Thinking mathematically...
What can I say? 2020, Covid, unprecedented, etc. You already know this. Well, since I m co-organising a Teaching and Learning Mathematics Online (TALMO) workshop today on lessons learned following the sudden switch to online teaching I decided to write down some of my lessons learned. The TALMO meeting can be found at Tackling Term 2: Top Tips from Term 1. Last term, apart from a single hour right…
With the current Covid-19 crisis many Higher Education Institutions (HEIs) are moving to take away exams which by their nature are open book exams. Many mathematicians do not have experience of take home open book assessments and this post is intended to help deal with this. This has been put together quickly and is intended to be practical rather than theoretical. I hope you find it of use. I…
I ve been attending a conference for the last few days and so didn t have much time to write a post. I did learn about the e-assessment packages Stack and Numbas. I will definitely be trying these in the future.
A common technique in teaching mathematics is to go from the particular to the general. We can look at a few examples and then state and prove the general result. We can do this for proofs as well. Instead of giving students a proof of a statement, give them the proof for a specific example of the statement and ask them to prove the general from that. A classic example of this is to prove the…
Writing mathematics clearly is a crucial part of a student s education. Too often students begin higher education with the misconception that writing mathematics merely involves putting down a sequence of symbols without paying too much attention as to whether they make sense to the reader. As long as the answer is there in some form and underlined, that s ok, the thinking goes. Since the marker…
An idea recently introduced to me is binary marking. Students receive either a 0 or a 1 for their weekly coursework mark. This makes marking easier no need to decide if this question is worth 2 or 3 out of 4 and no need for adding up at the end. Only a simple Have they made a reasonable attempt or not? is required. This could be determined by how much of the coursework they have attempted or by…
Writing a proof is very difficult even for experts. Here s an idea that allows students to think about and engage with a proof without starting from nothing. Take a proof and space out separate sentences (or two or three sentences). For each student or small group of students, print and cut so that each sentence is on a separate strip. Shuffle the strips. Then, let the students assemble the pieces…
Many students don t know what to call certain Greek symbols. They are happy with common ones like and but show them a or and they get a little shy. This shouldn t be a surprise but it is just their lack of familiarity. No one tells them what all the symbols are but as mathematics students they are expected to know them. If they don t pick up the less common ones after hearing them just a few…
Mathematicians use a lot of symbols. Everyone knows that. A symbol may represent a simple constant ( is the constant of integration) or represent a collection of difficult concepts ( is a group). Students need to be able to unpack the meaning from symbols and to do the reverse bundle up concepts into a few symbols. Asking students to turn words in symbols and symbols into words is a useful…
Lara Alcock wrote about Tilting the Classroom in the London Mathematical Society Newsletter. One of the activities she does that I don t do but should is what I ll call What goes in the gap? from her section on deciding. The example she gives is which symbol of , , goes in the gap in Clearly one can do this with many other statements not just symbolic ones For , is orthogonal is an isometry.…