Improving questions we ask students

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Improving questions we ask students

Richard Strausz
I found the following link when I was going through my too-large collection of old emails. I liked both examples, but am already thinking about the second one where negative exponents could be 'legal' too.

Do any of you have examples to share on improving questions?

http://www.doingmathematics.com/blog/asking-different-questions

Richard
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Re: Improving questions we ask students

Dave L. Renfro
Richard Strausz wrote:

http://mathforum.org/kb/message.jspa?messageID=9514171

> I found the following link when I was going through my too-large collection
> of old emails. I liked both examples, but am already thinking about the
> second one where negative exponents could be 'legal' too.
>
> Do any of you have examples to share on improving questions?
>
> http://www.doingmathematics.com/blog/asking-different-questions

The first question was:

"Explain, using your knowledge of scientific notaiton and exponents,
how to find out what (4.8 x 10^8) x (7.9 x 10^4) is."

The second question arose from a desire "to have something rich and
complex to talk about":

"Use each of the numbers 1-9 only once in order to create the
largest possible product.

(_ . _ _ x 10^(_)) x (_ . _ _ _ x 10^(_))"

I don't understand the point of the first one. I assumed it
was to get students to realize the product is (4.8 x 7.9) x 10^(8 + 4),
but because 4.8 x 7.9 does not (to me) have an immediately recognizable
single-written numeral value, there doesn't seem all that great of an
advantage to doing this (other than avoiding writing down a few zeros).

Better would be things like the following, which can then
serve as models for the types of things you want to aim toward
when making estimations:

(3.6 x 10^8) / (6 x 10^5)  [Hint: Rewrite numerator as 36 x 10^7.]

(2 x 10^4)(1.9 x 10^7)(5 x 10^5) [Hint: 2 x 5 = 10.]

I haven't given any thought to the second one, but I
will point out that one needs to be careful to keep something
like this from being a tedious "try all cases" situation.
Also, the wording "in order" leads to the question being
possibly ambiguous. One could think the question is asking
us to choose 4 digits to create the first factor and choose
5 digits to create the second factor, and in doing so, the
4 digits have to be numerically increasing from left to right
and the 5 digits have to be numerically increasing from left
to right.

Dave L. Renfro

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Re: Improving questions we ask students

Robert Hansen
In reply to this post by Richard Strausz

On Jul 9, 2014, at 7:10 AM, Richard Strausz <[hidden email]> wrote:

> I found the following link when I was going through my too-large collection of old emails. I liked both examples, but am already thinking about the second one where negative exponents could be 'legal' too.
>
> Do any of you have examples to share on improving questions?
>
> http://www.doingmathematics.com/blog/asking-different-questions
>
> Richard


List 10 questions, but without anything, like this…

1. ?
2. ?
3. ?
4. ?
5. ?
6. ?
7. ?
8. ?
9. ?
10. ?

And ask them to answer the even numbered questions. At least it involves math. In fact, have them write their own questions, but just the even numbered ones. I bet money they would be better than what this guy came up with.

I like this…

"We started thinking that by including "average," it implied that this was the best way to make decisions about what was best in this case, forced the teacher to instruct on how to calculate an average before the students had made sense of the idea, and turned the activity into a computational one rather than a conceptual one. We thought about the small change of just giving students this chart…"

This is just horrible. Most students have at least something to work with concerning averages just because of all the grading they have encountered. How can a teacher not even pick up on that? You hear about bad teachers all of the time but you really don’t get it till you see their work. I have a question. In your mind, how do students end up in a class like this? I understand some students do poorly in math, very poorly even, but these questions are so bad, they do even seem meant for any math class at any level.

Bob Hansen
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Re: Improving questions we ask students

Robert Hansen
In reply to this post by Dave L. Renfro

On Jul 11, 2014, at 3:15 PM, Dave L. Renfro <[hidden email]> wrote:

> I don't understand the point of the first one. I assumed it
> was to get students to realize the product is (4.8 x 7.9) x 10^(8 + 4),
> but because 4.8 x 7.9 does not (to me) have an immediately recognizable
> single-written numeral value, there doesn't seem all that great of an
> advantage to doing this (other than avoiding writing down a few zeros).

It has to have an immediately recognizable response? Your assumption is correct, it is to garner/test/reenforce fluency in handling numbers and operations in scientific notation, but the problem said explain, not compute. Granted, you were probably thrown off by the fact that the label *computation* has been tacked onto anything and everything having to do with mathematical procedure and all of the reasoning and thought developed thereof, that we take for granted. I know you don’t run around the house looking for batteries for a calculator you probably don’t have when you see 2 digit multiplication.:)

What I would like to know is why did the teacher want to ask the much more ambiguous question? Were the students so fluent in scientific notation that he wanted to entertain their success with a brain teaser? Or did he get bored trying to make them fluent and instead wanted to play with a brain teaser?

Bob Hansen
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Re: Improving questions we ask students

Richard Strausz
In reply to this post by Richard Strausz
>
> On Jul 9, 2014, at 7:10 AM, Richard Strausz
> <[hidden email]> wrote:
>
> > I found the following link when I was going through
> my too-large collection of old emails. I liked both
> examples, but am already thinking about the second
> one where negative exponents could be 'legal' too.
> >
> > Do any of you have examples to share on improving
> questions?
> >
> >
> http://www.doingmathematics.com/blog/asking-different-
> questions
> >
> > Richard
>
>
> List 10 questions, but without anything, like this…
>
> 1. ?
> 2. ?
> 3. ?
> 4. ?
> 5. ?
> 6. ?
> 7. ?
> 8. ?
> 9. ?
> 10. ?
>
> And ask them to answer the even numbered questions.
> At least it involves math. In fact, have them write
> their own questions, but just the even numbered ones.
> I bet money they would be better than what this guy
> came up with.
>
> I like this…
>
> "We started thinking that by including "average," it
> implied that this was the best way to make decisions
> about what was best in this case, forced the teacher
> to instruct on how to calculate an average before the
> students had made sense of the idea, and turned the
> activity into a computational one rather than a
> conceptual one. We thought about the small change of
> just giving students this chart…"
>
> This is just horrible. Most students have at least
> something to work with concerning averages just
> because of all the grading they have encountered. How
> can a teacher not even pick up on that? You hear
> about bad teachers all of the time but you really
> don’t get it till you see their work. I have a
> question. In your mind, how do students end up in a
> class like this? I understand some students do poorly
> in math, very poorly even, but these questions are so
> bad, they do even seem meant for any math class at
> any level.
>
> Bob Hansen

Bob, you do realize the target audience was 6th grade not high school, right?

Richard

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Re: Improving questions we ask students

Robert Hansen

On Jul 11, 2014, at 9:17 PM, Richard Strausz <[hidden email]> wrote:

> Bob, you do realize the target audience was 6th grade not high school, right?
>
> Richard

How does that make a difference? Are you saying that 6th graders deserve bad math? I was actually thinking of my son’s experience and classes when I wrote what I wrote, and he just finished 5th grade. He had to do averages in two of his last three science fair projects. 4th graders have enough awareness to learn averages, not just calculating them, understanding them. I also recall my son using “average” in a sentence in 3rd grade. It is just really bad pedagogy to think that *average* is just a calculation and it is no wonder these kids fail faster the further they go. You complain that your students are not interested. Well how interested would you be if your teachers gave up on mastering all of the mechanics, skills and operational knowledge required to even play the game of math because they thought it was stupid? You would be in the exact same position your students are in. Chew on that.

I don’t know anything about the teacher or the 6th grade class that he is referencing. I do know that he teaches 10th and 12th grade math at High Tech High. I know that 48% of the 9th grade students at HTH are proficient in Algebra 1, then 34% of the 10th grade students in Geometry, then only 16% of the 11th grade students in Algebra 2, with 2/3 of the students below basic by that point. Those numbers would be until you realize that 2/3 of the students were wasting time in the wrong class. I don’t understand why they don’t have a vocational math track, but that is the nature of the fraud today. I suspect his pedagogical ideas are born in that environment, as are yours. Where students are advanced through each level regardless of their preparedness. Isn’t that what you mean by *classroom teacher*?

Do you send letters home to the parents of your students informing them that their children are in over their head? I couldn’t be the type of *classroom teacher* you are. I wouldn’t last more than a minute staring into a parent’s eyes during a conference before I broke down and told them the truth. Your child is two years behind in math and we are not teaching algebra. We don’t even use real crayons. Surely you must be confronted with this dilemma often, no? What do you tell them?

Bob Hansen
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Re: Improving questions we ask students

Richard Strausz
In reply to this post by Richard Strausz
>
> On Jul 11, 2014, at 9:17 PM, Richard Strausz
> <[hidden email]> wrote:
>
> > Bob, you do realize the target audience was 6th
> grade not high school, right?
> >
> > Richard
>
> How does that make a difference? Are you saying that
> 6th graders deserve bad math?...

What I am thinking is that the approach given seemed a clever way to get students thinking about why an average is an important concept before hitting them with the rule and doing practice. It would take the teacher just a few minutes to prime the pump. If you think this is bad math that is okay with me.

Richard
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Re: Improving questions we ask students

Robert Hansen

On Jul 12, 2014, at 11:44 AM, Richard Strausz <[hidden email]> wrote:

> What I am thinking is that the approach given seemed a clever way to get students thinking about why an average is an important concept before hitting them with the rule and doing practice. It would take the teacher just a few minutes to prime the pump. If you think this is bad math that is okay with me.

You ask me a question, I answer it directly and honestly. I ask you a question and you evade it. Is this pattern part of your pedagogy as well?

I’ll try again.

You are Brian Mayer and you teach 12th grade mathematics with a pedagogy you invented. Almost all of the class fails the state exam with most more than just failing.

What do you tell the parents?

What do you tell the students?

Where is the cleverness in any of that?

Bob Hansen

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Re: Improving questions we ask students

Robert Hansen
In reply to this post by Richard Strausz

On Jul 12, 2014, at 11:44 AM, Richard Strausz <[hidden email]> wrote:

> What I am thinking is that the approach given seemed a clever way to get students thinking about why an average is an important concept before hitting them with the rule and doing practice.

All I am seeing in your examples are non-mathematical activities. And if students don’t yet know the concept of *average* then they can’t possibly be thinking about why it is important. These are 6th grade students. You don’t need to waste yet another day with math avoidance, just walk into the classroom and ask them “How do we (teachers) determine your final grade?” and go from there. Start with the average of two scores, then 3, 4 etc. Ask them why it is useful in the end to give an average score rather than a list of 30 scores.

And there isn’t a *rule* and I don’t know why you keep using that term. There is a generalized definition, the sum of the values over their count, but that has to be interpreted over many contexts. With a straight list. With something like 3 kids scored 100 and 2 scored 50, what was the average score? To something like, the average of two numbers is 30 and one of the numbers is 50, what is the other number?

It isn’t that I don’t find it important to make mathematics applicable to the student. I do this more than any activity you have yet to post an example of. And my manipulatives are not virtual or videos, they are real, visual, tactile and aural. It is that what you and your like keep calling *rules* is MATHEMATICS and it is that which we are trying to connect the student to. It is the 75% and when every example you post has none of it, it doesn’t take a genius to realize that you are avoiding it and then excusing that avoidance by referring to it as just *rules*.

I know why this non-mathematics pedagogy came to be. 40 years ago you would be teaching math for daily living. Somewhere in those 40 years the political forces decided that you should instead pretend to teach advanced courses like algebra to very unprepared students. Most teachers in your situation actually know this and when they talk about their lesson plans they put that disclosure at the very top. They don’t post a lesson plan involving coloring Fibonacci shapes and then ask the forum “Is this a good lesson?” only to respond to honest critiques with “Damn you, these are special needs children!”

Speaking of special needs students, I came across this activity…

http://abc7.com/education/donations-needed-to-help-local-special-education-students/178239/

These special needs students have jobs and they sure could use a shredder truck. I was thinking of donating to that cause. Or is that old fashioned and inhuman? Should I tell them “No way! They should be in college and be *learners* instead."

Bob Hansen
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Re: Improving questions we ask students

Gary Tupper
On 7/12/2014 6:28 PM, Robert Hansen wrote:
Rob:

I hesitate to respond to your message, in case I get drawn into an Alice in Wonderland tunnel... However I'll giver a try

>... And if students don’t yet know the concept of *average* then they can’t possibly be thinking about why it is important.

Perhaps they will benefit from an example of what an average is, prior to a statement of what the concept 'is'. I can imagine a teacher explaining to a class that they could put all their lunch moneys into a pile & then redistribute it equally so that each student has the same amount....  <Caution: if you are a teacher, be aware of the possibility of some involved parent taking umbrage at "income redistribution"!>

>These are 6th grade students. You don’t need to waste yet another day with math avoidance, just walk into the classroom and ask them “How do we (teachers) >determine your final grade?” and go from there.

But wouldn't the more astute little tykes say that teachers' pets get the higher marks & the trouble-makers lower?

>Start with the average of two scores, then 3, 4 etc. Ask them why it is useful in the end to give an average score rather than a list of 30 scores.

Students may not see the need for a single number, rather than two or five. The class might consider a student who has written 5 math tests. He can either tell his poor old man: "my average on the last 5 math tests was 64% - or - he could say "I got 80% on the 1st four and 0% on yesterday's."
Maybe his mom is trying to quit smoking: "I have had 7 cigarettes in the last week: 1 day on an average" vs "I had 7 cigs a week ago but none since"

So: Students: when would a single number be good enough? monthly class absenteeism? maybe to compare all the grade 6 classes. Or tardiness?

 >And there isn’t a *rule* and I don’t know why you keep using that term. There is a generalized definition, the sum of the values over their count, but that has >to be interpreted over many contexts. With a straight list. With something like 3 kids scored 100 and 2 scored 50, what was the average score? To something >like, the average of two numbers is 30 and one of the numbers is 50, what is the other number? It isn’t that I don’t find it important to make mathematics >applicable to the student. I do this more than any activity you have yet to post an example of.

These are the 'mathy' topics that should indeed be mastered. But if there is some context (why we might want to use averages) I would hope the success ratio might be higher, on average;)

> 40 years ago you would be teaching math for daily living. Somewhere in those 40 years the political forces decided that you should instead pretend to teach >advanced courses like algebra to very unprepared students.

Do I sniff a conspiracy? & if so, why?

> Bob Hansen

Gary Tupper

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Re: Improving questions we ask students

Robert Hansen

On Jul 12, 2014, at 11:05 PM, Gary Tupper <[hidden email]> wrote:

> On 7/12/2014 6:28 PM, Robert Hansen wrote:
>> Rob:
>
> I hesitate to respond to your message, in case I get drawn into an Alice in Wonderland tunnel... However I'll giver a try
>
> >... And if students don’t yet know the concept of *average* then they can’t possibly be thinking about why it is important.
>
> Perhaps they will benefit from an example of what an average is, prior to a statement of what the concept 'is'. I can imagine a teacher explaining to a class that they could put all their lunch moneys into a pile & then redistribute it equally so that each student has the same amount....  <Caution: if you are a teacher, be aware of the possibility of some involved parent taking umbrage at "income redistribution”!>

That is why we start with something they are familiar with and have been gaining familiarity with for 6 years.

>
> >These are 6th grade students. You don’t need to waste yet another day with math avoidance, just walk into the classroom and ask them “How do we (teachers) >determine your final grade?” and go from there.
>
> But wouldn't the more astute little tykes say that teachers' pets get the higher marks & the trouble-makers lower?

I’ve never seen this occur. I have been thinking a lot lately of the myths you hear in reformist-speak, like memorization, rote and procedure. Many have rightly pointed out here that these descriptions of traditional mathematics education don’t match our experiences with traditional mathematics education. For example, I don’t recall algebra being a task of memorizing rote formulas and procedure. Nor was arithmetic that, albeit the times table comes close to that description but it is also much more than just rote. My take on it is that these unfamiliar descriptions of traditional education were exaggerated and fabricated, like your example with teachers’ pets. We have tried to eliminate possible psychological causes of failure, real, imagined and fabricated, and things just get much worse. Unless you eliminate the tests, which was the original driver, as well.

>
> >Start with the average of two scores, then 3, 4 etc. Ask them why it is useful in the end to give an average score rather than a list of 30 scores.
>
> Students may not see the need for a single number, rather than two or five. The class might consider a student who has written 5 math tests. He can either tell his poor old man: "my average on the last 5 math tests was 64% - or - he could say "I got 80% on the 1st four and 0% on yesterday's."
> Maybe his mom is trying to quit smoking: "I have had 7 cigarettes in the last week: 1 day on an average" vs "I had 7 cigs a week ago but none since”

That was the purpose of starting with something they are already quite familiar with, like average scores. It works very well.

>
> So: Students: when would a single number be good enough? monthly class absenteeism? maybe to compare all the grade 6 classes. Or tardiness?
>
>  >And there isn’t a *rule* and I don’t know why you keep using that term. There is a generalized definition, the sum of the values over their count, but that has >to be interpreted over many contexts. With a straight list. With something like 3 kids scored 100 and 2 scored 50, what was the average score? To something >like, the average of two numbers is 30 and one of the numbers is 50, what is the other number? It isn’t that I don’t find it important to make mathematics >applicable to the student. I do this more than any activity you have yet to post an example of.
>
> These are the 'mathy' topics that should indeed be mastered. But if there is some context (why we might want to use averages) I would hope the success ratio might be higher, on average;)

Again, that is why we started with score averages. And we could start with a discussion of anything they could relate to. The point wasn’t about starting a discussion. The point was WHERE IS THE MATHEMATICS IN THAT OR AFTER THAT, in any of these examples.

>
> > 40 years ago you would be teaching math for daily living. Somewhere in those 40 years the political forces decided that you should instead pretend to teach >advanced courses like algebra to very unprepared students.
>
> Do I sniff a conspiracy? & if so, why?

Hold on now. I am not just some guy yelling “fire”. I do the due diligence and trace these teachers back to their schools and retrieve the reality of their students’ performance over time. I also compare what they think they are doing with what teachers with success are doing.

The bottom line is that they are teaching students who are way behind the level of the material they are trying to teach and when that happens, the mathematics gets dropped in favor of non-mathematical activities.

I am still curious as to how they relay the reality of all this to the parents and the students? Or is it just something they will figure out when the start college by taking remedial classes until they drop out?

Bob Hansen
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Re: Improving questions we ask students

Robert Hansen

On Jul 13, 2014, at 12:06 AM, Robert Hansen <[hidden email]> wrote:

> Again, that is why we started with score averages. And we could start with a discussion of anything they could relate to. The point wasn’t about starting a discussion. The point was WHERE IS THE MATHEMATICS IN THAT OR AFTER THAT, in any of these examples.

I want to emphasize this point. I am not against activities and discussion in math class. I do things with my son that make these activities look primitive and feeble. I bought an old record player with real knobs and albums just so he had the analog experience of how sound is reproduced. An old pen plotter so that he can witness a plot be physically drawn and hear the stepper motors whine at different rates. An adding machine so he can hear an algorithm. And when we discuss concepts we do it with the goal of mathematical awareness and increasing clarity. And that involves doing a lot of math as well.

I am not against activities, just activities that purposely avoid mathematics. I think I have made the case that these do indeed avoid mathematics, let alone the fact that it is these teachers' stated mission in most of these cases to avoid mathematics. Mathematics to them is just some dumb rules.

And I know why they do it, and most teachers that do it also know why and will be straight about it. Only a small fraction try to legitimize it like this. The students are not prepared for the material and the teachers themselves don’t understand deeply enough what mathematics is nor how it works. A lot of it just dumb rules to them. A reality that I blame the schools of education for entirely, not the teachers. I think they might understand it better if they started their careers with better students, but I don’t have any proof that this would work. I just know from years of study that when teachers form a theory of mathematics pedagogy based primarily on their experiences with failing students, the theory turns out very wrong.

Why we do this to students in the first place, advance them far past their readiness, is I guess a question of politics, not pedagogy. It wasn’t always this way, it developed mostly in the last 20 to 30 years. Part of me thinks (hopes) that it will eventually fade and we will have more vocational tracks. Some of that is actually happening. Maybe it will catch on. What I would like to see is for people to realize that it isn’t academics or vocational. Education must involve vocation in everything, whether it be algebra 2 and calculus or business math. Students should try different things, for sure, but not to the point where it loses all vocation. You can’t teach anything when there is no vocation.

Bob Hansen
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Re: Improving questions we ask students

kirby urner-4
In reply to this post by Richard Strausz
On Wed, Jul 9, 2014 at 4:10 AM, Richard Strausz <[hidden email]> wrote:
I found the following link when I was going through my too-large collection of old emails. I liked both examples, but am already thinking about the second one where negative exponents could be 'legal' too.

Do any of you have examples to share on improving questions?

http://www.doingmathematics.com/blog/asking-different-questions

Richard


I remember way back in 1997 when I was freaking out the NCTM with my funny web memo:


This memo shows their old logo, since changed.  

I was looking for an angle for some of the geometry I was into at the time (still am, in 2014).

Still learning the ropes, I called it NCMT for awhile.

Anyway, I'm sharing it in this thread because of the weird questions I was asking, as example questions from my futuristic math, later rebranded to Verboten Math, and after that to Martian Math, which it stayed -- I'm still getting value from that one.

Excerpt:

Relevant from Euclid

Diagonals of a parallelogram bisect each other (relevant to Step 5).

Which of the following are true about the volumes in this scenario?

a. T1+T2=O1
b. T1=T2
c. C1/3=T1
d. 2*(T1A+T1B+T1C+T1D)=O1
e. T1A/T1=1/4

Answers: b,c,e [click here for explanations]

Review questions:

[click here for hints]

Adding all surface angles:
a. One tetrahedron = _____ degrees
b. One cube = _____ degrees
c. One icosahedron = _____ degrees

Number of unit-radius spheres in a 9-frequency tetrahedron = ______

Frequency at which a tetrahedral sphere-packing first aquires a nuclear sphere = _______

Extra credit:

Write a 4D Logo program to draw T1 and T2 inscribed in C1, using different pen colors for each.

[click here to run example, source code not shown]



Kirby


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Re: Improving questions we ask students

GS Chandy-2
In reply to this post by Richard Strausz
Gary Tupper posted Jul 13, 2014 8:35 AM (http://mathforum.org/kb/message.jspa?messageID=9516786):
>
> On 7/12/2014 6:28 PM, Robert Hansen wrote:
> > Rob:
>
> I hesitate to respond to your message, in case I get
> drawn into an
> /Alice in Wonderland/ tunnel... However I'll giver a
> try
>
<snip>
Strikes me, from the response you've received (Jul 13, 2014 9:36 AM, http://mathforum.org/kb/message.jspa?messageID=9516787) that you've already been sucked into that "/Alice in Wonderland/ tunnel".

Enjoy!

GSC
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Re: Improving questions we ask students

Richard Strausz
In reply to this post by Richard Strausz
>
> On Jul 12, 2014, at 11:44 AM, Richard Strausz
> <[hidden email]> wrote:
>
> > What I am thinking is that the approach given
> seemed a clever way to get students thinking about
> why an average is an important concept before hitting
> them with the rule and doing practice. It would take
> the teacher just a few minutes to prime the pump. If
> you think this is bad math that is okay with me.
>
> You ask me a question, I answer it directly and
> honestly. I ask you a question and you evade it. Is
> this pattern part of your pedagogy as well?
>
Bob I can't keep up with your questions when we occasionally communicate here. Do you realize you have been averaging  :) 4 posts a day for 5 years here? I'll try to answer a few of these.

> I’ll try again.
>
> You are Brian Mayer and you teach 12th grade
> mathematics with a pedagogy you invented. Almost all
> of the class fails the state exam with most more than
> just failing.
I can't answer for anyone else but this is what I do when a parent ask me why I did something in class. I explain what we did, which is often different than what their students told them we had done. Close to 100% of the time my explanation is accepted. If necessary we talk about why the student is struggling and I suggest strategies.

>
> What do you tell the parents?
Furthermore, during Meet the Teacher night at the beginning of the year I give the parents a few examples of how their students' experience in Algebra or Geometry will be different than the parents' experience in those classes. A typical response afterwards is for parents to say they wished they had a class like mine when they were in school.

>
> What do you tell the students?
Take notes; do your homework; ask questions; see me for extra help.
>
> Where is the cleverness in any of that?
>
> Bob Hansen

Richard
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Re: Improving questions we ask students

Richard Strausz
In reply to this post by Richard Strausz
>
> On Jul 12, 2014, at 11:44 AM, Richard Strausz
> <[hidden email]> wrote:
>
> > What I am thinking is that the approach given
> seemed a clever way to get students thinking about
> why an average is an important concept before hitting
> them with the rule and doing practice.
>
> All I am seeing in your examples are non-mathematical
> activities. And if students don’t yet know the
> concept of *average* then they can’t possibly be
> thinking about why it is important. These are 6th
> grade students.
You might remember an earlier thread here when adults were discussing the values of different averaging techniques. Wouldn't it be interesting if different students advocated for something like the median or mode and not just the mean? If no one did, I am out 5 minutes and we can do averaging or move on to the next topic.

Richard

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Re: Improving questions we ask students

GS Chandy-2
In reply to this post by Richard Strausz
Responding to Richard Strausz's post dt. Jul 13, 2014 9:36 AM (http://mathforum.org/kb/message.jspa?messageID=9514171), and having looked quite carefully at all the responses at this thead to date:

Not being a math teacher myself (at any level), I obviously would not be in a position to suggest "examples that could help improve questions the questions teachers ask their students".

However, it is obviously an extremely important matter.  The teacher needs to provide questions that would, at each level:
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- -- help take the students somewhat further into the topics under consideration than they have currently reached;

- -- encourage them to think a little about various implications of the issues raised;

- -- encourage them to come up with sound reasoning to back up whatever points they may make in response to the questions put to them;

- -- as Robert Hansen (RH) has argued, in a math class the questions should have some *math content* in them - or at least should 'lead into' math content in some way that is appropriate for the teacher and his or her class.

(I do  not necessarily agree with RH that the specific questions posed in the "DOING MATHEMATICS" blog had no  real math content in them - I don't know the context in which Brian Meyer has asked his questions; his prior conversations with his readers; etc.  I do observe that at least a few of the readers seemed to be enthusiastic about the questions posed: this may because of the 'math avoidance' issues that RH has been raising; on the  other hand, it may well be on account of those questions showing them how they should perhaps go in their own classes).

And undoubtedly there would be many other desiderata that the teachers of specific classes and specific students in them].
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All said and done, I'd guess that this business of *asking the right questions* is probably one of the most important skills that should be honed by the teacher.  It's all the more important for classes of 'beginning math learners'.  Schools of education (in particular those training math teachers) need to consider this issue very seriously indeed.

(And, I must observe, I hugely admire the teacher who is able to come up with the right questions that would help keep his/her class bubbling with enthusiasm and interest in the subject/topic being addressed).

GSC
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Re: Improving questions we ask students

Robert Hansen
In reply to this post by Richard Strausz

On Jul 13, 2014, at 4:11 AM, Richard Strausz <[hidden email]> wrote:

> You might remember an earlier thread here when adults were discussing the values of different averaging techniques. Wouldn't it be interesting if different students advocated for something like the median or mode and not just the mean?

How are they going to advocate (with any understanding) something they haven’t been taught? As I told Gary, my point is not about activity or discussion, it is about the lack of mathematics and development in any of these examples. The dialog and thinking are supposed to become more mathematical and more sophisticated as time progresses. That clearly isn’t happening. With these teachers, you can’t tell if the lesson is the student's first or last. They all look the same and are equally devoid of mathematics, even across grades. This isn’t coincidence because we have seen 100’s of examples. It is a tenet of their teaching philosophy, that each day should be met as if the student hasn’t had any prior mathematical experience or success.

Also, and I made mention of this in the past, the only people I ever see discussing these things as adults, had a traditional mathematics education. Go figure.

I question if these kids are as unable in mathematics as these teachers make them out to be. I have looked into their classroom situations and they don’t appear to be teaching unruly juvenile delinquents. And they are not trying to teach adults, which is almost as impossible. I am pretty convinced at this point that these lessons reflect the teachers’ attitudes toward mathematics, not the students’.

Bob Hansen
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Re: Improving questions we ask students

Richard Strausz
In reply to this post by Richard Strausz
> ...(And, I must observe, I hugely admire the teacher who
> is able to come up with the right questions that
> would help keep his/her class bubbling with
> enthusiasm and interest in the subject/topic being
> addressed).
>
> GSC

I like the above sentence a lot; I love seeing questions (plural) that different skilled teachers use to reach different students. I chuckle at those who criticize teachers because when they teach one student they use a different methodology.

Richard

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RE: Improving questions we ask students

Bishop, Wayne
In reply to this post by Robert Hansen
Very well stated, Bob.  Don't forget the math.  And if there are several mathematical approaches accessible at the grade-level in question, compare and contrast.  If they can be seen to be different forms of the same thing, so much the better and certainly do not let that "teachable moment" be missed.

Wayne
________________________________________
From: [hidden email] <[hidden email]> on behalf of Robert Hansen <[hidden email]>
Sent: Saturday, July 12, 2014 10:14 PM
To: [hidden email]
Cc: [hidden email]
Subject: Re: Improving questions we ask students

On Jul 13, 2014, at 12:06 AM, Robert Hansen <[hidden email]> wrote:

> Again, that is why we started with score averages. And we could start with a discussion of anything they could relate to. The point wasn’t about starting a discussion. The point was WHERE IS THE MATHEMATICS IN THAT OR AFTER THAT, in any of these examples.

I want to emphasize this point. I am not against activities and discussion in math class. I do things with my son that make these activities look primitive and feeble. I bought an old record player with real knobs and albums just so he had the analog experience of how sound is reproduced. An old pen plotter so that he can witness a plot be physically drawn and hear the stepper motors whine at different rates. An adding machine so he can hear an algorithm. And when we discuss concepts we do it with the goal of mathematical awareness and increasing clarity. And that involves doing a lot of math as well.

I am not against activities, just activities that purposely avoid mathematics. I think I have made the case that these do indeed avoid mathematics, let alone the fact that it is these teachers' stated mission in most of these cases to avoid mathematics. Mathematics to them is just some dumb rules.

And I know why they do it, and most teachers that do it also know why and will be straight about it. Only a small fraction try to legitimize it like this. The students are not prepared for the material an
lves don’t understand deeply enough what mathematics is nor how it works. A lot of it just dumb rules to them. A reality that I blame the schools of education for entirely, not the teachers. I think they might understand it better if they started their careers with better students, but I don’t have any proof that this would work. I just know from years of study that when teachers form a theory of mathematics pedagogy based primarily on their experiences with failing students, the theory turns out very wrong.

Why we do this to students in the first place, advance them far past their readiness, is I guess a question of politics, not pedagogy. It wasn’t always this way, it developed mostly in the last 20 to 30 years. Part of me thinks (hopes) that it will eventually fade and we will have more vocational tracks. Some of that is actually happening. Maybe it will catch on. What I would like to see is for people to realize that it isn’t academics or vocational. Education must involve vocation in everything, whether it be algebra 2 and calculus or business math. Students should try different things, for sure, but not to the point where it loses all vocation. You can’t teach anything when there is no vocation.

Bob Hansen

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