Tag: research

Posted in Mathematics education

Top 5 Best Math Education Sites and Blogs

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Math teachers serious at improving their craft should find a wealth of resources in the following math education sites:

1. The Klein Project blog is a collection of vignettes written for secondary school mathematics teacher. The blog is unique in the sense that unlike other blogs for teachers, “the vignette is not about pedagogy, but inspires good teaching. It is not about curriculum, but it challenges teachers to reconsider what they teach. It is not a resource for classroom use, but source of inspiration upon which teachers can draw. The goal is to refresh and enrich teachers’ mathematical knowledge.” Each vignette starts with something with which the teacher is familiar and then move towards a greater understanding of the subject through a piece of interesting mathematics. It will ultimately illustrate a key principle of mathematics.

Here is a list of interesting vignettes from the blog:

2. The NCETM Portal contains excellent resources and support tools for math teachers continuing professional development.

My personal favorite in the portal is their collection of research study modules. I also highly recommend the Personal Learning section which includes the Professional Learning Framework, Self-evaluation Tools, as well as a Personal Learning Space for anyone registered with the NCETM, which is free. You can use these self-evaluation tools to check your and your understanding of the mathematics you are teaching and to explore ideas on how to develop your practice. Click How confident are you to teach mathematics for sample questions.

NCETM Math Teaching

3. NRich – is a collection of resources for teachers, students, and parents. It is hosted by the University of Cambridge. I love this site because it promote learning mathematics through problem solving. The following description about their resources in the Teaching Guide page should be enough make you signup to them. It’s free!

At NRICH we believe that:
  • Our activities can provoke mathematical thinking.
  • Students can learn by exploring, noticing and discussing.
  • This can lead to conjecturing, explaining, generalising, convincing and proof.
  • In a classroom, the students’ role is to focus on the mathematics while the teacher focusses on the learners.
  • The teacher should aim to do for students only what they cannot yet do for themselves.

4. Math Education Podcast  is a collection of interviews with mathematics education researchers about their recent studies. This is hosted by Samuel Otten of the University of Missouri. For math education students and researchers, this site is for you.

5. The Math Forum @ Drexel – offers a wealth of problems and puzzles, online mentoring, research, team problem solving, and professional development. The site need no introduction. Their most popular service is Ask Dr. Math.

Posted in Mathematics education

Forms of mathematical knowledge

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Anyone interested to understand how mathematics is learned should at first understand what mathematical knowledge consist of. The book Forms of Mathematical Knowledge: Learning and Teaching with Understanding describes various types of knowledge that are significant for learning and teaching mathematics. It defines, discusses and contrasts various types of knowledge involved inthe learning of mathematics. It also describes ideas about forms of mathematical knowledge that are important for teachers to know and ways of implementing such ideas. The book is a collection of articles/papers from well known mathematics educators and researchers.


Top in the list of forms of knowledge presented in the book is a discussion about intuition and schemata.
While there is no commonly accepted definition, the implicitly accepted property of intuition is that of self-evidence as opposed to logical-analytical endeavor. Now, what is the role of intuition in the learning of mathematics?

While in the early grades teachers are awed by intuitive solutions by our students, those handling higher-level mathematics would find intuitive knowledge to constrain understanding of mathematics. In the book, the author of offered examples of these. He also defined the concept of intuitions and described the contribution, sometimes positive and sometimes negative, of intuitions in the history of science and mathematics and in the teaching process. The author argues that knowledge about intuitive interpretations is crucial to teachers, authors of textbooks and mathematics education researchers alike. The author further argued that intuitions are generally based on structural schemas.

My favorite article in the book is about the description of mathematical knowledge as knowing that, knowing how, knowing why and knowing-to

Knowing why, meant having “various stories in one’s head” about why a mathematical result is so. For example, when partitioning an interval into n subintervals, one might recall that n+1 fenceposts are required to hold up a straight fence of n sections. Knowing why and proof are different — in many cases, the proof doesn’t reveal why. As an example, the author suggested that when primary teachers ask why (-1)(-1)=1, they want images of temperature or depth, not a proof, or even a consistency argument that negative numbers work like positive numbers.

Knowing to means having access to one’s knowledge in the moment — knowing to do something when it’s needed. For example, in evaluating a limit, a student might just know to multiply by a certain quantity divided by itself. This kind of enacted behavior is not the same as writing an essay explaining what one is doing — it often occurs spontaneously in the form of schemas unsupported by reasons, whereas explanations require supported knowledge.

Forms of Mathematical Knowledge: Learning and Teaching with Understanding is a must-read for teachers, educators, and those doing research in mathematics teaching and learning.