Week 14

“Discuss dynamic geometry and excel spreadsheets as a pedagogical tool. What are the advantages and disadvantages and why?”

Geometers Sketchpad could be used by a teacher with an interactive whiteboard, by individual students in an ICT suite or by  small groups of students working at a single computer. The Geometer’s Sketchpad is a dynamic construction, demonstration, and exploration tool that adds a powerful dimension to the study of mathematics. You and your students can use this software program to build and investigate mathematical models, objects, figures, diagrams, and graphs.

• With Sketchpad™, you can give your students a tangible, visual way to explore and understand core concepts—from numbers and operations, algebraic thinking, and geometry and measurement in elementary and middle school to algebra, geometry, trigonometry, precalculus, and calculus in high school and college. Concepts that students frequently find difficult become very clear when they see visual representations on the screen and interact with them using Sketchpad.
• Sketchpad has the flexibility to help you meet your teachingneeds regardless of your subject matter, technological expertise, grade level, or curriculum. You can take advantage of our subject-specific, ready-to-use activity books and sample activities or create your own activities and demonstrations to differentiate learning for all students.
• Sketchpad provides you with a faster, more dynamic and engaging way to demonstrate mathematical concepts than using transparencies or drawing on the board. Sketchpad works easily with your LCD projector, classroom computer, or SMART Board.
• Sketchpad can help you quickly explore variables, relationships, and the mathematics of change with your students. When you construct objects in Sketchpad, you can drag points and lines with the mouse. As shapes and positions change, all mathematical relationships are preserved, allowing you and your students to examine an entire set of similar cases in a matter of seconds.
• You can use Sketchpad across the mathematics curriculum, so you don’t need different software for each class, concept, or grade level that you teach.
• Sketchpad’s friendly user interface allows you and your students to get quickly up to speed so you can spend your time teaching mathematics, not software.
• You can quickly and easily generate teaching aids such as worksheets, tests, reports, and presentations with accurately measured figures by exporting Sketchpad files to word-processing programs and spreadsheets, other drawing programs, and the Internet.

GeoGebra is dynamic mathematics software for schools that joins geometry, algebra and calculus. GeoGebra is an interactive geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards. GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum.

Microsoft’s Excel is a wonderful application that can be used to achieve student learning outcomes. Applications like Excel’s ability to help you quickly organize and create graphical representations of data for easier analysis is becoming a dominate force not only in the educational arena, but in the corporate world.

It’s no wonder why many educators from all levels are fast learning that applications like Excel not only need to be introduced in a students’ K-12 program, but it need to be introduced early and revisited often to reinforce the skills associated with such applications. Yet, many educators seem to be intimated by the level of understanding and competence required to effectively use applications like Excel in their teaching. In fact, many of our staff developers are often told by the educators who they work with, “If I don’t understand it, do you think that my students will?” While this statement is no doubt true, we encourage teachers to think of using technology, in this case applications like Excel, as they would any other tool in teaching. As with anything newly learned, it takes time to develop a new skill.

**What’s Good About It?**

1.        Using Excel can enhance understanding of content within a graphic presentation of the information; it provides a visual representation of data that makes it easier to analyze.

2.        Excel reduces the difficulty of plotting data and allows students a means for interpreting the data.

3.        You can also reverse the traditional process of analyzing data by giving students a completed chart and see if they can reconstruct the underlying worksheet. This goes a long way toward helping them understand the relationship between the data and the chart.

4.        Excel can easily convert any chart or data set into a web page, making it very easy to share information among groups. Many universities are using this model for data sharing between students who aren’t even on the same continent.

5.        Excel’s ability to dynamically generate charts and graphs in seconds makes it easy to quickly demonstrate relationships between numbers.

6.        As a teaching tool, students can see how different types of graphs and charts can be used to represent the same series of data. As one teacher stated, “For years it took me three to five days to teach kids the use a pie chart, bar graph, and/or a line graph to accurately represent information. Now with Excel, it makes it so much easier because the kids are far more motivated to use the application to manipulate data and to chart any information.”

One of the best things is that you can compare data between any two or more variables. Using storage devices (disks), you can store data and use it to conduct a comparative analysis of any information that you have collected over time. For example, you can compare

Week 13

“Discuss the Webquest as a form of lesson planning? What are the advantages and disadvantages and why?”

A webquest is an inquiry-oriented activity that uses resources on the World Wide Web. Webquests pull together the most effective instructional practices into one integrated student activity. Webquests help students develop problem solving and decision making skills. An effective webquest develops critical thinking skills and often includes a cooperative learning component. Webquests help students analyze, synthesize and evaluate information.  Using webquests in the classroom can help build a solid foundation that prepares them for the future. Like any carefully planned lesson, a good webquest makes learning interesting for your students.

Week 12

“What (if any) pedagogical benefits do you believe graphic calculators offer and why?”

I believe graphics calculators are a great resource in the classroom as they provide an easy accessible tool for the students to check their work. Themes that need consideration is the student access to graphics calculators, the place of graphics calculators in the mathematics curriculum and the connection between graphics calculators and pedagogical practice.

Week 11

“What (if any) pedagogical benefit do you believe the interactive whiteboard offers and why?”

Interactive whiteboards can improve student achievement and are effective to educators who want to:

q       Raise the level of student engagement

q       Increase student motivation and attendance

q       Support students with special needs

q       Improve retention and facilitate review

Interactive whiteboards allows:

q       Teachers to present using text, sound, video and Internet links

q       Students and teachers can write notes and highlight points on whatever is displayed, including documents, diagrams and web pages

q       Students can interact with the boards by manipulating words, numbers and images

q       Teachers can show video, DVDs, CD-ROMs or television

All information presented on the interactive whiteboard can be printed, saved, emailed and posted to a website.

http://www.nytimes.com/2008/04/25/science/25math.html?em&ex=1209528000&en=10de70f5b0a8d0f8&ei=5087%0A

Week 10

“What are the key features of a teacher’s e-portfolio and why? Discuss the potential benefits of social book marking as a collaborative learning tool for teachers”

An e-portfolio is an online portfolio. It is an organized collection of documents that presents both your personal and professional achievements in a concrete way. A teacher’s e-portfolio can include your resume, reports, lesson plans and articles etc. This is a really effective tool as it allows other teachers to gather and exchange resources.

Social bookmarking is the process of organizing websites that a user would like to revisit. We are using delicious as our social book-marking tool. We are creating our own book marking list and making it public. This allows us the capability to share information with others who are looking for the same type of information. It does not only let us find links to sites that we might be interested in but also allows us to find out who has book marked your own site and how popular it is.

An unknown commenter sent this article to me and i thought it was quiet interesting. Click on the following click to view the document.

fullreport2006.pdf

My thanks goes out to you! 

Week 8 yet again…

I was allocated the following lesson on “Exterior Angles Investigation” to evaluate. First I attempted to actually do the lesson on Geometers Sketchpad myself. The lesson provided easy, clear instructions to follow.

What part (if any) of the NSW syllabus would this lesson be appropriate for?

This lesson will be appropriate for 8, 9 or 10-to support geometrical properties used in the syllabus.

What is the benefit of using the Geometer’s sketchpad software in this lesson?

Geometer’s sketchpad allows a visual representation of geometrical properties discussed in class. It allows the students to play around with the size of the shapes and to see that the property still holds.

Could the lesson be taught any other way? If so, how?

This lesson could be taught on Geogebra, using a similar approach.

While surfing the internet, i found the following articles:

Mathematics for Teaching.pdf

Teaching and Learning Mathematics.pdf

The importance of true-false statements in mathematics.pdf
and this newspaper article “Maths courses a minus: Gillard”.

The Dictionary: what mathematics professors say and what they mean by it

Clearly: I don’t want to write down all the “in-between” steps.
Trivial: If I have to show you how to do this, you’re in the wrong class.
It can easily be shown: No more than four hours are needed to prove it.
Check for yourself: This is the boring part of the proof, so you can do it on your own time.
Hint: The hardest of several possible ways to do a proof.
Brute force: Four special cases, three counting arguments and two long inductions.
Elegant proof: Requires no previous knowledge of the subject matter and is less than ten lines long.
Similarly: At least one line of the proof of this case is the same as before.
Two line proof: I’ll leave out everything but the conclusion, you can’t question ‘em if you can’t see ‘em.
Briefly: I’m running out of time, so I’ll just write and talk faster.
Proceed formally: Manipulate symbols by the rules without any hint of their true meaning.
Proof omitted: Trust me, It’s true.

A little song….

Week 7

Today we were introduced to Geometer’s Sketchpad. We learnt how to construct circles, triangles, and squares. I am yet to master the task of being able to rotate a shape without changing the dimensions of the sides but I am sure we will have another go at Geometer’s Sketchpad next week. I can see how this would be a handy tool to use in the classroom and also for creating worksheets. I found the following you tube presentation on discovering pi using Geometer’s Sketchpad:

Reflection on Readings

“Gough, J. (2007) Conceptual complexity and apparent contradictions in mathematics language, The Australian Mathematics Teacher, 63(2)”

I feel this article emphasized an important point - that mathematics is its own complex language. Mathematics “borrows words that already exist with everyday meaning” and in doing so changes the context of the word and therefore changes the meaning. This article gives lots of examples of words that are often mistaken in a mathematical context. For example; Power. If someone starts to talk about power our automatic train of though leads to strength or energy but in a mathematical context when we refer to power it is referring to what degree something is raised to. This can cause a lot of difficultly and impatience for the untrained mathematical mind. I felt this article also raised the important point that we (mathematics teachers) often forget what it was like to learn these mathematical concepts from ‘the beginning’ as it often seems plain obvious to us now. This article gives us some good teaching tips in how to limit this overlooking of a fresh mathematical concept to our students and emphasis the importance of our choice of words when talking about mathematics.

“Gough, J. (2007) Teaching square roots: Conceptual complexity in mathematics language. Australian Senior Mathematics Journal,21(1)”

This article follows on from the previous in that it discusses the importance of our choice of words when explaining a new topic and what misconceptions the students may have when we are introducing new words and their meanings. (By ‘misconceptions’ I mean the differences between the everyday meaning and mathematical meaning of words) I like how this article introduces “collarys” that students may discover while teaching a topic and how to explain square roots by using a geometrical representation of different squares.

Tutorial Task; Web Quest

For my evaluation of “The Origami Among Us” task, click on the following link.

Origami Among Us-WebQuest Task

Reflection on Readings

“Lee, C. (2006). Starting to talk in the mathematics classroom, in language for Mathematics: Assessment for learning in practice, Open University Press, Berkshire.”

 The main purpose of this article was to “look at ways to interact in the classroom to help pupils to learn to use mathematical language in order to deepen their understanding of mathematics”. In order to do this the article discusses different ways and insights to the organization of your classroom.  They include:

• If pupils can hear one another then teachers do not have to repeat or echo what pupils say
• If pupils can see and hear one another, they can listen to what is aid and build up an understanding of mathematical concepts
• When pupils can see and hear one another the discussion becomes a learning conversation between pupils which can be extended to smaller-group work.

 This article provides many examples of how we can support and promote students own learning of mathematics and the language or mathematics within the classroom.

 “Tapson, F. (2000) The Language of Mathematics. The International Journal for mathematics teaching and Learning”

I enjoyed this reading as it really made me think how complex the mathematical language is. “As teachers we need to be aware of, and sensitive to, the way we need and use language to convey our meaning. Possibly we are not as clear as we think.” This article gave some prime examples for where and how confusion can arise when using mathematical concepts. For example, “row, column”, “capacity, volume” “possible, probable”… Problem arises “because they refer to related concepts or objects which are connected in some way, and confusion arises over which word applies to which thing” In reading this article, I feel I am more aware of some misconceptions and problems that might arise when I am teaching.

A little catchy tune to remember the quadratic formula….

Reflection on Readings

“Barnett-Clarke, C. & Ramirez, A. (2004). Language Pitfalls and Pathways to Mathematics, in Perspectives on the teaching of mathematics, NCTM”

This article raised an interesting point- students may interpret and write 41 for the number fourteen. This is because for numbers like forty-two you write the four first. This idea can then have an impact on how the students understand and represent place value concepts. As teachers we must learn to carefully choose the language pathways that support mathematical understanding and simultaneously we must be alert for language pitfalls (like discussed above) that contribute to misunderstandings of mathematical ideas.

“Jamison, R.E. (2005) Learning the language of Mathematics, in language and learning across the disciplines, WAC Clearinghouse”

This article describes the use of language as a tool for teaching mathematical concepts. The articles’ main argument is that “once students understand how things are said, they can better understand what is being said and then do they have a chance to know why it is said” Think this is a very important idea and should be our basis for teaching every topic.