What place do calculators have in the 21st Century?
Some would argue, none, and that they never should have had a place even in the 20th Century. Certainly one of my earliest memories of TEL (Technology Enhanced Learning) was the replacement of the humble 'log book' by calculators in my Maths classes on the west coast of Ireland, back in 1986 or so.
This post is not about to debate an argument that is at least 20 years old, but I am happy to point you to this post which discusses the nuances of matter very well indeed.
I would like to highlight some comments made about calculator use by the renowned John Hattie, in his magnum opus, Visible Learning, where he says:
Calculators + Good Pedagogy = d = 0.72
"Ellington found that the effects were much higher when calculators were involved in the teaching process; for example, when used for composition problem solving, the effects were d = 0.72: "When compared with students who did not use calculators, students in treatment groups were able to solve more problems and make better decisions with regard to selecting methods for generating solutions"(Beddington, 2003, p 169)
For more on Hattie's meta - analyses, have a look at my other post here, but for now, take it from me that a rating of d = 0.72 is very good, no, not very good, it's astounding.
Now, I've been thinking for some time, what if you took the pedagogically sound use of calculators and applied them to a technological tool that is favoured by adults who work with numbers the whole world over? What do financial professionals use to manipulate numbers? Calculators?—you must be joking, no they use spreadsheets, why? Because,
Spreadsheets are the calculators of the 21st Century
|Maths Problem Solving with Numbers (click to enlarge)|
I can tell you that my work with students confirms this, in fact, if I take the liberty of tweaking Hattie's profound eulogising about the wonders of
"Hembree and Dessart (1986) found that the pedagogical use of
calculatorsspreadsheets improved students basic skills both in completing exercises and problem solving. Across all grades (and particularly above grade 5, when calculatorsspreadsheets become more prevalent) and across all ability levels, students using calculatorsspreadsheets lead to greater effects in students' basic skills in operations and particularly in problem-solving."
|Visualize Data with a couple of clicks (click to enlarge)|
"The effect on problem-solving seems to relate to improved computation and lower cognitive workload demands. They also found that there was a better attitude towards mathematics and an especially higher self-concept of mathematics for those using
calculatorsspreadsheets compared to those not using calculatorsspreadsheets.
|Transform number manipulation by moving it online, collaborative, social.|
"... this enhancement in attitude was probably because the use ofAdapted from Hattie J (2013). Visible learning, p146-147
calculatorsspreadsheets helped relieve students traditional dislike of problems expressed in words (by reducing the cognitive load of having to compute as well as problem solve)."
"Using manipulative materials and
calculatorsspreadsheets helps to reduce students cognitive load and allows them to devote their attention to problem solving."
Transforming Calculations & MathematicsAs powerful as spreadsheet applications like Excel and Numbers are, already leveraging SAMMS elements like access to the internet to gather data, clarify facts, strategies; move modes of operation from teacher centred/pushed data, to student centred/gathered data, and the the mutability afforded by the spreadsheet—what calculator has an undo key? What calculator allows you to grab aspects of data and literally tweak it, or even move it around the sheet, recalculating variables at the speed of thought?
But we can add even more SAMMS to the recipe. Moving the entire activity online, namely with a 'cloud' based spreadsheet application like Google Sheets, that allows us to add the transformative elements of ICT that are:
Situated:Now students and teachers can work anywhere, any place, any space, on the same sheet. From real time feedback using comments, to transforming 'homework' into just an extension of classwork,
Social:The sheet becomes a mini social network, a micro-community; allowing a group of students to collaborate on the same spreadsheet in real time, or to assign different aspect of a more complex problem to various member of the team, to be interconnected as the separate aspects of data are clarified, calculated and ratified by the team. At any point, any student can duplicate the entire sheet and continue work work separately, or move it to another tab within the same sheet.
All of the work you see here was completed with Grade 3 students, recently I have been able to continue this work successfully with students in Grade 2, using Numbers on the iPads. Here is one of our students to explain it for you:
If the only thing holding you back is lack of understanding of how spreadsheets work, don't panic, I have all the guidance you need right here:
Step by step, but to do the activity you see here really only requires a formula as simple as:
Answer (empty cell) = (click first number) + or any other operator, eg -,/,*) (click second number) Enter/return. Done.
|Answer = 1+1. That's it.|
See the Picasa Web Album below for some more examples:
Hattie J (2013). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge. P 146-147