QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.
The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
The calculus section will carry out differentiation as well as definite and indefinite integration.
The matrices section contains commands for the arithmetic manipulation of matrices.
The graphs section contains commands for plotting equations and inequalities.
The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.
One thing I’ve noticed more and more recently is how out of sync the transition is for mathematics students leaving primary (grade?) school and starting secondary (high?) school. I’ve worked in, and visited, a large number of schools at this point, and although certainly not always the case, I’d comfortably say the majority of schools I visit follow very similar, and in my opinion, flawed, year seven programmes for their eleven year olds.
Typically (I should be cautious using that word), students arrive on day 1 and are placed in mixed groups for the first few weeks. This period can last anywhere between two and six (!) weeks. This period is effectively a holding cell until departments determine the ability of each child according to their own internal tests and assessments, despite the fact that students are coming in with a lot of maths data attached to them from primary. The reasoning behind this is often cited as standardising across groups who have come from different schools, or protecting against students performing well or poorly in their final assessments in primary school, but not performing consistently at that level. Cynically one might say that this is all really about not trusting the data they come in on…
Once the students are finally re-assessed in Year 7 – which could be anything from a single test to three or four, students are then placed into sets – which could be anything as strict as a class-by-class hierarchy, or (my personal preference for what it’s worth) loose setting with three ‘bands’ that are essentially mixed within a couple of grade boundaries. Now I should reiterate that this is just what I’ve experienced, and certainly does not speak for the entire English school system, but as I said, I’ve seen a lot, and they usually fall into some kind of version of this structure. I’m really interested to hear about alternative approaches in the comments.
So what do students *do* in this interim period? Well, again, it differs, but often it’s looking at the basics of numeracy – number operations, proportion work, fractions etc. This in part is to help prepare them for the assessments, but also acts as a testing ground to see if students stand out as being higher or lower achieving than their data suggests. It can be completely detached from any kind of scheme of work or curriculum. I hear a lot about students ‘going backwards’ or ‘standing still’ in this time, simply because they (most of them) aren’t learning anything new, and much of what they’re being taught, or are revising, is stuff they did to death, successfully, at primary school.
At this point I should add a little balance. I’m not bashing teachers, and I understand that there is some truth when I’m told “they *should* know that stuff, but often they don’t, or they’ve forgotten it”, so perhaps this time is not wasted as such. In fact, in my own teaching experience I have frequently found that to be true with a lot of children, (but also false with others!). Certainly, if this entire process takes place over a week or two, then the implications of ‘not moving forwards’ are fairly light – the end justifies the means and all that. However I also feel that with all the massive overhauls of the primary curriculum, and the remarkable work primary teachers are doing (under impossible pressures I might add) with the new maths programs everywhere, that times have simply changed. Is a review needed? I think so.
What I’m seeing and hearing now is that Year 7 students coming into Secondary schools are, in general, much stronger at maths. They have a better conceptual understanding and ability with number. Of course not *all* of them, and of course there will be some areas where this difference is less obvious than others, but I do think the changes are having the desired effect. We could argue about the costs of those changes to everything else, but that’s not what I’m focusing on here.
With those changes in mind, the second thing I’ve noticed is that the entire Year 7 scheme of work is often blind to the new primary curriculum, which has been in place a number of years now. I don’t want to keep using anecdotal evidence here, so let’s take a look at an actual scheme side by side with the primary programme of study.
The picture above is taken from a scheme of work for Year 7 which is freely available on TES. A few disclaimers: anyone can put anything on TES. This was uploaded in 2010, but was updated in 2014. It has reviews from as recent as a month ago, so it is being used. It has been downloaded 20,000 times. There are more detailed breakdowns of the topics, differentiated etc but this is the broad overview.
From September to January there is literally nothing on there that isn’t taught at primary, several times over six years. Furthermore, almost all of it was taught at primary (several times across the six years) BEFORE the curriculum changes.
One could argue that we need to reteach things all the time (I agree), but typically we’d reteach it and add more content, go deeper, expand the concept. The above is taken from the Year 5 programme of study. It involves composite shapes, and is therefore arguably more advanced than what is listed in the Year 7 scheme of work (point 9).
Above is part of the Year 6 programme of study. It seems a lot more advanced than fundamental concepts of arithmetic using fractions (point 10), which is taught in January in Year 7 (for the scheme I’ve posted).
I won’t keep comparing, you get the point. The Key Stage 1 & 2 Maths Programme of Study is available here.
Many schools have fantastic schemes of work for Year 7, I have no doubt about that, and if you’re reading this thinking ‘yeah but we dont do that, this is rubbish’ then great, clearly you’re one of those schools.
All I’m trying to put across is that times have changed, and the Primary curriculum should, I think, feed directly into the Secondary one. The gap between Year 6 and Year 7 is no bigger than Year 5 and Year 6, so students aren’t forgetting anything more than they would normally. If you’re in secondary and aren’t familiar with the new (not that new now) programme of study, it’s well worth a quick read – particularly the Year 5 and 6 parts.
Any interesting contributions about how you structure your scheme of work (and your groups) in Year 7 are most welcome in the comments.