Where Teaching and Learning Matter
See below for a fantastic contribution to literacy and numeracy education at Unitec from Becca Black, Academic Advisor to the Faculty of Technology and the Built Environment. Diana
Which of our library study guides was chosen as a "Best of" site out of 400,000
contenders worldwide? The answer is DIY Maths, our online textbook of basic
mathematics. DIY Maths was first published in mid-2012 with only a basic algebra
section. It now covers all lower-level maths through basic trigonometry.
DIY Maths is surprisingly popular for a voluntary maths site. Last year, nearly DIY
Maths had nearly 30,000 page hits.
Building cognitive constructivism into the design of the site
The DIY Maths website was designed with cognitive constructivism in mind.
Cognitive constructivism highlights:
• The role of teacher as facilitator
• A reliance on the intrinsic motivation of the learner and on the ability of
learners to recognise the limitations of their existing knowledge
• The use of strategies that help learners assimilate new knowledge and
monitor their own learning
Below (in blue) are listed some elements of cognitive constructivism
from the "Teaching Guide for Graduate Student Instructors" website at UC
Berkeley (http://gsi.berkeley.edu/teachingguide/theories/cognitive.html). After
each quote is a reflection on ways the DIY maths website incorporates the element.
Teacher As Facilitator
"The role of the teacher is to facilitate discovery by providing the necessary resources
and by guiding learners as they attempt to assimilate new knowledge to old and to
modify the old to accommodate the new."
In DIY Maths, the activities and resources are sequenced and described so that
learners can decide where to start and which resources to use. Students who need
more guidance may refer to a detailed guide to using the site. In this way, DIY maths
provides two levels of facilitation: one for the more independent learner, and the
other for students who need more guidance about how to learn.
To help the learner decide which modules to study, each module link has a brief
description of what the learner will find within. For example, the "Introduction to
sine, cosine and tangent" module is described as:
In this module, you learn how to find sines, cosines and tangents, and you'll
also learn about a memory device called sohcahtoa.
In this way, independent learners are prompted to recall prior learning and are
guided to select the modules and resources they need.
Within each module, learners will find a link to a page explaining how to work
through the module. Students are advised to keep a maths journal for notes,
problems, and reflections. The student is also encouraged to search for more
information (search terms provided) and to seek in-person assistance if necessary.
In other words, students are encouraged to build knowledge and are provided with
the tools for obtaining help as needed.
"... cognitive learning theory sees motivation as largely intrinsic... Learners must face
up to the limitations of their existing knowledge and accept the need to modify or
abandon existing beliefs" (Teaching Guide website).
DIY Maths is entirely dependent on intrinsic learner motivation. In a way, learners
who purposely navigate to DIY Maths are already intrinsically motivated. Once at the
site, learners choose their own pathways of study based on personal preference and
on their own understanding of their existing knowledge.
To help students tease out incorrect prior knowledge, one or two common
misconceptions are included in each content module. For example, the following
statements are in the “All About Angles” module:
Did you know?
The number of degrees in an angle is unrelated to the length of its lines.
An angle’s measure has nothing to do with the direction the angle is facing.
The idea is to help students name their own misconceptions and prime their brain
Cognitive Constructionist Strategies
"... cognitivists... place greater importance on strategies that help students to
actively assimilate and accommodate new material. For instance, asking students to
explain new material in their own words can assist them in assimilating it by forcing
them to re-express the new ideas in their existing vocabulary…
"Because learning is largely self-motivated in the cognitivist framework, cognitivists
… have also suggested methods which require students to monitor their own
learning. For instance, the use of ungraded tests and study questions enables
students to monitor their own understanding of the material. Other methods
that have been suggested include the use of learning journals…" (Teaching Guide
Several cognitive constructivist strategies are suggested in the above quote:
Students are asked to explain the material in their own words, to monitor their own
learning, and to use learning journals. And teachers are asked to structure student
material in an organized way and to provide students with the opportunity to take
In DIY Maths, students can monitor their own understanding 1) by taking the
practice quiz at the end of each module and 2) by keeping a learning journal in which
they take notes, try problems, and explain the content of each module in their own
words. If they have trouble with the practice quiz, they are advised to take their
learning journal to their teacher or to a learning support specialist.
You can find DIY Maths at libguides.unitec.ac.nz/diymaths. If you have suggestions
for topics, videos or anything else, feel free to use the “Feedback” link found on
nearly every page of the guide.
In this blurb, I discuss the learning theory behind the design of DIY Maths. As you
read this article and if you visit the site, the important thing to keep in mind is that
this type of design can be transferred to many other knowledge areas. It would not
be too difficult to build a DIY Academic English or DIY Physics site. Contact me at
firstname.lastname@example.org if you’re interested in developing such a project, and I’ll help
you get started.
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