Portal:Primary school mathematics

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Welcome to the Wikiversity Division of Primary School Mathematics, part of the School of Mathematics. The face of the teaching of mathematics is in constant flux. This course, therefore is an attempt to stay in step with the current pedagogy(s) used in the teaching of mathematics to the primary grades. While educators should find this course helpful in learning or reacquainting themselves with some of the methodologies currently used, this course attempts to use as much lay language as possible to also be helpful to parents who, when looking over the shoulders of their children, are sometimes baffled by the "New Math". Those who wish to home-school their child(ren) may find the most value from this course; attempts will made to cover topics in depth, and many core components of learning will be discussed and incorporated into the topics being covered. It is hoped that teachers of mathematics will continually make updates to this course as these changes inevitably occur.

What This Course is Not

This course assumes that the reader has reached a certain level of competency with the topics it covers. As such, this course is not designed to teach math to the reader. Rather, it is meant to give the reader insight into how and why mathematical core understandings and skills are taught the way they are. A basic mathematics background should be all that is needed to find value in this course. Oftentimes parents (and even teachers) only understand a topic in the way they were taught it, but modern math curriculums are typically constructed such that topics are covered in many different ways in order to, among other things, accommodate the different learning styles of students.

There are many ways to teach any given mathematical understanding, and the depth of students' mathematical understandings are enhanced when they have explored it from multiple perspectives. For example, the Theory of Multiple Intelligences is but one perspective that teachers employ when leveraging student's individual strengths.

Because there are many learning styles, this course recognizes that there are many teaching styles. As such, this course is not necessarily intended to be a math curriculum, although it could serve as part of the foundation of one. For example, this course will not teach the reader in step by step fashion how to multiply two large numbers, but the various building blocks and algorithms that students can be introduced to in the process of learning this skill will be explained.

There are many very good texts/curriculums/approaches out there; there are even "schools" of thought that suggest that math is best taught without textbooks if the teacher is skilled enough. This course could never pretend to cover the range of curricula out there. Emphasis will be on content knowledge and how it can be taught to the primary grade student. Nonetheless, activities will be suggested in this course that support the concept or skill being presented, which may serve to present the reader with ideas for their own course content.

Connections

One of the overarching ideas that should be highly leveraged in the teaching of mathematics in the primary grades involves the connections students make in their learning. All of our mathematical understandings are intertwined. For this reason different skills such as multiplication and concepts like those learned from the study of geometry should not be explored by students in a vacuum. Rather, they should be taught together, in such a way that they reinforce each other. Internal links, when found in this course will purposefully be placed there to emphasize the need for an ever-present awareness of the connectedness of mathematical understandings.

Teachers should prefer not to "teach".  They should prefer to "guide".

So how do teachers not teach? They do this by inspiring students to insipre their own learning. The most inspiring inquirys are often born of students' own interests. Primary and even upper school teachers recognize that understanding mathematics in the abstract is not the goal of most students. They need to see connections to the real world to inspire their learning. Teachers should prefer to use real world problems that require the need for mathematical models (see below). Students should then be encouraged to make connections by looking for patterns, exploring extremes, and forming and testing conjectures.

Modern Educators realize that students gain true "ownership" of their understandings through, inasmuch as it is possible, making connections on their own - by way of their own work and explorations. "Telling them how to do it." does not respect their abilities. On the other hand, letting students explore concepts, learning from their mistakes as they go, ultimately leads to much stronger mathematical understandings. It also leads them to form learning habits that make their future explorations more efficient and successful.

Manipulatives and Models

One very important component of the contemporary methods used to teach math is the use of manipulatives (such as toys) and models (visual representations) to give added dimension to students' understandings. In each chapter of this course, the reader will find various examples of models used to teach different mathematical understandings. Often, they will find that these models serve to make connections to material covered in other sections. Keep in mind that teachers in the classroom tend to be very creative and resourceful. Often, the models found in this course have many possible permutations, and can come in various shapes, sizes, and guizes. They are purposely presented here in simple forms to facilitate for the reader their identification.

Course Contents

(arranged by content strand)

Numbers and Operations

Pre-Algebra

Measurement and Geometry

Data Analysis and Probability

Move on to High School Mathematics