# Tag Info

25

Absolutely! In fact, in my opinion, the most important "math skill" that should be taught in conjunction with, and using, word problems is checking whether the answers make sense. This is an absolutely invaluable part of making any practical use of mathematics, as opposed to just blindly applying formulas for the sake of passing an exam. There are several ...

20

I think there's a countervailing issue that the book you're describing is trying to deal with. I teach college students, so I don't know what the particular approach it's taking is age appropriate for a 6th grader, but it is trying to solve a real problem. What I would do about this is introduce them as separate topics, probably spaced far in time. Let ...

18

Consider these 5 problems: What is $35 \div 10$ ? We are in the store and want to buy packages of party plates for a birthday party. The plates come in packages of 10. There will be 35 children at the party. How many packages should we buy so that everyone will have a plate? 10 friends go out to get ice cream. The bill comes to $35. If the friends ... 17 The answers to a word problem should in my opinion make sense (within reasonable limits). The goal you mentioned that students should check their answers is one shared by many, as also witnessed by our recent question How to award points for sense-making at the end of a problem? Now, if it is not a given any more that the solution does indeed make sense, ... 11 Here are some suggestions for problem sources in English. Some of them are appropriate for very bright students studying geometry or Algebra II, but might nonetheless prove too difficult for students accelerated to this extent. -Mathematical Circles, Fomin et al. -Mathematical Problems: An Anthology, Dynkin et al. -Problems in Elementary Mathematics, ... 11 Does your colleague have any information about these students' reading comprehension? The reason I ask is that, in my opinion, difficulty with word problems is not always a matter of taking the content of the word problem and reformulating it as equations. Rather, it is often a matter of getting the content of the problem in the first place. In other words,... 11 DASL (pronounced "dazzle" and short for Data And Story Library) is an online collection of stories with matching data sets to be used for educational purposes. They are real data from real research. Searchable by statistics concept and by theme of the story. OzDASL is similar, but most of the data has an Australian or New Zealandish source. Personally I ... 11 Professional work in general, and scientific and mathematical work in particular, is done principally in writing. Requirements, specifications, orders, field reports, case studies, journals, grants, etc., are all disseminated and documented in writing. Symbolic mathematical notation is inherently a specialized system of concise writing (arguably, it is nigh-... 11 (edited) a. For all of these, I would think to expand the category into subcategories. So not just "bank account" but time value of money and NPV, bond details, etc. You learn something when doing this finer description. b. Maybe it fits under your (2) but radioactive decay is a huge one you did not mention. Applications include carbon (and other) ... 10 Yes, there is evidence for the claim; for example, consult the following: Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219-234. Link (no paywall). You will find in this piece that the authors, as you considered in your "soft evidence" proposal, modified mathematical questions (from ... 10 I suggest you break it down into smaller parts. In fact, don't start on equations. Start on translation of terms: Double of a number, translation:$2x$Sum of two numbers, translation:$x+y$The triple of a number after adding five units, translation:$3(x+5)$Next combine translations into equations: The double of a number is equal to the triple of ... 9 I feel like I always post the same thing in these threads, but this again sounds like an issue of blocking vs interleaving. In this case, the textbook may have started interleaving different problems a little bit too early, but generally it should be introduced earlier than feels intuitively right. That's because the algorithms for$\frac{1}{6}\times 90$... 8 Physically (or even economically) unreasonable answers are confusing. The student needs to be shown that math is a tool that can solve practical problems. Answers that are unreasonable send the wrong message. (That math is a logic game versus a commercially relevant skill.) Why do that, when there are so many easy problems to construct that don't make ... 8 Have your students covered division and multiplication yet? To me, these problems can all be solved using the "meaning of division" and the "meaning of multiplication". "Meaning of multiplication": If I have n groups of equal size m, then I have n*m total objects. "Meaning of division": There are actually two! (a) If I have m objects which are ... 8 I would say that this book is trying to get students to think about what the calculations mean, rather than simply execute an algorithm, and I strongly believe that is something that should be done right from the beginning, not saved for later or for more advanced students. I cannot tell you how many students I have worked with as a private tutor who, if ... 7 I think you have a very different understanding of what "mathematics" is than I do. Consider the following questions: What kinds of geometric properties are held by the figure you get when you join the midpoints of adjacent sides of a polygon? Under what conditions on the parameters$a,b$does an equation of the form$a^x = x^b$have a rational solution? ... 7 I do avoid using this phrase in all of my math classes. Not that I've ever thought of it as a particular goal, but I would want to reserve the word "term" to specify an addend. In your first example, I would specify, "Write a formula using the variable$x$". In your second example, I specify, "Solve the following equation for$y\$" (end of direction), ...

7

Recently, I got to teach a new high school class called "Essentials of College Math." It sounds like hard content, but it was basically just a transition course from Algebra II to Precal. Anyways, this is the teacher's manual for the course (which also includes all the student handouts). The first unit was called "algebraic expressions" and dealt with this ...

6

I only have anecdotal evidence but since you said it was welcome, I am adding my 2 cents from both the perspective of a teacher and an item writer, hired to write questions for standardized tests. I taught math to gifted elementary students. A small fraction of them were gifted in math and had reading levels below grade level. Students with poor reading ...

6

I work with gifted elementary school students, but one of my favorite sites, nrich has challenging problems that you could use for older gifted students. Try looking at secondary problems for stages 4 and 5. Here are some suggested problems to see if you'll like the site: You can also look at the Post-16 Curriculum on nrich here. See description below. ...

6

One of my colleagues introduced me to a strategy called "3 Reads" which he details in his blog Misteristhisright. This strategy has two major features: You remove the question from the problem. The problem only gives the context. This can be done with Dan Meyer's 3 act problems as well. You read the problem 3 different times in order to become familiar ...

5

(I came to mention DASL, but since it's already been mentioned, I'll give some other resources.) opendata.stackexchange.com often has mentions of useful sources of data, some of which are small (and others of which might be sampled to generate smaller data sets). It's also a good place to ask about data sets The datasets subreddit http://www.reddit.com/r/...

4

This is not a good answer, but I'll mention anyway that Mathematica now connects to vast "curated" data sources. It would take some effort to master these sources, but they could provide endless streams of real data. Here is one example I just ran (NB: Up-to-date in that no Pluto!).

4

I think there's a very basic answer to this. It's the very origin of math and numbers. Try to teach a child that 1+1=2 without the visual (or tactile) example of using fingers to show the concept of 1 and 2, and how the oneness of a single finger has something in common with the oneness of a single block. It's only when this sinks in, do we get comfortable ...

4

There are three direct benefits, as far as I can tell. Word problems answer questions like "why do I need to know this". If you have a student who thinks that learning math is pointless then you can use word problems to help them understand why math is important For some students math is very difficult when's it's just abstract numbers. For more ...

4

One basic model of atmospheric pressure has it decaying exponentially as a function of height above sea level. Two places to look for this are https://people.clas.ufl.edu/kees/files/AtmosphericPressure.pdf and http://nova.stanford.edu/projects/mod-x/ad-expatm.html.

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The website mathschallenge.net has pdfs of tiered problems with solutions. They are nicely posed problems, often with some humour, and are based on different stages of mathematical maturity. To begin with they have no real prerequisites, but eventually they require some of the 'canonical' mathematical knowledge. I just found them to be well organised, ...

3

Perhaps an example would clarify what you mean. Question 1: What number is obtained after reducing 40 by 5%? Question 2: Farmer John has lately been having problems selling his corn. He needs to start selling more of them soon, or they will start to go bad. It seems that the retail price of 40 cents is too high, so he decides to start offering a 5% ...

3

The premise of your question seems to indicate an undesirable precedent. When the students are able to solve a problem correctly it's immaterial what approach they followed. In fact, giving positive feedback to those who conjure creative methods (instead of following conventional approach taught in the class) is imperative. But, to be fair, your question ...

3

Catenary curves are the sum of two exponentials -- One concave upward but decreasing, and the other concave upward and increasing. They are a good model for the curve of suspension bridge cables. (The key assumptions are that the weight of the cables is small compared to the weight of the bridge deck, and the weight of the bridge deck is constant along the ...

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