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- This section of the School of Mathematics focuses on providing teaching tools for parents and educators, whether in traditional or home-schooling environments. A parallel project is underway to teach students directly, whether children or adults, at this Wikibooks page.
Welcome to the Wikiversity Division of Primary School Mathematics, part of the School of Mathematics. The face of teaching mathematics is in constant flux. This course, therefore, is an attempt to stay in step with the current pedagogue(s) used to teach 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 be made to cover a number of pedagogically related topics in depth; many core components (not necessarily math related) of learning will be discussed and links to more in-depth coverage of those topics will also be included. Also, if you have trouble with the material, links will be found on each page to other more basic and/or remedial sources in the Wiki community to help bring you up to speed. By providing links "in both directions" as described above, it is hoped that this course might serve as a starting point for those wishing to gain more insight into the teaching of mathematics to the primary grades.
Contents
What This Course is Not[edit]
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 mathematics to the reader. For a very elementary introduction to mathematics, for the child or for the adult who considers themselves mathematically handicapped, you may want to read a book in development in Wikibooks, Primary Mathematics.
This course 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.
Although the idea that there are many learning styles is not well supported by the research in this area so far, 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[edit]
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 inspire their own learning. The most inspiring inquiries 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. At the same time teachers should be aware that all mathematics, from basic numeracy upwards is an abstraction and that some ideas are better explained as abstractions or generalizations from what is already known, rather than by constructing tedious and implausible 'real world' examples. After all, how often do carpenters really use trigonometry to measure the height of a flagpole?
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 or celebrate 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. Connecting with a child's personal interests is also important. However, it is unrealistic to expect students to construct their own understandings of many areas in Mathematics. For example, calculus eluded mathematicians for centuries before it was created by Sir Isaac Newton. More appropriately for the primary school level, the long division algorithm is not something that students can be expected to figure out for themselves.
Manipulatives and Models[edit]
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 guises. They are purposely presented here in simple forms to facilitate, for the reader, their identification.
In this course, the word model is occasionally used in a subtly different context as well - one that is commonly used by teachers of any discipline. We like to model good mathematical habits just as we like to see any kind of good behavior modeled. Occasionally, teachers should model problems by doing them as if they are a student.
Course Contents[edit]
Note: a copy of some of the following pages initially was created from Wikibooks, but the content will start to diverge to take the two different audiences into account. See Wikiversity:Import.
Numbers and Operations[edit]
Pre-Algebra[edit]
- Negative numbers
- Powers, roots, and exponents
- Fractions
- Working with fractions
- Percentages
- Factors and Primes
- Method for Factoring
- Proportions
- Introduction to variables
Measurement and Geometry[edit]
- Polygons and Area
- Angles, see also: Angles
- Solids
Advanced topics[edit]
Links commonly found in this course[edit]
Move on to High School Mathematics
External links[edit]
- http://www.mathsproblemsolving.com/
- http://hub.mspnet.org/index.cfm/13083
- http://math.berkeley.edu/~wu/
- https://mathnuggets.com
- http://archive.aft.org/pubs-reports/american_educator/fall99/amed1.pdf
- http://www.teachrkids.com/
- http://nlvm.usu.edu/en/NAV/vlibrary.html
- http://archive.aft.org/pubs-reports/american_educator/issues/fall2005/aharoni.htm
- http://www.math.jhu.edu/~wsw/papers/PAPERS/ED/ee.pdf
- http://www.air.org/expertise/index/?fa=viewContent&content_id=598
- http://www.cs.nyu.edu/faculty/siegel/siegel.pdf
- http://www.helpinghandeducation.com/