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DrFrostMaths.com Homework Platform – written 25th April 2016
In a Nutshell
As part of my website DrFrostMaths.com, I am developing a new system which will allow students to
take online assessments on topics across the national curriculum (and beyond), either as homework
set by a teacher or for more informal practice. Teachers can manage students’ accounts and monitor
their progress. The system has a number of features which distinguish it from existing systems,
including greater capacity to accept algebraic input, and automatic differentiation in homework that
stretches the most able whilst allowing weaker students to maintain practice of more standard
questions.
What is DrFrostMaths?
DrFrostMaths.com is a library of maths resources created by me. These comprise of PowerPoints,
worksheets for lessons/revision along with other activities, and cover the National Curriculum from
Years 7-11, along with most of the A Level modules. There is significant push for enrichment and
most exercises include difficult extension questions, often from UKMT Maths Challenges and
Olympiads. In addition, there are resources for running maths enrichment club, the ‘Riemann Zeta
Club’ for example with its own scheme of work and comprehensive materials designed for preparing
for university entry and maths competitions.
The resources are popular, with 105,000 downloads on the Times Educational Supplement website
since August 2015 and 31000 unique users between January and April 2016 on my own site. I was
featured maths author of the month in the Times Educational Supplement
(https://www.tes.com/teaching-resources/blog/tes-maths-featured-author-collection) and am soon
to be interviewed on a TES podcast. The head of TES’ Maths Panel, Craig Barton, described my site as
“his find of 2015”.
New design of DrFrostMaths.com (design not yet live). The design uses a ‘responsive design’ model,
meaning the layout adapts depending on the size of the screen, and thus is optimised for viewing on
all devices, including tablets and mobile phones.
What is your background?
I did my undergraduate degree at Oxford University before working as a programmer for an
Investment Bank for a year. I made a rapid exit from the city world and returned to academia, where
I completed my PhD in Computational Linguistics (a blend of Statistics and Linguistics) in 2012. I was
extensively involved in the departmental/college teaching there along with interviewing prospective
Maths and Computer Science undergraduates. My love of teaching there led me to taking a week’s
holiday to spend at my old school, Tiffin, who kindly let me teach a number of lessons to get a
proper feel of the profession. The rest is history, and I have taught at Tiffin School since.
I have a few awards including:
Oxford University Teaching Prize 2012: Awarded to 4 academics within the Mathematical,
Physical and Life Sciences Division.
Microsoft Research Prize 2008: Awarded for Best Undergraduate Dissertation in the Oxford
University Computer Science faculty.
My department has been shortlisted for ‘Times Educational Supplement Maths Department
of the Year 2016’, in part due to the exceptional progress of students in maths competitions,
where the number of students qualifying annually for UKMT Maths Olympiads rose from 15
to 42 in a space of three years.
I regularly speak at the ‘Maths in Action’ events for The Training Partnership held at the Institute of
Education. Each event usually comprises of around 900 A Level students and teachers.
What is the new homework system you are developing?
The new system will allow students to take online assessments on topics across the national
curriculum (and beyond), either as homework set by a teacher or for more informal practice.
Teachers can manage students’ accounts and monitor their progress. There will also be tools for
teachers to build their own homeworks and add to a user-contributed library.
The currently planned types of questions are:
Textual (simple keywords).
Numeric (allowing accuracy to be specified).
Multiple choice.
Ordering existing items (e.g. ordering decimals or parts of a proof).
Numeric or algebraic expressions. I have developed an algorithm to determine if two
algebraic expressions are equivalent, whether ‘structurally equivalent’ (where the
expressions are equivalent if the operands of commutative operators can be reordered, e.g.
(ð − ð) × ð would be equivalent to ð(−ð + ð)) or ‘value equivalent’, where the expressions
are equivalent if they are equal for all possible values of the variables, e.g.
A technical tool developed by myself for the purposes of developing the homework platform,
which analyses the structure of two mathematical expressions (using rules of BIDMAS), and
determines whether they are (a) ‘structurally equivalent’ and (b) ‘value equivalent’.
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When writing questions (In the preliminary prototype I am building), different types of answers are
available. There is flexibility in the extent to which algebraic inputs must match the answer.
This very preliminary prototype allows homework designers to upload an image and drag answer
inputs over it. (Note that the above interface shows the old DFM design before the recent redesign)
Homeworks can be taken in two main different formats:
‘Linear’ homeworks: Students are presented with a predetermined sequence of questions
(which may be preselected by the teacher).
Differentiated homeworks: Students are presented random questions (from a large bank),
starting with easy questions. If students correctly answer all these initial questions, they
advance onto harder questions, otherwise stick with the easier level. The very hardest level
(known elsewhere on the existing DrFrostMaths site as ‘Killer Questions’) involve a large
degree of challenge.
Explanations are provided for the correct answer once students input their answer, additionally with
links to appropriate expository resources on my website.
Students will be incentivised with an appropriate points system with progress for weaker students
also appropriately rewarded.
Where there is a teacher account associated with a student one, teachers will be able to see which
questions students got correct and incorrect, and their progression over time if they have
reattempted an assessment.
This idea doesn’t seem new. How does it differ from say ‘HegartyMaths’?
The overarching idea of online assessments/homeworks/revision practice is not intended to be a
novel one, but instead my own interpretation of it and allow my own content, as well as combining
some of the best features from existing systems. The differences with HegartyMaths specifically are:
Greater support for algebraic input. This would mean A Level content would be covered
(which HegartyMaths does not).
A greater variety in how students can carry out the homework (as per the ‘linear’ vs
‘differentiated’ homework types described previously).
A greater emphasis on stretching more able students (although it should be noted the initial
impetus to develop the system was following a departmental meeting where we discussed
the range of support for weaker students in the school).
Since my homework builder system allows dragging of input boxes over uploaded images
(these images might be the slides of an uploaded PowerPoint/pdf), my system allows
multiple answer inputs per question.
Tools for teachers to build their own questions.
HegartyMaths advocates the ‘flipped learning’ model, where students first watch a video of
himself explaining content, before students can take an assessment to check their
understanding. Students do this in their independent time, with subsequent in-school
lesson time spent for subsequent consolidation and extension. Part of the monitoring
interface shows teachers how much time students have spent watching these videos. While
my assessments may link to relevant resources on my main site which may help with
understanding, the focus of my system is solely for students to practise questions and
teachers to set homeworks.
My interface will keep things simple, and while there will be many tools for teachers to
track student progress, I won’t be including tools for feedback on questions they
understand or teachers to ‘mark work’ online. Instead there will be simpler quantitativeonly
reporting of what questions students got right and wrong (with progress over time also
indicated) with teachers expected to follow this up in lesson time. This simplification is
intentional.
I intend to keep the entire system free for both students and teachers.
What is the intended development timeline?
1. April-May 2016: Recode and redesign the main DrFrostMaths.com website. This includes
restructuring the database to pave way for the new homework system.
2. May-August 2016: Recommence work on the homework platform. If a basic limited
prototype is ready, I may experiment on one of my Year 7-9 classes in the last half term
before the summer.
3. Sept-Dec 2016: More formally trial the system with classes within my school (including use
by other colleagues within the department), making further enhancements and additions to
the system.
4. Jan 2017: Make the system available to all teachers.
What do you need then?
While I am a former programmer by profession, I need a second pair of hands to share the
programming load, in part so I can spend a greater amount of time on content. The level of
involvement would depend on the experience and range of skills of such a person.
The following skills are required:
Proficient at web front-end coding: JavaScript, JQuery and CSS.
Proficient at web back-end coding: PHP and MySQL.
Familiar with ‘responsive design’ (i.e. interfaces which change layout depending on the
resolutions of the viewing device).
The following attributes would be beneficial:
An eye for good web/graphic design.
An interest in mathematics education.
The intention is to do a significant amount of the initial development together over the summer
holiday, with relatively minor refinements made over the course of the first year.
Provided I find someone suitable I will be applying for funding from the SHINE Trust of up to
£10,000. The intention is for the funds to be used only to pay the programmer and for server upkeep
costs.
Please contact jfrost@tiffin.kingston.sch.uk for enquiries.
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