Tap Posted September 23, 2014 Share Posted September 23, 2014 How would you figure out this math problem without Googling statistics. Specifically part A. (which city goes to which graph). Would your teenager be able to figure this out? None of her group could figure it out. from College Preparatory Mathematics Algebra 2 (regular public school math in our area). The image isn't very good but on the graphs, the blurry spot in the left corner is just the letters A,B,C,D,E,F. Under the lines, are the letters J,F,M,A....(months) and under those letters is the word "month". The sideways word is Temperature. There is nothing on any graph to indicate which graph goes to which geographic area. PS: I HATE public school math! Quote Link to comment Share on other sites More sharing options...
TrixieB Posted September 23, 2014 Share Posted September 23, 2014 I don't know if my teen could figure it out. I would say that the top right graph is Melbourne. Are there temperatures on the Y-axis? That would help me determine which graph goes to which city. Quote Link to comment Share on other sites More sharing options...
obsidian Posted September 23, 2014 Share Posted September 23, 2014 Top right is Melbourne (shape is different because winter months are opposite in the Southern Hemisphere), middle right is San Francisco (relatively cool and steady temperature), bottom right is Fairbanks (very cold). I believe Chicago is the top left (gets colder than the other two places). The other two are a bit more difficult, but if there are numbers on the y axis, it would be relatively easy to use part c to determine which is New Orleans and which is Salt Lake City. I am a teenager, but also currently taking AP Stats, so perhaps not your target audience for judging the difficulty of the problem. :p Quote Link to comment Share on other sites More sharing options...
Tap Posted September 23, 2014 Author Share Posted September 23, 2014 Top right is Melbourne (shape is different because winter months are opposite in the Southern Hemisphere), middle right is San Francisco (relatively cool and steady temperature), bottom right is Fairbanks (very cold). I believe Chicago is the top left (gets colder than the other two places). The other two are a bit more difficult, but if there are numbers on the y axis, it would be relatively easy to use part c to determine which is New Orleans and which is Salt Lake City. I am a teenager, but also currently taking AP Stats, so perhaps not your target audience for judging the difficulty of the problem. :p I have lived all over the mid-west to western states so I have a general idea what the different climates are. My daughter and the kids in her group have not. In our state (Washington), we have sea level areas that could be in the 60s on the same day as the high desert being in the 90s+, so just going by which state is closest to the equator is the warmest, makes little sense to her. And honestly, she couldn't do that without a map anyways. I I know she doesn't have any idea what the temperature ranges are between SF and NO or which is colder Fairbanks or Chicago.....and honestly what does that have to do with math class anyways? Sorry, just and odd late night rant, as I watch my daughter struggle though homework tonight. I told her to skip the problem. I'm pulling her from the class anyways. (She is going to home school math). Quote Link to comment Share on other sites More sharing options...
obsidian Posted September 23, 2014 Share Posted September 23, 2014 I have lived all over the mid-west to western states so I have a general idea what the different climates are. My daughter and the kids in her group have not. In our state (Washington), we have sea level areas that could be in the 60s on the same day as the high desert being in the 90s+, so just going by which state is closest to the equator is the warmest, makes little sense to her. And honestly, she couldn't do that without a map anyways. I I know she doesn't have any idea what the temperature ranges are between SF and NO or which is colder Fairbanks or Chicago.....and honestly what does that have to do with math class anyways? Sorry, just and odd late night rant, as I watch my daughter struggle though homework tonight. I told her to skip the problem. I'm pulling her from the class anyways. (She is going to home school math). Yeah, I've lived in/near or visited all the cities mentioned, so that part is not difficult to me, but I can see how it would be tricky. It seems like it has more place in Earth Science, as Heigh Ho mentioned above. Quote Link to comment Share on other sites More sharing options...
justasque Posted September 23, 2014 Share Posted September 23, 2014 Yes, this is a tricky problem, but I like it. :-) It forces the student to actually look at the graphs: The shape of the curve - what does it mean? Whether it curves up or down. How the months are arranged on the bottom axis, and how that relates to the seasons. Whether the scale of the Y-axis is the same for all of the graphs. How high and how low the temperature values are for each graph. The difference between the top line and the bottom line, and what it means in terms of climate. This kind of understanding - what a graph actually shows, what a line of a certain shape actually means - is not easy. So many students can crunch equations (or have their calculator do it for them) with no clue how to actually *use* the resulting graphs. Which is all the more reason to include this kind of problem in an upper-level math class. Kids in Algebra 2 are usually in 10th or 11th grade. That's plenty old enough to know that Australia is in the southern hemisphere and thus has opposite seasons (and thus is the upper right graph). Alaska is probably the coldest (and thus is lower right, which is the coldest by far). From there it gets a bit trickier, which forces them to look at the graphs closer for clues. How are the remaining four graphs different? Middle left has a pretty big difference between high and low. Lower left and middle right never go below zero. Upper right has the coldest winter days. Where are the cities on the map, even roughly? Chicago is much farther north than the rest; that's probably a good choice for the upper right graph. Question (e) gives you the range for New Orleans, so that can be picked off the graph, so you're only left with San Francisco vs. Salt Lake City. Question (d) needs you to know which graph is SLC, but you can easily do the problem for both of the remaining graphs, and thus get partial credit at minimum. And of course nowadays the actual climate info is only a quick Google search away - no need to even get up off the couch to find it.I think it's valuable for students to face this kind of tough problem, so they can be encouraged to look deeper and see how much they can actually reason out, and how they can at least partially do the rest. If this was on a test, and the student skipped the whole problem, they'd get no credit at all. Taking a stab at it gives them a much better chance of a decent grade. Tests and grades aren't everything, of course math has real-world applications too. And I'm increasingly hearing about job interviews where they ask open-ended questions for which there isn't a clear answer, just so they can see the applicant's reasoning skills. Those who simply say "I can't do it" typically don't get the job, or the decent salary and benefits that come with that kind of position. I would encourage her to take another stab at it. And I'd be glad she had a teacher who assigns the hard stuff, instead of letting them skate by without really facing a challenge. Quote Link to comment Share on other sites More sharing options...
CaffeineDiary Posted September 24, 2014 Share Posted September 24, 2014 Yes, this is an awesome question! The domain for the graphs is the months of the year, and the range is the possible temperatures. Melbourne is easy, as being in the southern hemisphere it's going to have an inverse relationship from the others. For the northern hemisphere cities, I'd probably as a first cut assume that Fairbanks is going to have the lowest absolute mean temperature in winter, and then I'd stack the rest of them upin order of highest mean temperature in July to lowest and assume that that was their rough ordering south-to-north. And subquestion (e) implicitly tells you which one of the graphs is New Orleans. Quote Link to comment Share on other sites More sharing options...
kiwik Posted September 25, 2014 Share Posted September 25, 2014 I have never heard of Fairbanks. But I don't live in US. You don't have to get everything correct though so just work out the ones that are obvious and make educated guesses for the rest. Quote Link to comment Share on other sites More sharing options...
Word Nerd Posted September 25, 2014 Share Posted September 25, 2014 How is "public school math" different from "homeschool math"? Quote Link to comment Share on other sites More sharing options...
justasque Posted September 25, 2014 Share Posted September 25, 2014 Somes public schools integrate across the curriculum, so you see an Earth Science ? Such as this one In math, or a math question in social studies, etc. Some homeschools do not integrate, especially if they are leaving out word problems, so that is the difference. My son's DE calc class last year didnt have word problems, so he was surprised to get what he thought was a physics question in math this week...got him thinking of more applications. Also, in public school, on a nonblock schedule, the student doesnt have time to play with more complicated problems as he does in home school or on block schedule. The student is under pressure to finish by bedtime...and there is a firm deadline to hand the work in. Wait, what? A higher level math class without word problems????? I suppose I could see it for an upper-level college theory class, but high school? Especially calc? I'm speechless. WHY on earth would a teacher teach math techniques without also teaching when and how you would apply those techniques to actual real-world problems??? (I hear you on the bedtime pressure - but I think it's still wise for a student to do what they can of a problem, and there was quite a bit a student could do on this one without being geography-savvy or spending much time on it. Even if they don't get answers, they can work with it enough so that they know where they are stuck and can follow the teacher's explanation the next day in or after class.) Quote Link to comment Share on other sites More sharing options...
kiana Posted September 25, 2014 Share Posted September 25, 2014 Wait, what? A higher level math class without word problems????? I suppose I could see it for an upper-level college theory class, but high school? Especially calc? I'm speechless. WHY on earth would a teacher teach math techniques without also teaching when and how you would apply those techniques to actual real-world problems??? I agree. ?!?!?!!!!!! Quote Link to comment Share on other sites More sharing options...
Tap Posted September 25, 2014 Author Share Posted September 25, 2014 How is "public school math" different from "homeschool math"? Problem 1 with public school math in our area: Our city has 4 school districts, that have different curricula. Teens transferring between school districts lose out on math instruction due to the different styles of math. One district of the 4, only offers integrated math. Instead of Algebra 1, Algebra 2, Geometry and Trig (pre-calc), the program is "integrated". Integrated 1 is part algebra part Geo Integrated 2 is part algebra 1, part geo, part algebra, 2 with some trig introduced Integrated 3 is part algebra 1, part algebra 2, part geo , and some trig. Integrated 4 is part of algebra 2, part geo, part trig If you start in 9th grade in this school district and finish in this district, the kids are fine. BUT, for anyone transferring in, they have gaping holes in their math program and are automatically behind concepts that have not been introduced yet. My son transferred into the school in 10th grade but in what would have been trig in a traditional school. He is very gifted in math, but was completely lost in the integrated class because they were still teaching some algebra concepts, some geo concepts and he was missing the beginning concepts of trig that had already been taught 2 years prior. He had to stay after school every day to work with the teacher to figure out the holes. The district requires 3 years of math, so kids who only take 3 years are missing parts of algebra 2 and geometry. That may not seem like that big of a deal, but it absolutely causes these students problems when testing into college level math (according to the college testing administrator I was talking to.) Integrated math isn't a bad idea, but having only one school district of the 4 in our area using it...is a bad idea. I think the entire state of NY is integrated, I am fine with that, because at least the one state is using the same format, not individual districts. The school my son attended used to offer both formats, for kids who transferred in, but they stopped. It contained a STEM magnet in the high school, so lots of kids transferred in. The students were told to just stay after every day and catch up. :0( Problem 2 Our district, with my 15yo is currently attending, is not integrated but uses CPM Math which is heavily reading based and is designed to be done in groups. Her teacher lightly introduces a concept and they are turned out into groups to figure it out. The problem with this is that the quality of students in her math group, greatly vary and often have often no idea what to do. When she asked the teacher for help she is turned away and told to work it out with the group. The group doesn't always figure things out correctly, so she has learned to do the work wrong. Here is a link to CPM Math , scroll down so you can seen an example of a math lesson for basic algebra. Note, the lack of instruction on what they are supposed to do. The whole book is this way. DD15 transferred into this school from a private school at mid year break last year. She knew that there would be a transition between curriculum but not to the extent that she ran into. Her private school was actually a bit ahead of public in math, so she should have had a bit less of a transition in to that program. When dd needed help figuring out how to do a lesson, she had to go back and read lesson after lesson, to try to see if there was an example of what to do, or hope there is a reference saying which lesson to look back at to review. I have seen her spend 30 minutes trying to figure out how to do a basic algorithm, because the program prioritizes broad learning of concepts, not the fundamentals of math. My 20 yo son, s gifted in math, was in college calculus 3 at 16yo and has been a math tutor for 4 years. There were times in her basic geometry last term, that he has no idea what the problem was trying to get the student to do, and couldn't figure out where the concept was taught in her book to review it. Then we figured out that they only get 1/2 of the book each term, so that prior concepts may be in the other book. :0( I can't say that CPM style math isn't a good way to understand math ( I fully support the quality of questions), but if the kids are lost on what to do, then the group concept fails miserably. It is also Horrible for a kid who struggles in reading, like my dyslexic daughter. She is very good at math, she just reads slow and back tracks a lot. There are also issues like in the example I linked, where the students are told to refer to a graph on the 'overhead'. If they are not in class when the are doing the lesson, they don't have these bits of information for the lesson. Since DD was good at problem solving, she could make an answer work for the problem, but it was laborious and unnecessarily difficult for a math class. I hear that CPM is a good program for the teacher, reducing work by having preplanned lessons and good explanations. But if the teacher only refers kids back to the 'group' for helping when there is some confusion, and the book lacks the supports for the student to figure it out themselves, where does that leave the students? Both of my kids are 'A' students in math. I am not whining because they aren't getting good grades. What I hate is that they come out of these math classes and they both say.....I have no idea how to actually do the math. DD15 had an A in geometry last year, but told me that she only learned half of the material introduced. It was a class graded on a curve, so I can't imagine what the kids retained who got Cs. We just got the approval to switch her out of public school math and back to home school math. She wants to use Teaching Textbooks again because she feels like when she used TT before, was the last time she actually had mastery of her math program. When I talked to her counselor about it, he just smiled and said he completely understood why we were doing that. LOL Quote Link to comment Share on other sites More sharing options...
PinkyandtheBrains. Posted September 25, 2014 Share Posted September 25, 2014 I don't understand the idea of no word problems. Completely befuddled. Quote Link to comment Share on other sites More sharing options...
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