Popham, Chapter 1 Pondertime, Chapter 2 Pondertime, Due 1/11/2012


Chapter 1 Pondertime, pg. 26, #5

5.  Do you think the movement to discourage the use of the terms intelligence and aptitude is appropriate?  Why?

"We’ll look back on this as a dark age in education." So says Toronto playwright, math scholar and dabbler in the philosophy of education John Mighton. He’s also a math tutor who, with his non-profit organization, Junior Undiscovered Mathematical Prodigies (JUMP), has helped turn 1,000 one-time struggling kids into virtual math whizzes. Mighton, 45, attributes our pre-enlightened state to a school culture that neglects what he calls the "psychological aspect of learning" — that is, nurturing a child’s confidence and excitement about school. (Ferguson, 2003)

First, I would like to say that we don’t need another movement to change terminology.  Especially since according to Popham (2011) “the tests…although they have been relabeled, haven’t really changed that much.”  What really needs to be discouraged is the false notion, but notion is almost not strong enough a word, since Mighton compares the impact of that notion to be so widespread it has cast a dark pall over the whole endeavor that is education.

Second, and to state a more positive action, I like being a proponent of change that starts spreading the sentiment that all children can learn mathematics, that all children can get to calculus, and that any failure to do so is a failure of the educator and not the student.  That seems to get at the root of the issue, but is of course, far harder and more far-reaching.

Come join me!  The challenge is to take prejudice couched in language like:

“Subitisation skill as a predictor of math ability”

and replace it with

“This student isn’t getting it right now, what are *you* going to do about it?”


Ferguson, S. (2003). The Math Motivator. (cover story). Maclean’s, 116(38), 20.

Popham, W.J. (2011). Classroom Assessment: What Teachers Need to Know. (6th ed.). Boston ,MA: Pearson Education, Inc. pg. 20.

Chapter 2 Pondertime, pg. 58, #1, #2, #3
1.  I t was argued in the chapter that most classroom assessment tasks call for criterion-referenced approaches to measurement.  Do you agree?  Why or why not?

I like criterion referenced approaches since we are in day-to-day instruction involved in imparting specific knowledge which is easily measured per student and per functional task or piece of information.  That assessment can be formative or summative, but it must be in the end criterion-referenced.  That is the only way the assessment will perform the most needed function which is an immediate gauge of the effectiveness of instruction.

2.  Why should/shouldn’t classroom teachers simply teach toward the content standards isolated by national groups?  If teachers don’t, are they unpatriotic?

I assume the reference to patriotism is a thinly veiled reference to the performance of students in the USA relative to other countries when it comes to national mathematics exams.  If so, the assumption is that the content standards if adhered to for instruction would help students here do better.

Perhaps the reference to patriotism is merely that rank-and-file teachers should respect national authority.  Since when is blind allegiance to authority prized in this country?

Again, I would ask here what the stakes are.  If there is an exam at stake, then teach toward that exam, it may or may not agree with national content standards.  If you are averse to teaching to the exam, first do that, then if you time or inclination allows, diversify your instruction with national content standards.

NOTE:  with the Common Core standards coming to WA, show your patriotism and get informed on that (webinars at this link)  http://www.k12.wa.us/CoreStandards/updatesevents.aspx

3.  If you discovered that your state’s educational ability tests (a) attempt[ed] to measure too many content standards, (b) are based on badly defined content standards, and (3[c]) don’t supply teachers with per-standard results, how do you think such shortcoming would influence your classroom assessments?  How about your classroom instruction?

Let me be perfectly clear here.  As far as classroom assessments go, the gold standard is the test (assessment) so (a) Teach to the test.  (b) Teach to the test.  (3 [c]) Teach to the test.  When it comes to classroom instruction, I would endeavor to (a) Teach to the test.  (b) Teach to the test.  (3 [c]) Teach to the test.  And while you are at it, put the best minds in the country on designing the test (bias free, reliable, engaging).  This is the only way to ensure that everyone is being pulled to a higher standard.

My classroom assessment and instruction in all of these cases would be to teach to the test.  My Gedankenexperiment for (a) is as follows:  I as the teacher have limited time, the test is also administered in finite time, there thus cannot be “too many content standards” on the test, the test has as many content standards as it has.  Therefore, study the test (prior editions), learn how to assess like it is assessing, i.e. know how it is designed, how it is put together, how it is administered.  There is some statistical inference that needs to go on to decide what the most central content standards will be on the test, teach to those first, then try to cover the rest.  In all cases teach test-taking skills so that students don’t turn a cognitive assessment into an affective assessment.

Let’s think a moment about “badly defined content standards”.  That can really mean only a few different possible things:  the standard is either too narrow, too broad, or unrelated.  Here is the example:

1.  Students will be able to simplify 5x + 13 = 28 (too narrow)
2.  Students will be able to recognize and solve equations of one variable (too broad?)
3.  Students will be able to walk & chew gum at same time.

All it would take is one sample test, or gathering recollections of tests from students to ascertain where each standard was lacking.  I also really do not think that too narrow standards is the problem, otherwise teachers would teach the exact standards, the tests would cover those standards, and we wouldn’t be having this discussion!

The real problem must be that standards are invariably somewhere between #2 and #3.  In which case we are really a subset of question (a), namely there is too much being covered on exams relative to state standards.  But I counter that here again information about the exam is crucial for determining where the instruction and assessment should tend.

I just don’t get what I consider to be the arrogance of a teacher saying they don’t teach to the standardized test.  Are they teaching something better?  Great, so teach enough so that students ace exams and then add your own flavor.  Or are they saying that the exams and standards are flawed?  Fine, design your own, but first cover the ones that exist otherwise your students and parents will go elsewhere as they realize that you are more high-minded than the high stakes exams that are bearing down on your students every day!

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