- Toh, Pee Choon

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# Toh, Pee Choon

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Toh, Pee Choon

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peechoon.toh@nie.edu.sg

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Mathematics & Mathematics Education (MME)

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- PublicationOpen AccessHow formal should calculus in the school mathematics curriculum be: Reflections arising from an error in a calculus examination question(Association of Mathematics Educators, 2023)
; ; ; ; Lee, HenryShow more This paper examines the calculus curriculum in the current Singapore secondary and pre-university levels. Two concepts, (1) increasing and decreasing functions and their derivatives, and (2) the second derivative test for the nature of stationary points, are elaborated. An example of an incorrect calculus item in a national examination is brought up in relation to conditional reasoning involving calculus concepts. We reckon that the current emphasis on procedural knowledge in calculus is useful. However, we argue that formal conditional reasoning should not be introduced prematurely for school students.Show more 278 190 - PublicationOpen AccessOn some congruences for Andrews’ singular overpartitions
Show more Andrews’ singular overpartitions can be enumerated by Ck,i(n), the number of overpartitions of n where only parts congruent to ±i (mod k) may be overlined, and no part is divisible by k. A number of authors have studied congruences satisfied by singular overpartitions. In particular, congruences for C3,1(n) modulo 3, 8, 9, 18, 32, 36, 64, 72 and 144 have been proved. In this article, we prove new congruences modulo 108, 192, 288 and 432 for C3,1(n).Show more 215 123 - PublicationOpen AccessFine-tuning in a design experiment(2013)
;Ho, Foo Him; Show more Quek, Tay, Toh, Leong, and Dindyal (2011) proposed that a design-theory-practice troika should always be considered for a designed package to be acceptable to the research users who, in this case, are teachers and schools. This paper describes the fine-tuning to the MProSE problem-solving design made by the teachers in the school after first round of teaching. This process involved teacher input from their experience, and detailed time-consuming discussions and learning between the researcher-designers and the teacher-implementers.Show more 114 162 - PublicationOpen AccessOn a certain vector crank modulo 7
Show more We de ne a vector crank to provide a combinatorial interpretation for a certain Ramanujan type congruence modulo 7.Show more 120 123 - PublicationOpen AccessMathematical problem solving for everyone: Infusion and diffusion (MinD)(2016)
; ; ; ;Quek, Khiok Seng; ;Dindyal, Jaguthsing ;Ho, Foo Him ;Hang, Kim HooYen, Yeen PengShow more 240 209 - PublicationOpen AccessConstructing an exemplary mathematical justification: Why is it so hard for mathematics teachers?(National Institute of Education (Singapore), 2019)
;Chua, Boon Liang; Yap, Von BingShow more 106 99 - PublicationOpen AccessTwelve erroneous proofs
Show more Assessing how well students understand proofs is difficult. One way to achieve this is to present an erroneous proof and require students to identify the error. Twelve erroneous proofs on various topics in mathematics at the Secondary school level are presented as examples.Show more 100 93 - PublicationOpen AccessCalculus for teaching and learning (CASTLE): An exploratory study(National Institute of Education (Singapore), 2022)
; ; ; ; ;Tan, VictorTang, Wee KeeShow more 275 132 - PublicationOpen AccessOn representations by figurate numbers: A uniform approach to the conjectures of Melham
Show more Using known formulas for R(a;b)(n), the number of representations of n as a times a square plus b times a square, we prove 21 conjectured formulas of Melham on the number of representations of n as sums of triangular, pentagonal and heptagonal numbers. We also demonstrate how our technique can be used to prove the other 277 conjectured formulas of Melham concerning representations by other gurate numbers.Show more WOS© Citations 3Scopus© Citations 5 138 120 - PublicationOpen AccessPutnam grasshopper problem: Collaborative problem solving, generalisations, and computational thinking(Association of Mathematics Educators, 2023)
; ; ; Tong, Cherng LuenShow more This paper considers several generalisations of an interesting problem posed in the 2021 William Lowell Putnam Mathematical Competition. We describe how the authors embarked on a collaborative problem-solving journey which resulted in solving two of these generalisations and how computational thinking guided our approaches.Show more 12 92

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