Beyond Mere Knowledge of Mathematics: The Importance of Knowing-to Act in the Moment

Mason, John; Spence, Mary

doi:10.1007/978-94-017-1584-3_7

Cited by 61 publications

(78 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Theoretical knowledge (deep learning) involves being able to make abstracted or generalised statements going beyond particular instances. Metatheoretical knowledge is knowledge about the process of abstraction and theory building (Krause et al, 2007;Mason & Spence, 1999).…”

Section: Implications Of the Literature For Teaching Statisticsmentioning

confidence: 99%

Students’ Understanding of Statistical Inference: Implications for Teaching

Reaburn

2018

Structuring the Thesis

View full text Add to dashboard Cite

Section: Implications Of the Literature For Teaching Statisticsmentioning

confidence: 99%

Students’ Understanding of Statistical Inference: Implications for Teaching

Reaburn

2018

Structuring the Thesis

View full text Add to dashboard Cite

“…It does not seem to occur to the teacher that the difficulty could be more global and to do with the student's problem in managing large-scale aspects, such as breaking down the task for themselves. When understanding a worked example, more important than 'knowing the next step' may be how the student knew to make that the next step (Atkinson, Derry, Renkl, & Wortham, 2000) -having it 'come to mind' (Mason & Spence, 1999). The term zone of proximal development (ZPD) (Vygotsky, 1978) has sometimes been misused to defend teachers forcing their approaches onto students and pushing them into mathematical actions that they would never do if left to themselves.…”

Section: Path-smoothing Of Learningmentioning

confidence: 99%

Resisting reductionism in mathematics pedagogy

Foster

2013

The Curriculum Journal

View full text Add to dashboard Cite

Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on bite‐sized learning objectives and a tendency for mathematics teachers to path‐smooth their students’ learning. I argue that a reductionist mathematics pedagogy severely restricts students’ opportunities to engage in authentic mathematical thinking and deprives them of the enjoyment of solving richer, more worthwhile problems, which would forge connections across diverse areas of the subject. I attribute the rise of a reductionist mathematics pedagogy partly to an assessment‐dominated curriculum and partly to a systemic de‐professionalisation of teachers through a performative accountability culture in which they are constantly required to prove to non‐specialist managers that they are effective. I argue that pedagogical reductionism in mathematics must be resisted in favour of a more holistic approach, in which students are able to bring a variety of mathematical knowledge and skills to bear on rich, challenging and non‐routine mathematical tasks. Some principles for achieving this are outlined and some examples are given.

show abstract

“…These two types of knowledge covered both the "L" dimension and the "C" dimension in the ELC framework of this study, but they were of quite different nature. Based on their review of previous literature, Mason and Spence (1999) distinguished two types of knowledge: knowing-about which includes "knowing-that (factual), knowing-how (technique and skill), and knowing-why (having a story in order to structure actions) (p. 135)" and knowing-to which is the active knowledge that enables one to act and respond to specific new situations. Of the two aforementioned types of knowledge the elementary teachers developed through their engineering teaching practice, the former one would be classified as knowing-about while the latter as knowing-to.…”

Section: Discussionmentioning

confidence: 99%

“…According to Mason and Spence (1999), knowing-about, albeit important, is not sufficient to enable teachers to handle particular learning and teaching situations. To be able to do so, teachers need to develop their knowing-to.…”

Section: Discussionmentioning

confidence: 99%

From Knowing-About To Knowing-To: Development Of Engineering Pedagogical Content Knowledge By Elementary Teachers Through Perceived Learning And Implementing Difficulties

Sun

2014

AJEE

View full text Add to dashboard Cite

The present study sought to reveal how elementary teachers develop their engineering pedagogical content knowledge (PCK) after leaving professional development programs to practice engineering teaching in real classroom settings. Participants of this study were the elementary teachers who received one-week training of engineering education provided by EfF (a P-12 Engineering teaching and learning institute in a Midwestern university). Data of this study were collected from these elementary teachers through face-to-face interviews and an online open-ended survey. Based on a phenomenological research method and a constructivist ELC (engineering instruction, learners, and contexts) framework developed by the researchers to investigate engineering PCK development

show abstract

Beyond Mere Knowledge of Mathematics: The Importance of Knowing-to Act in the Moment

Cited by 61 publications

References 15 publications

Students’ Understanding of Statistical Inference: Implications for Teaching

Students’ Understanding of Statistical Inference: Implications for Teaching

Resisting reductionism in mathematics pedagogy

From Knowing-About To Knowing-To: Development Of Engineering Pedagogical Content Knowledge By Elementary Teachers Through Perceived Learning And Implementing Difficulties

Contact Info

Product

Resources

About