi-part but not really open-ended. I did that intentionally to provoke a reaction. Having done the same here in NJ while serving on various state assessment committees and receiving the same non-reaction is what I’ve come to expect. Generic discussions of the pros and cons of open-ended questions will not lead to improvement of quality. That will only happen when highly knowledgeable educators such as the respondents here attempt to write or rewrite their own open-ended questions assessing particular standards. Writing such high-quality questions is highly challenging but then the discussion becomes authentic… ]]>

As long as examiners are reading natural language explanations (ie, not going by multiple choice) why not just have the examinees write out their math solutions and score those?

btw, do we have sample answers with their scores from the test manufacturers?

]]>On the exam? I can see how it helps some learn to do mathematics, but if doing math is our goal should we not be testing exactly that?

Maybe I am too “old school”, but I think it dangerous (and hard to score!) to get away from testing the pure maths.

When do the scores come out? π

]]>My caution is that we must keep some balance in mind. If we push too hard for precision β or in assessment terms, reliability β we may sacrifice validity: actually assessing deeper thinking. (Or at least this has often ended up being the case with the constraints of finite budgets.) Certainly items should be good, but I worry about beating on them for absolute imperfections without keeping the relative tradeoffs in mind. Similarly, pushing for better items is in tension with releasing them each year (which is a great resource for teachers and students, but which means you have to make new ones for next year).

I entirely agree that having such items on the “big tests” is not “the whole game” – but itβs at least a start. Teachers definitely look at items from large-scale tests, and they influence instruction. The process should get scrutiny and be pushed to improve, but we should also ensure that we don’t set such a high bar that open-ended items are driven out, leaving just multiple choice items standing.

]]>How many decades of open-ended questions like these have been around and still we’re discussing quality. Since the 80’s I’ve argued that open-ended does not = vagueness and ambiguity.

What we need to do is rewrite the question, i.e, “model” it for them!

Here’s a stab at it but I know others could do better…

(a) Show that the width of the walkway is not 4 meters.

(b) Express the dimensions of the overall figure (garden and walkway) in terms of x, the width of the walkway.

(c) Write an equation that can be used to solve for x.

(d) Solve the equation and state the value of x.