Published 2011 Revised 2012

It seems to me that good times are on the way for future STEM undergraduates. Since I became explicitly involved in STEM matters in 2009 I have noticed a growing awareness that a holisitic approach to a school STEM education can benefit, motivate and inspire school students who plan to move on to a university STEM course. Schools, universities, government and industry appear to be giving a united
message: The UK needs a skilled STEM workforce; a workforce of creative, innovative problem solvers; a workforce from which world leaders in STEM will emerge. We ought not let this evolve by chance and, fortunately, there has been lots of work done recently which give us insights which allow us to grow a decent STEM workforce: Research on STEM education has been done; STEM resources have been
invented, dusted off, and refined; important STEM collaborations between diverse groups have formed. As a result, students are now being given a fighting chance of seeing the bigger picture prior to embarking on their university course. As a teacher, you are the guardian of this bigger picture.

The STEM material on NRICH is part of a wider offering in which teachers can help students to see connections between their school science, technology and mathematics. As a mathematics site we hope through stemNRICH problems to provide a real understanding of how mathematics is the life-blood (or at least a component, such as the platelets) of rich engagement with advanced STEM. What is our focus? In a nutshell I want our students to receive an*education* in STEM, rather than learn to answer exam questions on topics in subject silos.

For the remainder of this article, I'll look at three matters: some Golden Rules concerning good STEM practice; some of the mathematical issues facing STEM students; and some tips and suggestions for teachers in schools who wish to help students in their overall STEM education.

**Part 1: Key Elements of Good STEM Practice**

**Golden rule 1: Respect**

Have respect for different departments and no sense of any subject being better or more important or more fundamental than any other: the differences are real and significant, but there are also commonalities. Talk to people in other departments so you know what the differences and commonalities are.

**Golden rule 2: Use positive language when talking about mathematics**

It is still unfortunately seen as OK to dismiss maths as un-cool, pointless, geeky or to confess to being pretty bad at it. This has a very negative impact on students who either wish to study mathematics or might encounter a lot of mathematics in their university course.

**Golden rule 3: Build on learning from other subjects**

Don't try to teach things from scratch that students might have encountered elsewhere.

**Golden rule 4: Be aware of the difficulties in applying mathematics**

Don't assume that an 'easy' piece of maths is easy for students when it is located in a context where they wouldn't expect to find it. Don't assume that the maths is easy for students just because you think it is obvious.

**Golden rule 5: Be open-minded about STEM**

Be aware that your particular interests are not necessarily the particular interests of all of your students. Try to find the hidden gems in any topic area, even if it is not your personal favourite. Good enthusiastic teaching is a wonderful device. No topic is really intrinsically dull or boring, even if you think it is. Who knows, you might find thinking about STEM re-energises your teaching on a jaded area of the curriculum.

**Golden rule 6: Celebrate the subtle and complex skill of good teaching**

Be aware that the role of the teacher is as a learning facilitator in many cross-curricular activities, rather than the transmitter of all of the knowledge. It is OK not to know 'all' the answers. In fact, it is desirable to provide contexts in which you do not know all the answers to all possible questions! How else are students to learn how to solve real problems?

**Golden rule 7: Don't try to force links where none meaningfully exist**

I feel that a poorly conceived STEM task can cause more harm than good. The universe is wonderfully constructed. There are many brilliant STEM contexts around - don't try to make STEM links for the sake of it.

**Golden rule 8: Make technology a fundamental part of learning**

Whatever your students end up doing, they will end up doing a great deal of it using a very wide range of technologies (many of which won't yet exist). Pencil and paper tasks are still very desirable, but so is good level of techno-literacy.

**Golden rule 9**: **Don't forget the STEM history of the educators**

Many teachers, lab assistants, TAs and others involved in education will have had experience of STEM matters in various contexts. Celebrate these! Don't feel that as a maths teacher you have hide the fact that you did engineering or biochemistry - celebrate your quantitative past history and bring it into the education of your charges where appropriate

**Part 2: Quantitative matters**

Why would clever students struggle with the mathematical aspects of their university course in science, technology or engineering? There are several possible reasons which I have encountered many times.

**Part 3: Some quick tips for the classroom**

There are various ways in which you can bring STEM into the classroom, from the light-touch reference here and there to the full off-curriculum week. Here I list some of my favourite quick ways to get STEM moving in your schools

**General references**

Prepare for university http://nrich.maths.org/university

Mathematical Preparation for the Cambridge Natural Sciences Tripos http://nrich.maths.org/6884

Interactive Workout - Mathmo http://nrich.maths.org/7088

Maths in the Undergraduate Physical Sciences http://nrich.maths.org/6864

Algebraic Fluency of Advanced Students http://nrich.maths.org/8628

The NRICH - Transkills Project http://nrich.maths.org/6326

stemNRICH http://nrich.maths.org/stemnrich

stemNRICH - advanced http://nrich.maths.org/stemadvanced

http://sfh10.wordpress.com/2012/11/29/superficial-contexts-in-stem-problems/

The STEM material on NRICH is part of a wider offering in which teachers can help students to see connections between their school science, technology and mathematics. As a mathematics site we hope through stemNRICH problems to provide a real understanding of how mathematics is the life-blood (or at least a component, such as the platelets) of rich engagement with advanced STEM. What is our focus? In a nutshell I want our students to receive an

For the remainder of this article, I'll look at three matters: some Golden Rules concerning good STEM practice; some of the mathematical issues facing STEM students; and some tips and suggestions for teachers in schools who wish to help students in their overall STEM education.

Have respect for different departments and no sense of any subject being better or more important or more fundamental than any other: the differences are real and significant, but there are also commonalities. Talk to people in other departments so you know what the differences and commonalities are.

It is still unfortunately seen as OK to dismiss maths as un-cool, pointless, geeky or to confess to being pretty bad at it. This has a very negative impact on students who either wish to study mathematics or might encounter a lot of mathematics in their university course.

Don't try to teach things from scratch that students might have encountered elsewhere.

Don't assume that an 'easy' piece of maths is easy for students when it is located in a context where they wouldn't expect to find it. Don't assume that the maths is easy for students just because you think it is obvious.

Be aware that your particular interests are not necessarily the particular interests of all of your students. Try to find the hidden gems in any topic area, even if it is not your personal favourite. Good enthusiastic teaching is a wonderful device. No topic is really intrinsically dull or boring, even if you think it is. Who knows, you might find thinking about STEM re-energises your teaching on a jaded area of the curriculum.

Be aware that the role of the teacher is as a learning facilitator in many cross-curricular activities, rather than the transmitter of all of the knowledge. It is OK not to know 'all' the answers. In fact, it is desirable to provide contexts in which you do not know all the answers to all possible questions! How else are students to learn how to solve real problems?

I feel that a poorly conceived STEM task can cause more harm than good. The universe is wonderfully constructed. There are many brilliant STEM contexts around - don't try to make STEM links for the sake of it.

Whatever your students end up doing, they will end up doing a great deal of it using a very wide range of technologies (many of which won't yet exist). Pencil and paper tasks are still very desirable, but so is good level of techno-literacy.

Many teachers, lab assistants, TAs and others involved in education will have had experience of STEM matters in various contexts. Celebrate these! Don't feel that as a maths teacher you have hide the fact that you did engineering or biochemistry - celebrate your quantitative past history and bring it into the education of your charges where appropriate

Why would clever students struggle with the mathematical aspects of their university course in science, technology or engineering? There are several possible reasons which I have encountered many times.

**Procedural thinking**- Mathematics exams can often be passed by learning the content
*procedurally.*This means that students can answer certain types of question by following a recipe. The problems in applying mathematics arise because even minor deviations from the precise recipe cause the student to fail to know what to do.

- Mathematics exams can often be passed by learning the content
**Inability to translate mathematical meaning to scientific meaning**-
- Students who are very skilled at mathematics might have trouble seeing how to relate a mathematical process to a real-world context; this hampers the use of common sense, so valuable in quantitative science.

**Inability to make estimates or approximations**-
- Mathematical contexts in real applications are rarely simple. In order to apply mathematics predictively, approximations will need to be made. To make approximations requires the student to really understand the meaning and structure of the mathematics.

**Poor problem solving skills**-
- Mathematical issues in applied mathematics problems are not usually clearly 'signposted' from a mathematical point of view. The student must (perhaps subconsciously) assess the situation, decide how to represent it mathematically, decide what needs to be solved and then solve the problem. Students who are not well versed in solving 'multi-step' problems in mathematics are very likely to struggle with the application of their mathematical knowledge.

**Lack of practice**-
- There are two ways in which lack of practice can impact mathematical activity in the sciences.
- First is a lack of skill at basic numerical manipulation. This leads to errors and hold-ups regardless of whether the student understands what they are trying to do.
- Second is a lack of practice at thinking mathematically in the applied context.

- There are two ways in which lack of practice can impact mathematical activity in the sciences.
**Lack of confidence**-
- Lack of confidence builds with uncertainty and failure, leading to more problems. Students who freeze at the sight of numbers or equations will most certainly under-perform.

**Lack of mathematical interest**- Students are hopefully strongly driven by their interest in science. If mathematics is studied in an environment independent of this then mathematics often never finds meaning and remains abstract, dull and difficult.

There are various ways in which you can bring STEM into the classroom, from the light-touch reference here and there to the full off-curriculum week. Here I list some of my favourite quick ways to get STEM moving in your schools

- Data collection in SET then analysis of the data in maths; possibly with a feedback into SET.
- Create an equation/make a prediction/do a calculation for a physical process in a maths lesson and then test out the prediction by performing the experiment in science.
- Introduce a task in a SET lesson (to ensure the pupils all have the SET knowledge required), continuing to work on it in a maths lesson (using maths skills) and then complete it for a double homework - marked by both maths and SET teacher with their particular subject focus.
- Introduce a short, regular and scheduled 'discussion' or circle time in both maths and SET lessons (perhaps 10 minutes a fortnight). Give students a chance to comment on the SET that they have noted in maths and vice versa and also to ask teachers/other students of wider questions concerning the mathematics they have seen in SET or the SET that they have seen in maths.
- Set a half-termly cross-curricular review homework:
- Maths: Review SET books for mathematical content; make links with the mathematics that they have learnt during the term.
- SET: Review maths books and suggest SET links or connections with the material covered. Look for parts of maths which have the most common uses.
- Joint poster project: Choose a theme and work on the same poster in both a maths and SET lesson, where the focus is finding the maths/SET related to a big theme, such as global warming.
- Use snippets of problems/weekly challenges as starters when students enter room. Choose topic to give a flavour of the main theme of the day and plan for appropriate content in schemes of work.
- Include some cross-curricular display material in corridors and classrooms.
- Ask student newspaper to interview members of science and maths departments to find out their 'STEM history' in terms of the STEM experience at university, hobbies or other jobs.
- Build on the clear links between 'investigation cycles' in science, 'design pentagon' in D&T and 'data handling cycles' in maths.
- Use data loggers, light sensors, paper and other patterns, and other hands-on technology in maths.
- Show a picture of an experiment/activity as used in SET to act as stimulated recall in maths at the appropriate time.
- Have AsSTEMblies - assemblies which focus on some aspect of STEM
- Form a STEM club or a maths club or both. Form links between these clubs and clubs from other schools.

Prepare for university http://nrich.maths.org/university

Mathematical Preparation for the Cambridge Natural Sciences Tripos http://nrich.maths.org/6884

Interactive Workout - Mathmo http://nrich.maths.org/7088

Maths in the Undergraduate Physical Sciences http://nrich.maths.org/6864

Algebraic Fluency of Advanced Students http://nrich.maths.org/8628

The NRICH - Transkills Project http://nrich.maths.org/6326

stemNRICH http://nrich.maths.org/stemnrich

stemNRICH - advanced http://nrich.maths.org/stemadvanced

http://sfh10.wordpress.com/2012/11/29/superficial-contexts-in-stem-problems/