AP Stats

Discussion in 'Secondary Education' started by JimG, Apr 20, 2018.

  1. JimG

    JimG Comrade

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    There is a chance I could teach AP Stats next year due to the current teacher transferring. She basically built the curriculum from scratch, so that is definitely a plus to have a framework in place already. Still, I am apprehensive because I have never taught AP and because stats is a little bit of a different beast compared to other math courses.

    Anybody have experience with this course? What were the biggest surprises or difficulties you ran into the first year?
     
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  3. TrademarkTer

    TrademarkTer Groupie

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    @futuremathsprof can help you out if....if he's not too busy objectively or subjectively debating robots and computers with the rest of the gang. I don't know anyone else on here involved with it.

    In my district, AP Stats is toxic---no one wants it except the one teacher teaching it. She's been teaching it for at least 10-15 years. When she retires in a few years, it will be interesting.
     
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  4. GTB4GT

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    I have taught stats but not AP (although that may be on the table for me next year). I love the material because it relates to the real world in ways that other mathematics can't. My observations: because the problems require excellent reading and comprehension skills, people who are good at "traditional" math - (algebra, trig, calculus) - can struggle. Conversely, people who don't do well in other math can love statistics. All the problems are word problems which is intimidating for some students. There is no more "solve for X, given this equation or information".

    The actual math is simple in stats - it's reading and analyzing the problems, understanding what information you have been supplied with, and selecting the appropriate methods, techniques and formulas that provide the challenge. Because one problem may take 15 - 30 minutes to solve, students who take stats may need to spend more time outside of class than in traditional math courses. (I teach them how to work the formulas before teaching them how to use their graphing calculators but you may not have that time luxury available in an AP class, which is unfortunate as I feel like you have to have an understanding of the formulas to really master the underlying ideas.)

    Students fall into two camps with this class - love it or hate it. One other note - because they have been exposed to simple things like histograms, means, medians, modes, etc. they can tend to come into the topic underestimating the rigor of the class. Good luck, I hope you have the same experiences as I do - as I said above, I love the subject and teaching it to my students.
     
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  5. futuremathsprof

    futuremathsprof Phenom

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    What do you mean AP Stats is toxic? I’m curious about that?
     
  6. TrademarkTer

    TrademarkTer Groupie

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    It's like computer science. No one in our department has interest in teaching it is what I mean. It's like "who will get stuck with stats and who will get stuck with comp sci?"
     
  7. futuremathsprof

    futuremathsprof Phenom

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    Look at other AP Stats teachers’ syllabi to get a feel for the contents of the course and what it entails. You will have to write your own or modify and borrow another teacher’s to get your syllabi approved by Collegeboard. You need to do this to have your course approved by Collegeboard and so you have access to AP Course Audit.

    Take an AP Stats summer institute course. Seriously. I say this because I took it the summer following the first year I taught AP Stats and I benefited from it immensely! It was taught by an actual grader so I learned what answers were suitable for the FRQs, in particular.

    Here is a general breakdown of the course:

    -Exploratory Analysis (20-30% of the exam)
    -Planning and Conducting a Study (10-15% percent of the exam)
    -Probability (10-15% of the exam)
    -Statistical Inference (30-40% of the exam)

    I recommend that you have students get a TI-84/TI-89. The N-spire is not that great, IMO, for AP Stats and most books are tailored to Texas Instrument calculators anyway.

    For every chapter, starting from the first chapter, make the students do practice MC and practice FR questions! I cannot emphasize this enough.

    Make sure that you know the calculator functions through and through, such as: invNorm, invT, binomcdf, binompdf, geometcdf, geometpdf, normalcdf, normalpdf, stats plot, one-variable stats, two-variable stats, how to construct box plots and modified box plots, how to plot scatter plots, how to calculate the least-squares regression line/line of best fit, how to use the hypothesis test commands, how to do a chi-squared GOF test and chi-squared test for independence, how to construct and interpret confidence intervals, the zoom function to quickly locate the bulk of your data in a plotted graph, how to adjust the window of various graphs, how to construct histograms, etc.

    Also, make sure that you know how to construct tree-diagrams, two-way tables, and Venn diagrams, and to read and interpret relative cumulative frequency histograms (ogives) and to assess the normality of various graphs given various sample sizes. Plus, know the difference between disjoint and nondisjoint events, the contrast between marginal and conditional distributions, what a density curve is, the difference between a normal distribution and t distribution, etc.

    For inference testing, know how to identify and write null and alternate hypotheses and define parameters of interest, and the four-step process for statistical inference problems (the “state” part is the first step of said process, BTW).

    I hope this helps. Don’t worry, teaching AP Stats is easy! Enjoy!
     
    Last edited: Apr 29, 2018
  8. futuremathsprof

    futuremathsprof Phenom

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    I’ve always wondered about AP Computer Science. Do you have to have an endorsement to teach it? I’ve secretly wanted to teach it, but I don’t know if you have to have an authorization to teach it. I do have knowledge of Putty, Matlab, JavaScript, C, and C++ programming languages. Is that enough or do I have to take a certification test or something?

    Why wouldn’t someone want to teach computer science? It’s fun and awesome!
     
  9. TrademarkTer

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    Nope---no special certification required. I was asked to teach it, but I told my boss I would do better teaching AP Biology or AP English Lit than AP Comp Sci. I took one comp sci class in college, and all we learned was Maple so I would be completely useless teaching that course.

    Our district is looking to add more comp sci courses besides AP too, but they are having trouble getting anyone willing to teach them because none of us have a comp sci background. We once had to have the media center specialist teach a section of AP because there were 6 sections last year, and each teacher only teaches 5 so the regular AP teacher couldn't do them all.
     
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  10. futuremathsprof

    futuremathsprof Phenom

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    Oh, this is great news! I might ask my principal to teach AP CompSci once I take a class on how to teach it. I was worried I wasn’t qualified because I only have a full Single Subject teaching credential to teach math to grades 5-12 and so I thought I was not able to. Thanks!
     
  11. TrademarkTer

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    Yep, my certification is in 6-12 math, but it seems anyone and their mother is allowed to teach it.......they just don't want to. Come on over to Jersey, and we'll give you a full teaching load of comp sci. :)
     
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  12. futuremathsprof

    futuremathsprof Phenom

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    Haha! I would except I LOVE California. And I couldn’t possibly give up my beautiful private school and teaching AP Stats, AP Calculus AB/BC, Pre-Calculus, plus else. I will just ask my P to pay for the summer institute course (they pay for professional development classes when you take on a new AP class) in the coming year or so. :D
     
  13. futuremathsprof

    futuremathsprof Phenom

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    Break everything down into lay terms. For example, when introducing z-scores to students, tell students that the z-score is a measure of spread or variability of data and it measures the spread about the mean of a standard normal distribution. Relate this to the area under the curve and how the area to the left of the z-score corresponds to the area under the curve, which is the same thing as the proportion of data to the left of z, which is the same thing as the probability of that event occurring. Also, tell the students that in order to compute a z-score, the distribution has to be approximately normal or normal (i.e. standardized or normalized first) because symmetry is essential to compute the probability. You will also want to introduce the notation N(mu, sigma) so that they identify the type of word problem once they see it.

    What works really well for me is having the students read through the problem, underline important information like the mean and standard deviation, as well as the type of distribution (if directly stated), and then to write down what we know. This “bookkeeping system” allows students to quickly deduce what methods or techniques to utilize to solve the problem. In this case, they will be told the distribution is approximately normal and the mean and standard deviation, and then will be asked to find a standardized value of some sort. That is an indicator that they will need to use the z-table/z-score formula or graphing utility (invNorm) to find said value.

    Now, if it is a mean problem, and the students are told the sample was taken from a large population instead of being provided with its shape, then they should be able to figure out that the sampling distribution is approximately normal regardless of the sample size due to the Central Limit Theorem. Then, proceed like before to compute the z-score or compute the critical value using invNorm and solve. By contrast, if this were a proportion problem and the population standard deviation is unknown, you could NOT apply the Central Limit Theorem and you would have to use a t score/t distribution instead.

    The key to students succeeding is show them each type of situation and breaking down each problem so they know when to do what. Finally, have THEM write a table of which functions and commands to use when given certain pieces of information. :)
     
    Last edited: Apr 21, 2018
  14. GTB4GT

    GTB4GT Cohort

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    OP, this is good advice for a new teacher of stats.The students need to know not only the HOW but the WHY probably more than they do in a 'regular" math course.
     
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  15. a2z

    a2z Virtuoso

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    What do you mean by this? Have you had experience programming or have you just played around?

    I think it is a disservice for someone to try to teach AP Comp Sci if they haven't had any experience programming especially if this is the students first experience with programming. If someone doesn't really understand programming it is like teaching math when you don't understand the theory but know the procedures.
     
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  16. a2z

    a2z Virtuoso

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    How well do you understand statistics? Unless you know it well, teaching AP is not the way to start.

    You might want to get the AP stat's book and see how well you would do taking the practice test. I am a strong believer you can't teach something you don't understand and do it service.
     
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  17. futuremathsprof

    futuremathsprof Phenom

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    Um, I took several programming courses in college in my math program because they were graduation requirements. I understand them well enough, but thanks.
     
  18. a2z

    a2z Virtuoso

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    I've known people who claim to "have knowledge of" programming languages who just played around with them on-line but couldn't really do anything substantial with them. They didn't take courses but claimed to know them. But you know that "knowledge of" is a highly subjective term.
     
    Last edited: Apr 20, 2018
  19. futuremathsprof

    futuremathsprof Phenom

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    Oh, gotcha. Why would someone claim to know something when they don’t? That will almost certainly come back to bite them in the butt later. Yes, it is certainly subjective... LOL
     
    Last edited: Apr 21, 2018
  20. a2z

    a2z Virtuoso

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    Inflated ego, want a job that requires the skill and hopes they could learn on the fly, wanting to impress (not claiming you were doing this), or many other reasons. Some can pull it off, but most can't. Depending on the situation they can sometimes blame everything but the truth for why things aren't working out as others expected.
     
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  21. JimG

    JimG Comrade

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    Thanks for the lengthy advice FMP. I had already looked up a summer course and am waiting to hear back on funding for the registration and lodging. I feel confident myself with the material, but pedagogically I am still trying to determine a the best game plan. The “book keeping” with each problem is a good idea.
     
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  22. JimG

    JimG Comrade

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    I am confident in MY understanding. It is more the curriculum structure and pedagogy that I am researching.
     
  23. futuremathsprof

    futuremathsprof Phenom

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    Happy to help a fellow math teacher out! :)
     
  24. a2z

    a2z Virtuoso

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    Great to hear. I know a few AP Calc teachers who say they survived stats in college during their major but would never be able to teach it. It wasn't my most favorite math course.

    Good luck with your decision and if you do end up teaching it. As others said, definitely take the AP course to get your footing.
     
  25. TeacherGroupie

    TeacherGroupie Moderator

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    In California, teaching computer science may not be that simple. See https://www.ctc.ca.gov/docs/default-source/leaflets/cl603.pdf?sfvrsn=b8e7b402_0. Better yet, talk to the credential analysts at the local county office of education. Topics in computer applications (yes, I know this isn't your issue) come under the heading of business education; topics in computer science per se come under the purview of industrial and technology education; both business education and industrial and technology education are considered part of career and technology education as opposed to belonging to math or one of the other core subjects.
     
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  26. futuremathsprof

    futuremathsprof Phenom

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    This is great to know! Thanks TeacherGroupie. However, Intro to CompSci (Javascript) and AP Computer Science A are the only computer classes offered at my private school besides keyboarding, digital animation, digital arts media, film production, advanced film, etc, etc. My P has been looking for someone to teach the AP CompSci A and Intro to CompSci classes since the current teacher is looking to retire soon. I’m interested in taking on the position because there is a 10k incentive (;)) to do so as computer science teachers are the most difficult teachers to come by.
     
  27. JimG

    JimG Comrade

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    How much do you emphasize being able to do by hand vs. being able to use the calculator functions? In my first exposure to stats, we were able to do everything with scientific calculators and some distribution tables. E.g. if X~Bin(n, p), I would physically work out P(X=x) = (n!/(x!(n-x)!)(p^x)((1-p)^(n-x)). Do you still require them to know the formulaic way to do things, or do they only learn the graphing calculator functions?
     
    Last edited: Apr 29, 2018
  28. futuremathsprof

    futuremathsprof Phenom

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    I teach them the formulaic way first along with the theory behind it and then after they do enough exercises using the formula by writing it out, I just have them use the calculator functions. However, they are still required to identify the setting, so whether it’s normal, binomial, or geometric, and then set up the problem using normpdf/normcdf, binompdf/binomcdf, or geometpdf/geometcdf. After they compute the probability, they have to provide context for the situation.
     
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  29. JimG

    JimG Comrade

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    Makes sense. Thanks.
     
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  30. HMM

    HMM Cohort

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    you have a small typo

    P(X=x)=(n!/(x!(n-x)!)(p^x)((1-p)^(n-x)).
     
  31. JimG

    JimG Comrade

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    Fixed.
     
  32. PetrMishikoff

    PetrMishikoff Rookie

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  33. JimG

    JimG Comrade

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    I am using some time this summer to plan ahead for the course. I looked for a way to send a private message but could not find a way to do so.

    Regarding the layout of the course with the four main themes, I have a concern. Another teacher who has taught AP Stats before had the course laid out with "Planning and Conducting a Study" as the first major unit and "Exploratory Analysis" as the second major unit. Apparently, this was a tip picked up at an AP Summer Institute. I guess the thinking is along the lines of learning how to collect data first before representing and summarizing it. However, the textbook has the units laid out in the order you wrote which also corresponds with what is written on the AP Statistics College Board Website.

    Have you any experience teaching the first two themes out of order? If so, what are your thoughts on which way works better?
     
  34. futuremathsprof

    futuremathsprof Phenom

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    I personally feel that the ordering in the textbook is optimal. The AP exam actually covers very little on planning and conducting studies. There is a just a small handful of questions in the MC section on that and maybe one part of one problem in the FRQ section, if any. Thus, I don’t spend a lot of time on that section because of this — I have exams all the way back to 1997 and that is the common spread.

    What helped me structure the class was using a spreadsheet that listed the relative frequencies of the types of questions that are asked year to year on the AP test. For example, I noticed that interpreting the slope and y-intercept of a least-squares regression line shows up time and time again, as well as using z-scores to compare data sets, and explaining what a type II error means in context, and so I gave my students plenty of practice on those. I, of course, review the lessons on planning and conducting studies, but it mainly just entails having them identify the different types of sampling methods (i.e. cluster sampling, stratified sampling, multistage sampling, systematic random sampling, and simple random sampling) and knowing when it’s more advantageous to use which depending on the situation. However, I definitely make sure they know how to design an experiment using a completely randomized design (CRD) or block design and how to randomly allocate their experimental units/subjects using a random digits table, the hat method, the randInt( function on their graphing utilities, and other miscellaneous methods.

    Look for problems that show up again and again and that will tell you how long you should focus on certain topics.

    You can switch up the order, but I feel there is no need for that. My students do just fine going along with the textbook and I think your students will do fine, too.

    Lastly, I feel students should be able to model and manipulate data before they collect it. My thinking is this: If students collect the data and can’t interpret it or know what to do with it numerically or graphically and/or cannot identify periodic trends, then what’s the point?
     
    Last edited: Jun 13, 2018
  35. JimG

    JimG Comrade

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    That makes sense, and I agree on many points. I also like your strategy of the spreadsheet with past exam question topics; I may steal that myself!

    I am still waivering on which order I will present for a couple reasons.

    1) The very first section of Part II in this book focuses on distinguishing between population and sample, and I feel those are very fundamental concepts that are good to wrap one’s mind around early on. I remember in my first exposure to stats as a student, I did not understand the importance of knowing the difference, and that led to struggles down the road.

    2) The first-semester project involves students designing a survey that will intentionally be biased and then interpreting the results. Last year’s teacher told me their plans/drafts were due for approval by the end of October with the actual project due in early December. I am not quite sure how the timing of instruction will work out yet, so I would fear not having proper time to cover Part II before the due date of their plans/drafts. Perhaps as I delve more into planning this summer, I will have a better idea of the timing of everything.

    As usual, I appreciate that you took the time to give such well-thought-out advice. Thanks!
     
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  36. TrademarkTer

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    I have not taught AP Stats before, but the difference between population and sample is usually explored in a typical algebra 2 course so they should have at least some exposure coming in.
     
  37. JimG

    JimG Comrade

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    True, ASSUMING the Algebra 2 teacher made time for a statistics unit amid all the material they are already hard pressed to cover AND that the teacher did an adequate job covering it. Personally, I am going to teach as if the students have little to no statistical background to avoid any confusion caused by overly optimistic assumptions.
     
  38. TrademarkTer

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    True. In our school, every algebra 2 teacher spends around a month on stats as it is covered on PARCC assessments. Every teacher who teaches the same course teaches the same thing each day so we are all on the same page, and I am able to make assumptions about what they had the previous year.

    I guess it would be more difficult if there is more a "free-for-all" mentality in a particular school.
     
  39. JimG

    JimG Comrade

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    Our department is similar to yours when it comes to syncing up what is taught in each class regardless of the teacher. Just there is not a big emphasis placed on stats in Algebra 2 in this area.
     
  40. JimG

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    Alright, after thinking it over quite a bit, I think I have decided to teach Part II first, and the main reason actually deals with teaching students about variance and standard deviation in Part I. Bear with me, and please point out any evident flaws in my logic that you may see.

    In Part II, topics covered include population vs. sample, bias, and simple random samples. As I have been thinking about how I would explain variance and standard deviation to my students in Part I, in a way that gives them a clear, concrete understanding of what is going on, I feel I need to invoke each of those terms in the explanations, as follows.

    The population variance is the average squared distance from the population mean. The population standard deviation is the square root of the population variance and gives a relatively good estimate of how far any given data point may be from the mean, give or take.

    The sample variance is used to estimate the population variance, and the sample standard deviation is used to estimate the population standard deviation. So why does each of those formulas divide by (n-1) instead of just n? Well, if you take a bunch of simple random samples from a population, and compute each sample's standard deviation using the formula that divides by n, the distribution of those calculated values would always have a center that is smaller than the population standard deviation. The reason for this is that in picking a simple random sample, you are unlikely to pick many extreme values at either end of the distribution, resulting in a smaller spread and an apparently smaller standard deviation/variance. This means that such a formula would have a negative bias in approximating the population standard deviation. To correct this bias, the sample standard deviation divides by (n-1), a slightly smaller denominator, which makes the overall calculated value slightly bigger. If you plot of distribution of all of the sample standard deviations using this correct formula, its center would be exactly at the population standard deviation, making the formula with (n-1) the ideal, unbiased estimator of the population standard deviation.

    To aid in the visualization of what is described above, I have created a demonstration that I plan to present that illustrates this. In it, I listed the population of all possible sums from rolling three fair, six-sided dice (e.g. {3, 4, 4, 4, 5, 5, 5, 5, 5, 5, ...., 17, 17, 17, 18}). Its standard deviation is about 3. To avoid unnecessary confusing details, I would probably just tell them it is a made-up population and not discuss where it comes from. I then took thirty simple random samples from it with ten values in each, incorrectly calculated the sample standard deviation of each using Sigma(xi - xbar) / n, and then correctly calculated the sample standard deviation of each using Sigma(xi - xbar) / (n-1). The five-number summary of the former was 2.0, 2.6, 2.9, 3.1, 3.8. The five-number summary of the latter was 2.1, 2.8, 3.0, 3.2, 4.0. Looking at the box plots, it is clear to see how the former (n formula) is negatively biased while the latter (n-1 formula) is centered exactly on the population standard deviation 3.0. This supports that the formula to calculate the sample standard deviation is an unbiased estimator of the population standard deviation and why it is crucial to use (n-1).

    I know that is a lot. Like I said, based on your experience, feel free to poke any holes in this that you may see. Standard deviation is such a central idea in the course, so I really want to make sure the students have a good intuitive sense of what it is going on. The description above is how I best understand it, but I want to make sure that I don't present things in such a way that it goes over students' heads, so to speak.
     
    Last edited: Jun 15, 2018
  41. futuremathsprof

    futuremathsprof Phenom

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    Jun 15, 2018

    I actually think this is a logically sound demonstration if you wish to teach Part II first. However, I would define what an unbiased estimator is and use lay terms when defining statistical terms in the beginning. For example, your formal definition for population variance makes sense to us as we’re mathematicians, but I think it safe to assume that it won’t mean jack for most students, even the top-level performers. That’s another reason why I model data first and have them identify trends beforehand in Part I. Yes, we want to encourage students to use academic language, but this course is very vocab heavy and students can quickly get lost just with the vocabulary words, let alone the formulaic parts.

    I use lay terms initially and various graphical displays to get them to develop an itutitive idea of what a standard deviation is, for example, (i.e. the spread about the mean) before I introduce definitions. This is because they need to see working examples with pictorial representations for the various concepts and not just formulas and definitions. In your case, I would include a side-by-side box plot of the five-number summaries so students can see how one is an unbiased estimator through visual inspection, and not just computationally.
     
    Last edited: Jun 15, 2018
    JimG likes this.

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