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E. Oldham TCD Maths Syposium Presentation

E. Oldham TCD Maths Syposium Presentation - Mathematics...

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Unformatted text preview: Mathematics Education Mathematics at Second Level A Teacher’s Views Teacher’s E. E. Oldham E. with Neil Hallinan Members of the Irish Mathematics Teachers’ Members Association Association Symposium on “The Place of Mathematics Symposium Education in Ireland’s Future” Education 2nd February 2010 Why me (a third level lecturer in mathematics education)? It’s a school day… … difficulties with regard to substitution and supervision! Lecture prepared with IMTA colleague, Neil Hallinan Neil’s background Neil’s Experienced secondary teacher … with a track record of reflective and innovative approaches innovative Longstanding member of the IMTA Dublin Branch Committee Editor of and contributor to the IMTA Editor Newsletter [mathematics education journal for IMTA members] IMTA Ex officio on IMTA national Council My background Former second level teacher In my fortieth year of membership of the IMTA Time in many different schools / classrooms Role as H. Dip. Ed. / Postgraduate Diploma in Role Education supervisor etc. Education Former Education Officer (NCCA) Experience of cross-national studies of Experience mathematics curriculum and achievement mathematics SIMS, TIMSS, PISA Context Context Ireland was deeply involved in the Ireland curricular changes in mathematics in the 1960s… 1960s… Not my IMTA colleagues! … but was slow as a general concern and at general system level to focus on issues of the 1980s system 1980s and onwards with regard to teaching and learning rather than curriculum content learning Problem solving, modelling, applications Teaching for / learning with understanding “Realistic Mathematics Education” “Voices crying in the wilderness” … … “Sowing the wind and reaping the whirlwind” Project Maths! So consider “a teacher’s views…” So Mathematics education has a central role in Mathematics central Ireland’s future Ireland’s Essential for recovery from recessionary present Mathematics teachers act as guardians of a Mathematics mathematical culture that they have mathematical received received To be maintained and transmitted to the next To generation of practitioners generation Questions on teachers’ practice Questions 1. 2. 3. 4. 5. Who do we teach? What is mathematics education for? for What do we teach? How do we teach? Where has mathematics teaching been and where is it going? going 1. Who do we teach? 1. Almost everyone! Almost everyone More students sit Leaving Certificate More Mathematics than sit any other subject Mathematics • 2009: Maths. 51 905; English 51 033; Irish 45 643… 2009: Implications for performance / achievement Students have priorities reflecting the current Students reflecting current culture culture Passing examinations rather than learning Social networking, social skills, etc. 2. What is mathematics 2. education for? In our teaching we are conscious (not always In explicitly) of the role and purpose of education in mathematics education Transmitting culture Transmitting culture Developing skills for employment Developing skills Assessing intelligence Assessing intelligence Assessing character (diligence, perseverance…) Assessing character Developing intelligence, logical skills and Developing intelligence logical visualisation skills visualisation ./. ./. And also Developing appreciation of methods of proof Developing appreciation methods as well as beauty of structure beauty Developing models of reality for better Developing models understanding and use understanding Preparing for further mathematical Preparing achievement (developing fluency as well as achievement developing fluency understanding) understanding develop recreational options, self-fulfilment develop and satisfaction of insight and … all in a crowded curriculum… …with less time than formerly given to Mathematics at 1st & 2nd level 3. What do we teach? 3. This includes Numerical skills Geometric-spatial skills Symbolic representation skills Visual representation skills Practical instrumental skills Logical skills Procedural skills Problem-solving skills There is limited time for skill development! There limited For a future intending to place more emphasis For on time-dependent skills than in the past, it is necessary to consider the implications of this for the whole set of skills involved whole Achieving deeper understanding, more fluent Achieving skills and better problem solving will require More time… … or acceptance of content reduction content • … unaccompanied by shouts of “dumbing down” unaccompanied • …or by further reduction of time given to mathematics! 4. How do we teach? 4. Under pressure! Under pressure “Covering” the syllabus Having very limited resources (room space, Having laboratories, technology…) laboratories, Methods used Often those designed to increase the “delivery” Often of concepts per unit of time ratio of Insufficient opportunity for “up close work” with students with Note There are, and always have been, many good There teachers in our schools teachers • Dedicated to and knowledgeable about the subject knowledgeable • Vibrant and gifted in developing knowledge and love of gifted the subject in (many of!) their students the They may be “traditional” in using whole-class They teacher-led approaches, but teaching actively actively • Emphasising (relational) understanding, encouraging Emphasising questions from students, identifying and addressing misconceptions, describing applications, etc. misconceptions, They may be “progressive” in using discovery They learning and hands-on (and “minds on”) methods learning Project Maths is emphasising the latter way Yes, we can do with more of it… … but there may be those (teachers and students) whom it does not suit whom • Variety to suit different needs can be good And yes, there are other teachers as well as And yes there those described on the last slide those For example, some teachers of other subjects who For are asked to teach mathematics… are … and may not have the vision / content knowledge / specialised knowledge of teaching mathematics specialised … so teach rules without reasons rules Examples Take it over and change the sign… Why? Take That’s the rule! That’s Why are we doing this? It will be examined in Why Paper 2, question 6, part b (ii) Paper • [and if they put it in part b (i), that’s a dirty trick [and and how could you possibly be expected to answer the question?] the A parody, but … … and students tend to reinforce this “didactical contract” 5. Where was / is mathematics teaching going? teaching Teachers have been (and are, and are willing to Teachers be) to the forefront in developing new syllabuses and teaching approaches syllabuses One of the most appropriate developments is One the LC Certificate Foundation level course LC … which was not given adequate recognition for recognition what it contains… … so students take Ordinary level and the culture of rote learning / teaching is reinforced rote For strong students, teachers support Young For strong teachers Scientists and Mathematics Olympiad entrants Scientists … though the PISA study indicates we have comparatively few high-flying students… comparatively … but also comparatively few low achievers (hence, but “average” [mean] performance) “average” A thought on the gate-keeping role of the LC thought gate-keeping Getting through the gate is often seen as much more Getting much important than what you bring with you… important Incentivising through rewarding Mathematics is not Incentivising not the answer? the Give a 10% bonus in every other subject done by a Give every student of Higher Mathematics?! student Hard problem! Hard The syllabuses have LONG advocated learn- ing with understanding rather than by rote ing understanding For decades we have tried to increase uptake For of Higher levels, but the “base-line” pattern of but was established in the 1960s and before… 1960s …so issues arise in aiming for greater so uptake / depth / understanding vs. “dumbing down” down” If it were easy, we’d have solved it long since ...
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