Active learning for maths and stats

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					    Maximising
Student Engagement
              and

Knowledge Transfer
              in
    Large Classes
 Teresa Bradley/ Majid Ghanbari
 LIT Centre of Expertise -MSTL
         May 25th 2010
Challenges for the IoT sector
 Transition to third level

 Most students have ordinary level
 mathematics
 Maths skills are weak (from diagnostic tests)

 Students tend to be active learners

 Large classes, particularly first year
Transition to Third level (survey 2000, TB)
 Findings included…
 52.2% found lectures difficult to understand
 63% found understanding certain subjects difficult
 45% like practicals
 But students had little time to study because
   Travel home every weekend (58% live away from home)
   Part-time work (58% work part-time)
   Social life
 77.6% expect a full time course to be no more
  than 9.00- 5.00 Monday to Friday
 Retention linked to LC maths (p < 0.05)
         Table A.4(a): LC_MATHS * Results (S & A) Crosstabulation for
                         cert/diploma/degree courses

                                          Resul ts (S & A)
                                                             l eft or di d
                                pass         not pass           not si t     T otal
LC_M AT HS      A (pass)             83              7                   8         98
                                 84.7%           7.1%               8.2%     100.0%
                B (pass)           141              28                 26        195
                                 72.3%         14.4%              13.3%      100.0%
                C (pass)           103              29                 25        157
                                 65.6%         18.5%              15.9%      100.0%
                D (pass)             49             15                   9         73
                                 67.1%         20.5%              12.3%      100.0%
                E (pass)              2                                             2
                                100.0%                                       100.0%
                A (hons)              3                                             3
                                100.0%                                       100.0%
                B (hons)              6              1                1             8
                                 75.0%          12.5%            12.5%       100.0%
                C (hons)             15              1                1            17
                                 88.2%           5.9%             5.9%       100.0%
                D (hons)             18              2                3            23
                                 78.3%           8.7%            13.0%       100.0%
T otal                             420              83               73          576
                                 72.9%          14.4%            12.7%       100.0%
 Retention linked to ‘Difficulty with certain
 subjects’ p < 0.00005
Table A.8: Difficulty with Certain subj ects * Results (S & A) Crosstabulation

                                         Results (S & A)
                                                           left or did
                                pass        not pass         not sit     Total
Certain     very difficult         153             47               40      240
subjects                         63.8%        19.6%            16.7%     100.0%
            difficult              168             27               22      217
                                 77.4%        12.4%            10.1%     100.0%
            not difficult          219             27               27      273
                                 80.2%          9.9%             9.9%    100.0%
Total                              540           101                89      730
                                 74.0%        13.8%            12.2%     100.0%
Diagnostic tests 2008_09 and 2009_10
 Some results for STEM courses

 2008: n = 382 (complete details)

 2009: n = 341 (complete details)
Test consists of three sections..
 Numeracy, Algebra, Trigonometry
 1 mark for correct answer. 0.5 marks for method and no
    more than one minor mistake.
   Mark scheme (maximum marks 6 per section )
   Marks 5.5 to 6 Inclusive (Green): competent in basic
    skills – keep it up
   Marks ranging from 3 but less than 5.5 (Amber): there
    are serious gaps in basic skills.
   Marks less than 3 (Black): there are very serious gaps in
    basic skills..
Comparison of average results
08_09 vs. 09_10


         Numeracy   Algebra   Trigonometry


  2008     3.61      3.13         2.96


  2009     3.44      2.78         2.52
 Data from diagnostic tests 08_09
                        LC Grades (Ord) 2008, 2009

                                                               2009
20.00%                                                         2008
18.00%
16.00%
14.00%
12.00%
10.00%
 8.00%
 6.00%
 4.00%
 2.00%
 0.00%
         A1   A2   B1     B2    B3   C1   C2    C3   D1   D2    D3
Lower cognitive skills are weak
(Blooms Taxonomy)

 Remembering…

 Understanding

 Applying
For example, Section 2: Algebra (n = 382)

7.   Evaluate      b   b 2  4ac
                         2a                 44.04%
                                            correct 08
      when a = 1, b = - 3 and c = - 4

 8. Rearrange the following formula:
     in the form   T=?
                                                44.76%
                            PV                  Correct 08
                                nR
                            T
  9. Write the following as a single fraction
                     1    1
                                               16.54%
                     R1   R2                    Correct 08
Learning Styles Profiling
(Dr M O’Brien, LIT)
 Visual vs. Verbal

 Active vs. Reflective.

 Sensing vs. Intuitive

 Global vs. sequential
Different Learning styles
Report on Learning Styles Profiling (Dr M O’Brien)

LIT       Active      Reflective       Intuitive   Sensing


n = 316      61.39%     38.61%            23.10%      76.90%




LIT       Verbal      Visual
                                       Global      Sequential



n = 316     20.25%      79.75%           41.46%        58.54%
         Active learning
 Getting students to do something course-
 related other than watching and listening to
 the instructor (Felder 2008).
         Active learning

 Active learning occurs when the learner

 organises selected information into coherent
 mental representations, and integrates it with
 prior knowledge. (Mayer 1999)
                          Active Learning
    Good Practice Encourages Active Learning. Learning is not a spectator
    sport. Students do not learn much just sitting in classes listening to
    teachers, memorizing pre-packaged assignments and spitting out
    answers. They must talk about what they are learning, write about it,
    relate it to past experiences.
   I ask students to present their work in class.
   I ask my students to relate outside events or activities to the subjects
    covered in my courses.
   I encourage students to challenge my ideas, the ideas of other students,
    or those presented in readings or other course materials.
   I give my students concrete, real-life situations to analyze.
   I encourage students to suggest new readings, projects, or course
    activities.
Chickering and Gamson, "Seven Principles for Good Practice in Undergraduate Education," AAHE
   Bulletin, March 1987
            Active teaching

a. Recognize the different learning styles.

b. ‘Instruction begins when you’ the teacher, learn

   from the learner. Put yourself in his/her place so
   that you may understand what her learns and the
   way s/he understands it (Kierkegaard)
Current Initiatives
 Practicals

   Practical exams constitutes 15%- 30% of

    many maths courses
 Moodle

 Learning Support
The Challenge of Large Classes-
Some active learning techniques
TAPPS (thinking aloud pair problem solving)…
  n Short problems (30 sec to 3 min)
  n Longer problems… circulate, give hints and
     check understanding
Give handouts with gaps
Use of classroom response systems
– being researched at present
Research in the effective use of ICT
  LIT Centre of Expertise in Mathematics and
  Science Teaching and Learning (Oct. 2009)
  Two post graduate students

 Majid Ghanbari (Maths)
 Regina Kelly (Science)
…a distributed centre of NCE-MSTL
Initial trials on ‘Clickers’ are very positive
            Project Outlines

      To develop an innovative classroom
engagement technique and use technology for
 the enhancement of teaching and learning of
   mathematics with emphasis on IoT sector
                 Majid Ghanbari
           Educational Goals
 To maximise interactivity between lecturers,
  students and the learning materials
 Raising interest and motivation in students
 To enhance the learning experience
 To establish students’ basic maths skills and
  challenge them to think critically (Blooms taxonomy)
 Maximization of transfer of learning
                 Formative Teaching
                       (Active Teaching)
  Professor John Hattie showed that feedback had
  more impact on learning quality than any other
  single factor.
  Sadler '89 analysed feedback to show that for
  learning to take place the learner needs to know:
 The Goal
 Student’s present position
 How to close the gap
http://www.teacherstoolbox.co.uk
Cambridge Regional College
                                     Good-Questions
It is a pedagogical strategy that aims to raise the
visibility of the key concepts and to promote a
more active learning environment.
Such questions









http://www.math.cornell.edu/~GoodQuestions/
Maria Terrell, PI, Robert Connelly Co-PI
 Good questions build progressively…

 Quick check: Designed to quickly check students' basic
   understanding of the material

 Probing: Usually requires some thought and extension
   beyond basic concepts

 Deep: Difficult questions that will usually require
   instructor intervention to help guide students in the
   right direction
http://www.math.cornell.edu/~GoodQuestions/
Maria Terrell, PI
Robert Connelly Co-PI
       Example of a Quick-check Question

                  
                      4
                    5x dx   equals

(a)    x c
        5



(b)   20x  c
            3


    1 5
(c)   x c
    5
      Example of a probing Question

                       
                         2
                         x dx   equals

          1
(a)    x  c
               3
(b)     2x  c
          1
(c)      c
          x
(d) Both (a) and (c)
      Example of a deep Question

                    
                         1
                      x dx    equals

          2
(a)     x  c
        1
(b)       c
        x
(c)    Ln( x)  c

(d)      Doesn’t exist
             Classroom Response Systems
                      (clickers)
• Allows for two-way communication between an instructor and
   students regardless of the size of a class
• Instructors receive instant feedback on understanding and
  misconceptions of the whole class instead of relying on responses
  of few who are willing to speak out
• Students receive instant feedback regarding their understanding,
  comparing themselves to the rest of the class and consequently
  building their confidence
                                   Q5
Q4




                           Q5 Instructor’s handset
http://www.qwizdom.co.uk
                  Question Types
 Multiple Choice -You can have up to 6 choices
  (A,B,C,D,E,F)
 Yes/No
 True/False
 Numeric
 Sequence
 Multiple Mark
 Rating Scale
 Vote (Multiple Mark)
 Text Input -
  This is a text input question, only available for the Q5 remotes,
  this allows for up to 30 characters in the answer.
 Demographic
Public Response Graph
Excel Report
Flash Reports
           Research to Date

 Literature review
 Familiarisation with technology
 Decided that the clickers satisfy the
  educational goals and are suitable for large
  classes
 Clickers have been piloted in a 1st year
  electronics engineering class
   (app. 80 students)
Next.....
 Design slides (Good Questions) for selected
  topics in 1st year engineering maths
 Implementation in semester one, 2010
 Evaluation
The Independent (UK) 5 January 2009
-a study by the KPMG foundation-
 ‘Numeracy    difficulties are linked to …
 exclusion from school
 health risks (more likely to suffer from
  depression)
 increased involvement with the criminal justice
  system.
    Legal costs £164.8m a year…
Thank
 you

				
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