Dr Duncan James > UPmaths

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UPmaths now

I am a maths tutor and this page has links to my customised learning resources. In September 2019 I hope that this will suddenly change as I release lots of new content: watch this space!

Brief topic guides

Numbers
Arithmetic, Bidmas, Fractions, Decimals, Prime Numbers, Percentages, Ratios, Surds, Units and Conversions, etc.
Algebra
Simplifying, Solving, Factorising, Expanding, Binomial Expansion, Fractions, Quadratic Equations, Inequalities, Simultaneous Equations, Functions, Factor Theorem, Algebraic Trigonometry, Logarithms, etc.
Indices
Simplifying, Calculating, Numbers, Algebra, etc.
Geometry
Transformations, Coordinates, Lines (Parallel, Perpendicular, etc.), Intersections, Triangles, Pythagoras, Trigonometry, Exact Trigonometry, Circles, Regular Polygons, Areas, Volumes, Density, Nets, Loci, etc.
Graphs
Sketching, y=mx+c, Describing, Transforming, etc.
Vectors
Addition, Mid-Points, Ratios, Dot-Product, Intersections, etc.
Calculus
Differentiation, Integration, Trapezium Rule, Rate-of-Change, Chain Rule, Product Rule, Quotient Rule, Integration by Substitution, Integration by Parts, Parametrics, Implicit Differentiation, etc.
Sequences and Series
Algebraic, Geometric, etc.
Sets
Set Notation, Logic, etc.
Logic
Notation, Even and Odd Numbers, etc.
Probability
Tree Diagrams, Venn Diagrams, etc.
Statistics
Mean, Median, Mode, Histograms, Interpolation, Skewness, etc.
Mechanics
Resolving Forces, Centre of Gravity, etc.
Exam Questions Worked Solutions
I have occasionally made a video solution to an exam question for one of my students.

Non-verbal reasoning

I have a set of four question sheets: Non-Verbal Reasoning, Join the Club, Matching Pairs and What Comes Next. These cover a lot of the basic skills for these kind of tests and each progresses from easier to more difficult examples. I have a Non-Verbal Reasoning Solutions Sheet (PDF) so you can check your answers. You are welcome to download, share and print these for free (as long as you don't charge for them or change them).

The Number Line Race game

The Number Line Race is a game to help you learn about negative numbers and the number line. You are welcome to download, print, cut out and play it for free.

Multiple choice boxes

If you are doing a multi-choice exam you might find this multiple choice answer grid useful. You are welcome to download it and use it for free.

Online maths tutorial setup

I have an online maths tutorial setup page with archived information about connection speed, how to connect to a whiteboard, etc.

UPmaths is organised into four levels

Remember, much more is on the way in September 2019!

I am currently on sabbatical from regular maths tutoring and using the time to create a completely new set of UPmaths resources. The overall approach will be to ask real maths questions that you can try to answer yourself and then watch me describe one or more possible solutions. I will use the solutions to illustrate powerful ways that mathematicians think and learn. This will simulate exactly how I teach in my maths tutorials. Watch out for the big launch in approximately September 2019.

You can subscribe to my newsletter for quarterly-ish emails that will keep you up to date with the latest UPmaths news.

“In September 2019 I want UPmaths to be another of the small steps that myself and other content creators have made to bring high-quality learning to everyone regardless of wealth or inherited advantage.”

Dr Duncan James

“A teaching technique I recommend is showing an incorrect solution and encouraging your students to find the mistake. I find this develops important skills including error-checking, team-work, communication and intuitive understanding.”

Dr Duncan James (can be done from the earliest stages, for example by counting and using a number twice)

“There is a moment when advanced techniques start to take longer. You need to accept this drop in speed so that you can gain the ability to deal with more complex questions.”

based on the ideas of Ian Thompson

“Mathematics can be very difficult to teach. I find that the ‘right/wrong issue’ overshadows this subject. I try to praise method, including attention to detail and double-checking instead of the correct answer.”

Dr Duncan James

“I like to think of maths as a written language. I often avoid talking with my students and communicate just by writing to save time and cut straight to core of the subject.”

Dr Duncan James (on the topic of more advanced mathematics) (also true for mental maths where it is possible to see an answer intuitively without a good reason)

“True dialogue occurs when teachers ask questions to which they do not presume to already know the correct answer.”

Lemke in Talking Science, 1990 (I agree with this and if I know an answer I am upfront about it before asking the question.)

“Every child has the right to express their views and feelings and have them taken into consideration.”

Paraphrasing of article 12 of the UN Convention on the Rights of the Child.

“Since when was fidgeting illegal? If it is not too disruptive let it be: it often helps a student concentrate.”

Dr Duncan James

“If a pupil does not understand and says nothing about it: either they do not want to say or they do not realise that they don't understand. Do not assume the first. If it is the second they may not understand what they are supposed to be doing or they may lack skills in self-monitoring.”

Nicholas Bielby in Teaching Reading 1999

“I have a lot of personal experience with teaching maths and using the word ‘more’. This word can mean different things. Suppose you have a box with capacity for 6 eggs with 5 in it and a box with capacity for 12 eggs with 7 in it. Which box has more? Many people will answer the box with 5 in it has more than the box with 7. This is because it is closer to being full. This answer is one of many possible good answers as it uses a common cultural meaning of the word ‘more’. When teaching maths I usually deal with this kind of situation by explaining that there is a particular ‘fashion’ in maths for what particular words mean and it is good to get used to it so we can talk to other mathematicians more easily.”

Dr Duncan James

“Set high standards for your own speaking. Do not ask: ‘What colour is the next flower?’ Do you mean the one to the right, underneath, in the same photo, on the next page, the next one you like the look of, the next one that a typical person might spot, the next one which is different to any we have already talked about, the next one you personally are looking at? All of these are legitimate meanings of such a vague question.”

Dr Duncan James

“Mathematics is easier without tricks.”

Dr Duncan James