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  • Mr B 12:01 pm on August 30, 2014 Permalink | Reply
    Tags: lifelong learner, Professional Development   

    COURSERA: Professional Development on your own Computer? 

    Professional Development is absolutely one of my passions. Yes, I am a lifelong learner and believe all educators should be. All research shows that the best way to improve learner’s proficiency is to ensure educators are continuously professionally developed.

    But, attending courses may be expensive and most of the time it takes place at times that does not suit us. What if you can get classes from the best lecturers from the top Universities in the world for free and in your own time?

    Coursera is an education platform that partners with top universities and organizations worldwide, to offer courses online for anyone to take, for free. They envision a future where everyone has access to a world-class education. They aim to empower people with education that will improve their lives, the lives of their families, and the communities they live in.

    Currently (30/08/2014), they have 9,072,743 students doing 744 courses from 110 universities.

    Start your own journey and go visit their site by clicking on the picture below:

    RADIO-COURSERA 05-11-13-

    (Picture used without permission in the hope that Coursera will forgive me as I am promoting their website. Obtain from:

    Also read: You, your e-class and copyright: Being a Role Model Digital Citizen

  • Mr B 11:53 am on August 30, 2014 Permalink | Reply
    Tags: Copyright, creating content, Creative Commons, e-learning, Public Domain content   

    You, your e-class and copyright: Being a Role Model Digital Citizen 

    But I can do that, I am using it for the school and do not make money off it as it is educational use of copyrighted material under the claim of Fair Use. How many times did you hear teachers making this statement? How many times do we find a good worksheet from the internet, copy it and hand it out to the class. Even better, the class ask you to post it as a PDF on Facebook or on your Blog!

    Are you really sure this is true? Do you know the difference between Copyrighted Material, Creative Commons and Public Domain content and when can you really claim Fair Use? Don’t you think that it is vital to consider this?

    And here the low blow: Think how quick you are to lecture your students about plagiarism …….. Now ask yourself if you are modelling good digital citizenship for your students? Or is it a do as I tell you relationship?

    It is for these reasons that it is vital for educators to become familiar with this while they embark on creating e-classes. It is also vital that schools should consider developing a school policy in regards to copyright and even going beyond that by advocating for good digital citizenship.

    Fortunately a lot of the work was already done (can I use it and if I want to how can I use it?) and I would like you to go read the following Blog-links:

    There is also a link to a free online course on the Coursera-Website: (Also see my posting about COURSERA)

    Make sure you stay relevant but never lose your values!

    (O, and in the spirit of openness and copyright: My daughter directed me to the post on “Langwitches”. Hope I have declared everything now, and can sleep with a clear conscious?)

  • Mr B 1:18 pm on August 29, 2014 Permalink | Reply
    Tags: Statisticians   

    Statisticians have been described as the showgirls of the market place because they live by their figures alone. – FRANK A. FRIDAY
  • Mr B 9:03 pm on August 23, 2014 Permalink | Reply
    Tags: median; statistics; teaching statistics; teaching mathematics; learner misconceptions; teaching   

    Median: The middle of what? Grade 10’s misconceptions 

    Teaching the concept of median to my grade 10 class on Thursday 21/08/2014 I made the following interesting observation:

    (More …)

    • Piet Human 4:19 pm on August 24, 2014 Permalink | Reply

      This misconception by learners (I would expect it to be quite common) is probably the result of the torrid curricular practise to rush into the “summary statistics” before learners have developed the habit to consider the nature of distributions first when they engage with data sets, eg by ordering the data from smallest to biggest.

      It is a curricular misconception rather than a learner misconception.

      An easy way to protect learners against (naturally) forming this misconception when confronted with “mean, median, mode” before they have had sufficient experiences with distributions of different kinds, is to simply hold “mean, median. mode” back till grade 10 or even later.

      I think it is wise, when dealing with misconceptions, to always first ask “did curriculum teaching possibly cause this misconception” and if so talk to the teachers/curriculum-makers.

      To be currently practical with respect to those grade 10’s:

      Just let go of “mean, median, mode” for three lessons and let them compare data sets by just ordering he data from smallest to biggest. By that time median and mode will be natural self-constructed ideas, if the data sets were well chosen.

      There are two fundamentally different ways of trying to get a sense of how the data in a set is distributed:
      A. To group the data into intervals of equal width (histogram)
      B. To group the data into bags with the same number of data items in each bag (e.g. quartiles or centiles or whatever choice about the number of bags with equal numbers of data items you choose, you can also have twintiles, octiles or pentiles or hextiles for example)

      In the case of A, the percentages of the total number of data items that are in each interval gives you a summary picture of how the data is distributed.
      In the case of B the intercentile (or interquartile, or interoctile or twintile what have you) points provide a quick picture of the nature of the distribution.

      The median is a thing which belongs to tile-analysis (B) of distributions and makes little sense outside that context.

      Including it earlier in the curriculum gives rise to a lot of completely crap questions being dished up to learners.

      Liked by 1 person

      • Mr B 5:25 pm on August 24, 2014 Permalink | Reply

        Insightful, I have to agree this is more of a curriculum caused misconception than a learner misconception. I also agree that the activity of arranging the data from minimum to maximum can help but I am concerned that it may be a contributor to the idea that it is in the “middle” of a “line”.

        However, stacking the data that are the “same” as in my example can do more to reduce this idea. This is nothing new as Cobb, McClain, and Gravemeijer and their team at Vanderbilt University, Nashville, USA and Arthur Bakker from the Freudenthal Institute in Utrecht (Netherlands) pointed to this practice. Both studies clearly showed that by using computer software data that are manipulated as “stacked” data is better in the development of the understanding of these concepts. (See references below.)

        Bakker even suggest that it may even be a good idea to even continue this “stacking” approach and super impose it on box-and-whisker diagrams to continue the development of seeing the “bump-effect” in distribution. It supply far more support for learners in the development of their diagrammatic reasoning about the distribution.

        Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Utrecht: Freudenthal Institute.
        Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003, Jan/Feb). Design Experiments in Educational Research. Educational Research, 32(1), 9-13.


        • Piet Human 6:42 am on August 25, 2014 Permalink

          The challenge for a fourth world country is to design materials that can do the same without technology and software being available.


        • Mr B 7:45 am on August 25, 2014 Permalink

          This is why I am advocating simple drawings. If we use the box-and-whisker, show the data stacked on the number line that learners can see how many “pieces” are in each “bag” but also develop a sense of the “range” that these “pieces” cover. Both ensure a greater development of distribution.


    • Helena Wessels 9:32 pm on August 24, 2014 Permalink | Reply

      From my experience with undergraduate education students, I agree that working with stacked data fosters understanding of spread. Exploring data sets with software such as Tinkerplots (always followed by rich discussions) is also very useful in this regard.


  • Mr B 7:23 am on August 20, 2014 Permalink | Reply  

    Another brilliant Podcast: Dov Zazkis from Oklahoma State University discusses the article, “Proof scripts as lens for exploring students’ understanding of odd/even functions”, published in the Journal of Mathematical Behavior, Volume 35.

    Proof scripts as lens for exploring students’ understanding of odd/even functions

  • Mr B 5:54 pm on August 18, 2014 Permalink | Reply  

    Life is good for only two things, discovering mathematics and teaching mathematics Siméon Poisson (via allofthemath)
  • Mr B 5:51 pm on August 18, 2014 Permalink | Reply  

    Always remember to be 3 standard deviations above the mean and it’s okay to be highly unusual.
    Statistics Teacher (via mathprofessorquotes)
  • Mr B 5:51 pm on August 18, 2014 Permalink | Reply  

    There are two kinds of people in this world. People who love math, and people who haven’t realized they love math.
    Math Teacher (via mathprofessorquotes)
  • Mr B 5:47 pm on August 18, 2014 Permalink | Reply  

    What an Effective Teacher’s Classroom Looks Like… 


    What an Effective Teacher’s Classroom Looks Like

    This isn’t the most surprisingly list persay, but it’s interesting to see everything laid out. Here are a few from the effective teacher portion of the list:

    • Lessons are inviting and exciting.
    • The students do most of the talking and the doing, prompted by the teacher’s questioning and guidance.
    • Routines and procedures are evident. Students know exactly what is expected of them.
    • There are no teacher warnings for student misbehavior. If a rule is broken, a consequence follows. If a procedure isn’t followed, the teacher provides more practice.

    Basics, back to basics. Do you agree with this?

  • Mr B 5:42 pm on August 18, 2014 Permalink | Reply  


    Libby Nelson:

    The PISA scores suggest American students aren’t particularly good at real-world math, or at least at the problems they’re tested on. But education policy doesn’t usually exist in a vacuum. Lately, it’s been part of an economic argument: for the US to stay competitive, American students need to learn more than they do now.

    [source: mme rss]

    And I thought we have problems in South Africa?

    This is one of the unfortunate results when the economic debate enters Education. Or what do my learnered friends think?

    Does it even matter if Americans are terrible at math?

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