Jane Hart, of the Centre for Learning and Performance Technologies, has published her annual list of Top Tools for Learning. The list, released on 24 September 2018, has been compiled from the results of the 12th Annual Digital Learning Tools Survey.  Jane Hart’s analysis includes details of the contributors as well as her commentary on trends.

Like last year, she has three sub-lists including Top 100 Tools for Education. As Jane indicates only 23% of the votes came from the Academic Sector, so it is interesting to look at the sub-lists as well as the overall list. The sub-lists are:

1. Top 100 Tools for Personal & Professional Learning 2018 (PPL 100)
2. Top 100 Tools for Workplace Learning 2018 (WPL 100)
3. Top 100 Tools for Education 2018 (EDU 100)

The infographic made available by Jane Hart is a four-page pdf which lists the overall 200 top tools and also the top 100 tools on each of the sub-lists.

It is fascinating to note the tools which have made it onto all 12 lists, as well as looking at the enduring tools over the last 5 years or so. Using the 2007-18 A-Z I thought I would have a look at these and created a spreadsheet to see which tools are in all 12 lists, also an average position over the last 3, 5 and 7 years.

Looking at the new entries on the 2018 list, I am delighted to see a personal favourite, WolframAlpha which has finally made it onto the top 100 list for Education!

Looking further at the Top 100 Tools for Education (filter EDU100, note you can choose to show all 100 on the list) I see some personal favourites!
(Top Tools 2018 – Education– for an Excel Spreadsheet).

Excel is quite rightly highly placed. I regularly use Excel resources; just a few examples of some favourites:

• Mike Hadden’s Excel Files
• STEM earning – Descriptive Statistics
• Dynamic Maths – David Watkins
• Virtual Textbooks – STEM Learning    

See STEM Learning, part of the A Level (16+) Resources series.

A few more for investigation …
Kahoot (Classroom response tool) is very easy to use and free for teachers and students. In a few minutes, I created a quiz on Directed Numbers … (not very exciting – just a test, very easy to create.) 

Another popular quizzing tool I know some of my colleague’s use is Quizlet.

Seeing Padlet (online discussion board) ascending the list reminded me of this very easy to use tool. I shall try this with Year 7!

Unsplash – beautiful free photos to do anything you like with!

Photo by Marivi Pazos on Unsplash

Apart from illustrating Unsplash, I can have pictures of flowers to illustrate a mathematical connection! From Science News reading Fibonacci’s Missing Flowers we discover that the most common number of petals is five and whilst there are many flowers with the number of petals a Fibonacci number there are also flowers with four, six, seven or nine petals!

Looking forward to the first London Maths event of the year, I was reminded of Colin Foster’s wonderful Mathematical Etudes site. To quote Colin Foster:

Mathematical Etudes are creative, imaginative and thought-provoking ways to help learners of mathematics develop their fluency in important mathematical procedures. They are an alternative to traditional, tedious exercises.

(The session charge of £10 covers you not only for this session but also for the 5 remaining sessions of the 18/19 academic year. The sessions are free for trainee teachers in their ITT year.)

Note the Etudes by topic at the foot of the page; Number, Algebra, Geometry, Probability & Statistics are available. Looking at Algebra for example, under Solving Equations we see Connected Quadratics. Intrigued by Lyszkowski’s method of factorising quadratics mentioned led me to another excellent lesson plan of  Colin Foster’s on Quadratic Equations. I really like the starting activity in this lesson which should promote a deeper understanding of factorising quadratic expressions.

I have written before on the ‘Box Method‘ for factorising quadratic expressions where the coefficient of x² is not 1 and note Quadratic Grids from Underground Mathematics will help students develop and understand the method.

Lyszkowski’s method seems even simpler, avoiding the manipulation required by conventional methods.

Lyszkowski’s method 

I think I’ll see what year 11 think of this!

crashMaths Skills Checks

crashMaths has been added to the 16+ series of pages. The growing library of resources now includes a set of very useful Skills Checks, with solutions, on Pure content from Year 1 of the A level specification. The site includes many practice papers and mark schemes.

With all A Level courses now linear, Retrieval Practice is essential. From crashMaths these AS Maths Key Skills Check worksheets will be very valuable for Year 13 in the second year of their A Level course. The Skills Checks are all on Pure Mathematics.

Further recent updates to Advanced Level resources include:

From Edexcel, A Guide to using GeoGebra when teaching AS and A Level Mathematics. This guide links to numerous GeoGebra files clearly mapped to the specification content.

This guide has been added to The Use of Technology Page, also to the latest update of this file on technology resources mapped to content which can be found on The Use of Technology Page. The file includes links to instructions for the Casio ClassWhiz calculator.

Updates to the Further Mathematics content include this link to a post on Maclaurin Series for students which includes Desmos pages. The post also links to some useful notes and examples for students.

For Further Maths, this post on the new topic of Differential Equations may be useful. Again, notes and examples are linked to, also instructions on using WolframAlpha to check work on Differential Equations. WolframAlpha is also useful for checking work on Matrices.

The teaching of Polar Coordinates offers an ideal opportunity to use Technology.

Dr Frost Maths: Full Coverage – Algebraic Proofs involving Integers

On Dr Frost’s site, it is possible to browse all his excellent resources by topic so if, for example, we search on KS2/3/4 then Algebra, we see Algebraic Proofs. Under Proof the Year 9 file PowerPoint file is excellent for high ability students,  you will also see a very useful worksheet on counter-examples. I do like Dr Frost’ Full Coverage resources which are compilations of GCSE questions (GCSE – UK qualification taken at age 15-16). Answers are provided at the end of the document. Explore this outstanding site full of very high-quality resources, all Dr Frost’s clear indexing make the resources simple to find.

MathsBot – GCSE Questions

MathsBot is another superb site and very easy to find questions by topic, the GCSE Exam Style Questions are a good example. Select any filters and note the many question topics.

Maths4Everyone – Algebraic Proof Workbook

This search of TES resources returns several highly rated free resources on proof.
Try Algebraic Proof – Expressions and Proofs from  James Clegg, the worksheet “teases out expressions to show certain situations (e.g. the sum of 2 consecutive odd numbers) and features options on an “answer grid” at the bottom of the page.” There are also some questions to try. From the excellent Maths4Everyone this Algebraic Proof (Workbook with Solutions) has numerous problems to try as well as very clear examples. Answers are provided – highly recommended (as are all the resources on Maths4Everyone by David Morse).

See also: Proof Resources

From CIMT who are one of my favourite sites for a reason – see this GCSE additional unit on Proof.  A favourite site because if you are ever short of examples it is highly likely you will find something on CIMT who have everything from resources for little people to Advanced Level and everything in between!

CIMT-Proof

Nrich has this collection Reasoning, Justifying, Convincing and Proof for Lower Secondary. A search on Nrich on Proof returns a wonderful selection for all ages and stages. We have tasks to introduce ideas of proof to younger children through to preparation for STEP examinations.

Also from Nrich, try this Interactive Proof Sorter example which works on my phone as well as on my laptop. This would make a good starter – if you want to give out paper copies for students to work on as they come in, you can easily fit 4 copies to an A4 page!

Teachit Maths, though a subscription site offers an extensive collection of activities as free pdf files. A search on Proof returns some great resources. I do like this Worksheet on Proof which has 20 varied tasks aimed at older students 16-18, though some would be accessible to younger students. Full teachers notes on solutions are provided. In the task illustrated here, a full proof is given and students asked to explain each step.

TeachItMaths – Proof Tasks

Don Steward – Multiple Proofs

From Don Steward on Median, we have many wonderful proof resources. Try always and never or multiple proofs. Why just multiply out brackets when we can do a little proof?