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## 4. Why Integrate? What's in it for us?

As a teacher of mathematics for many years, I am quickly able to identify ways in which I believe that teachers of mathematics should be more like teachers of science. I am excited by the possibilities offered by data loggers in mathematics classrooms, bringing the real world in all its messy wonder into our students’ learning. I am inspired by those teachers of both subjects who effortlessly cross boundaries in connecting the functions and problems they encounter in their study of mathematics with aspects of the world around us. This is active mathematics; this is engaging and experimental learning, which draws from the real world and so is immediately applicable and significant to our students, especially in the middle years where there is an identified need for work to be seen as relevant. For too long the cries of "When are we ever going to use this?" have drifted down the corridors from mathematics classrooms, and far too often unanswered!

It is easy for me to see ways in which we maths teachers may learn from teachers of science. But what of the other way around? In what ways might science teachers learn from teachers of mathematics? I find this question far more challenging, although I do not know whether this difficulty is a result of my own lack of recent experience in teaching science, or whether there may indeed be little we have to offer others in terms of good teaching practice?

And if the benefits of integration are one-sided, what then? What incentive is there for science to join with mathematics if there will be no substantial benefit for both parties?

There may be other arguments which you will arrive at upon reflection on this question, but I will share one that I believe has some value.

Recent years have seen a transformation, if not in every or even most mathematics classrooms, but in many. This transformation extends and arises from the work of most teacher training institutions and reflects principles of constructivism, quality pedagogy and a wealth of research, all of which point to the substantial failure of our traditional methods of teaching mathematics for the majority of students. Any subject from which the majority of students emerge with deep-seated feelings of anxiety, fear and, indeed, hatred, combined with an inability to apply what has been learned in any practical context, cannot be perceived as successful.

And so we are working on it, and we are making progress at most levels. One thing we have learned from bitter experience is this: we have to work hard to make our subject interesting and relevant to our students. We have to put a lot of effort into finding good questions which will engage and excite our learners. And we are doing this: increasingly, we begin with good questions which are rich, connected and engaging, which cross boundaries and link what is being learned to background and cultural knowledge; which demand higher order thinking of our students, involving them in substantive communication and result in deep learning and deep understanding This is an exciting time to be a teacher of mathematics.

Now I do not for one moment imply that these are not common features of science classrooms, but I ask this question: science has always been experimental, practical, hands-on. Students are frequently physically engaged in conducting, recording and interpreting the results of these experiments.

But to what extent do science classrooms begin with the experiment, rather than the "good question"?Is it possible that science teachers might need to work a little harder at finding the good question, rather than the contrived experiment?Perhaps this is what teachers of mathematics have to offer their colleagues in science: being busy is not enough: we need to aim

beyond engagement to deep learning, and this means basing our teaching upon principles of intellectual quality, creating a quality learning environment and doing all we can to ensure that what we offer our students is significant on several levels. These are the principles of Quality Pedagogy and they provide a challenge to us all. And at their heart, we find a core element concerning integration.In the classrooms I envisage in coming years it will be difficult to tell where science ends and mathematics starts: as students engage in rich, connected and significant learning drawn from worthwhile enquiry:

Which is the best spot to sit in the classroom, and why? Take readings of temperature, light and sound and justify your response.

Which is better to buy: MacDonalds or Hungry Jacks? Why? Collect nutritional information from each and justify your response.

Which is better: a bath or a shower? Why? Collect information concerning your family’s water usage for one week, and describe ways in which this might realistically be reduced.

Which of the popular antacid tablets available are most effective? (Which would you buy?) Justify your response.

Use a motion detector to capture the motion of someone on a swing, in terms of distance/time and velocity/time. Find as many other naturally occurring examples of this type of motion and explain why these are related to the motion on a swing.

Where does the mathematics end and the science begin? And did you notice that many of these "good" questions bring value judgements along with them, often raising ethical and even moral issues: elements too often missing from both mathematics and science classrooms of the past. This integrated classroom brings with it benefits for all: teachers of science and mathematics, but, most importantly, for the quality of learning by our students. And this is the greatest challenge of all.

For comments & suggestions, please e-mail Steve Arnold.