Students also confuse histograms with time series graphs. They describe a graph as, for example, 'starting low, increasing then decreasing again'. It's easy enough to see how they get this approach from their school maths. It's much more difficult to get them to see a histogram as rather more like a map, to be viewed from above. (I must admit to being something of an offender here. I emphasise the role of the inflexions in the normal curve as the only points on the peak which are identifiable without reference to the scale - except for the maximum - so can be used to measure the width of the peak. To describe them I ask students to imagine that they are riding a motor bike along the curve, The inflexions are where they momentarily straighten up....)
Alan Carl Lee wrote: > > Using introductory statistics as an example, concepts are built in a certain > sequence. If students get lost at a certain stage, s/he will have difficulty > to connect the later concepts together. Therefore, it is crucial to test the > understanding of the connection (or relationship) among related concepts. For > example, you may be surprised that the concept of histogram is much more > difficult for students than we thought. Try the following problem in your > final exam, you may be surprised by the outcome: > > If you collect a random sample of 100 salaries of working individuals who are > 40 years or older. Ask students to describe the shape of the histogram that > is more likely to occur, and their reason. Then, ask students to verbally > describe the Y-axis and X-axis of this histogram. > > I have collected data for this problem for several years. When I first asked > this question, I was shocked that 80% of students got confused between > scatter plot and histogram. I began to pay attention and used a variety of > strategies to help students. We usually think people have seen histograms all > the time, it must be simple. However, this test problem seems to indicate > that we may have overlooked simple concepts such as this. > > If we think about the construction of histogram a little more, we see that a > histogram is a transformation of raw data into two-dimensional presentation > for a response variable. This indeed is very different from our common > experience of two-dimensional plot, which is usually involved with two > response variables, a scatter plot. > > One assessment tool I use to test student's understanding of concepts is to > test how well they understand the relationship among related concepts, not > just stand-alone concept. For example, the relationship among time series > plot, box plot, histogram, outliers, mean, median, standard deviation and > range is important for understanding variation, distribution and later the > sampling distribution of sample mean. I have developed a series of questions > for testing their understanding of the relationships using the project of > investigating stock prices. There is no formula neither computation is > required by students in answering these questions. > > Another assessment tool that I use is to ask students give the reasons of > their answers verbally. Again, no formula neither computation is needed. What > I intend to find out is how they think and how they solve the problem. This > has helped me greatly to study how students learn a variety of statistics > concepts and which concept students tend to get lost at the early stage of > their learning. > > Assessment, learning and teaching are closely connected. And understanding > how students learn is most important of the three. A first step toward > understanding how learning take place is to conduct a good assessment, > especially assessing the process of reasoning. Teaching strategies and > instructional material can then be better prepared. > > Carl > ---------------------------- > Carl Lee, Professor of Statistics > Assessment Coordinator of CMU (1999-2001) > Department of Mathematics, Central Michigan University > Mt. Pleasant, MI 48859 > e-mail: [EMAIL PROTECTED] > Learning without Thinking, I am soon confused. Thinking without Doing, I can > never fully understand it. > ---------------------------------- > > Donald Burrill wrote: > > > On Wed, 14 Nov 2001, Alan McLean wrote in part: > > > > > Herman Rubin wrote: > > > > > > > > A good exam would be one which someone who has merely > > > > memorized the book would fail, and one who understands > > > > the concepts but has forgotten all the formulas would > > > > do extremely well on. > > > > > > Since to understand the concepts almost always means understanding > > > (and hence knowing) the formulas, I would interpret someone who has > > > 'forgotten all the formulas' as understanding the concepts only in > > > the most superficial manner, and so should do badly! > > > > Non sequitur. To know formulas (in a deep sense of understanding them) > > is one thing; to be able to write them verbatim is another thing > > altogether (and something that xerographic copiers do better than people > > do, by and large). Of course, it is easier to ask questions about the > > details of formulas than to probe a student's deepr understandings... > > > > > Overall, the evaluation of students is driven mostly by budget, > > > (lecturers') time, lecturers' interest, the number of students, > > > politics - the best one can do is to assess students as honestly as > > > possible within the range allowed by these factors! > > > > Sadly, this is true; and not infrequently exacerbated by administrative > > rulings (not to say interference!). At the university where I teach > > part-time, for example, course marks are to be submitted within 72 hours > > of the final examination. Not a circumstance that encourages (let alone > > rewards) setting the kinds of exams that Herman describes. > > > > -- Don. > > ------------------------------------------------------------------------ > > Donald F. Burrill [EMAIL PROTECTED] > > 184 Nashua Road, Bedford, NH 03110 603-471-7128 > > > > ================================================================= > > Instructions for joining and leaving this list and remarks about > > the problem of INAPPROPRIATE MESSAGES are available at > > http://jse.stat.ncsu.edu/ > > ================================================================= > > ================================================================= > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > ================================================================= -- Alan McLean ([EMAIL PROTECTED]) Department of Econometrics and Business Statistics Monash University, Caulfield Campus, Melbourne Tel: +61 03 9903 2102 Fax: +61 03 9903 2007 ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
