EDUC4105

The interactive whiteboard offers quite a few benefits to our teaching. There is the opportunity to engage students with an interesting presentation of the topic. The smartboard allows the teacher to concentrate on delivery of the lesson, minimising time with their back to the class. This helps with the flow of the lesson and supports good classroom management. A busy and engaged class is less likely to to be involved in disruptive behaviour.
The smartboard also gives the teacher access to the huge amount of resources available on the internet. Pedagogically this means a larger variety of strategies may be employed to teach a particular concept, catering to the needs of students with particular learning preferences. For example an animation of the behaviour of a function may benefit a visual learner who may struggle with algebraic or static two dimensional explanations.
An important advantage of the interactive whiteboard is that it encourages students to be active participants in the lesson. This not only increases engagement but supports the students own construction of their knowledge. By allowing students to experiment with the whiteboard, we can give them a sense of ownership of their learning and see the teacher not as a body of knowledge but someone who is there to guide their own discovery of mathematics.
Its important to remember this is only a tool and can only be of use if it is used in conjunction with a well prepared and relevant lesson.

The main features of a teachers e-portfolio would include information about your teaching qualifications, experience and strengths as a teacher. These are basic reqirements of any document you would present to a possible employer. In addition to this you may include your personal teaching philosophy, including the pedagogy you would use with examples of lessons and resources. This gives any school an insight into the type of teacher you wish to be. In addition to this a section on different types of resources, for example technology, would demonstrate your ability to seek out and use a variety of resources in your lessons.
Social bookmarking is a powerful tool for teachers. To have access to a large variety of resources and to be able to communicate and get feedback from other teachers helps us to become more confident and reflective about our teaching. For teachers who are physically isolated, social bookmarking brings them into contact with with other colleagues, not just to swap teaching ideas, but also issues that they face as teachers in their communities.

Mathematish, the use and understanding of mathematical symbols, involves the rules of using such symbols (or the grammar of mathematish as the authors put it) and how it conveys ideas by the way it is used. They point out that our own proficiency in mathematish may make us unaware of our lack of attention to the grammar needed by students who see it as a foreign language. The authors argue that matematical texts are bilingual, that is they have concepts and symbolic language. A lot of mathematish is taken for granted by teachers who are not explicit about the rules or origin of the features of the language, resulting in the knowledge becoming ‘tacit’ by nature, that is, not expressed or reflected on. Many students view of maths as a fragmented group of topics is due to a lack of understanding of the general language. If they knew the grammar, as in any language, they could see that the rules they learn are applicable across all topics. This requires a dialogue, as the authors state, playing the language game, allowing students to learn the rules through social interaction. I thought it interesting that as teachers of maths our tacit knowledge places us apart from most of our students and many of their problems don’t come into our thinking. This is something to be conscious of at all times. It was also interesting to consider the way textbooks amalgamate mathematical representations as if they were the actual objects and our expectation that students should believe such a ‘lie’. If, from an early age , we can teach students that mathematish is seperate from specific applications of it, that is they can see it as a general tool, then they may learn an important insight into the general nature of mathematics.

This paper discusses the idea of a mathematical register that enables us to construct our mathematical knowledge through the interaction of oral and written language, symbolic notation and visual displays. The author also notes the grammatical features of the register as having patterns of technical vocabulary, dense noun phrases and implicit logical relationships. She argues that learning new technical vocabulary may be easier than vocabulary which the student already knows a meaning in another context. Furthermore that although teachers may be aware of the challenge of learning technical vocabulary, many are not aware of the grammatical patterning associated with it. This has ramifications when teaching attributive and identifying processes, especially for students who speak English as a second language, where these relationships may have a different meaning in the grammar of their first language.
The teachers oral language may also adds more complexity, whereby processess are talked about as if they were things and classroom discussion may be conducted from different points of views without the teacher or the student being aware of it. To support students learning they need opportunities to practice their use of the mathematics register. Teachers also need to ‘unpack and explain’ meanings of symbols and explicitly focus on the language, expecting their students to use technical language in the classroom. This is important for students, for example learning algrebra depends on being able to formally talk about patterns and having students verbalise their thinking provides feedback for teachers and students about their understanding. Discussions should also focus on the reasoning students are using rather than their answers. Schleppegrell suggests that these discussions are vital in constructing meaning for learners and students need to be able to handle technical language which is first introduced orally in the context of odinary language before leaping into the technical.

This second article by Gough dicusses the artificial symbolic nature of mathematics, with its reliance on many non verbal ways of representing information. He makes an interesting point when he suggests that we need to be able to describe what we are doing in non-mathematical language as well as mathematical language. This use of students’ own understanding and explanations when dealing with new ideas is important as it connects the new knowledge with established structures that can later be refined to be more in line with conventional definitions. This, Gough asserts, is social constructivism (remember Piaget ?). I also liked the idea for imagining a square root as thinking of a number as a square and a square root as a side of that square, which makes you think geometrically and calls on previous knowledge of squaring something. Finally, though we should encourage students to talk in mathematical English, at times it is appropriate (and neccessary) to talk about examples in normal English to aid discussion and the deeper understanding that comes from such a free flowing discussion.

In this article, Gough discusses the nature of the technical language of mathematics and how the use of normal English in our instruction can lead to difficulties for students. He makes a good point when he describes how we all feel a sensory version of words, for example, to talk about increasing at a decreasing rate can make us feel a bit whoozy, but to decrease at an increasing rate can have us (and our students) feeling confused or maybe slightly nauseas. Our spatial interpretation of terms can often be at odds with the numerical meaning, making it neccessary for the teacher to be aware that the language they are using may be misinterpreted by their pupils due to the student’s strong intuitive meaning they have of some terms. The real difficulty of teaching maths in terms of language is that we do use everyday language interspersed with mathematical language that has usage of common terms with different meanings. This has further implications for students whose first language isn’t English. Tho only way to know what your students are thinking is to ask them often and encourage them to talk to you and each other about the contradictions between the language they use and the language they are trying to learn. As Gough points out it is easy to forget the confusion of technical terms once they have been learnt and even easier to blame the students for having trouble when they have been subjected to ambiguity and ’slippery words’ from teachers. The recommendations at the end of the article are an excellent checklist to help teachers avoid confusing students and increase students’ understanding of new concepts and terms, while remaining aware of the student who struggles with vague explanations.

This site was rated highly by our expert panel, for more details, read on.

Efficiency
The task is large, but gives a deep understanding of the uses of logarithmic scales. The process link ensures clear understanding and focus on the task. A weakness of the webquest is that there are many tasks and a lot of reaearch for two people.
Link to logs
Technofile
The strengths of this site were good links to next page from the bottom of current page and good use of pictures, fonts and colours. However the tables could have been in excel to do the graphs and the worksheet template could be on word so students could type straight in.
Altitudinists
The task really only required the gathering of information. There wasn’t any synthesis of ideas though some degree of thought and problem solving would have to be done to work out scales to plot different size objects on a sheet of paper. The task also requires the student to connect logarithms to uses in the real world.
From the viewpoint of the NSW Syllabus.
This webquest addresses how to represent a wide ranging set of data and phenomina that changes logarithmically on a easy to plot and read graph. Data is represented on both linear scales and log scales and the advantages of a log scale are discovered by the student. There is good use of technology with great links that explore scales with interesting and relevant examples, from size of bacteria to diatances in space. There are no direct links to outcomes as it is American, so some localising of the aims would be good from a syllabus perspective. Still, a good webquest.