# Improving questions we ask students

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## Improving questions we ask students

 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-questionsRichard
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## Re: Improving questions we ask students

 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-questionsThe 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

 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

 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

 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

 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....  >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

 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 > 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

 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

 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