By Jocelyn Dagenais, secondary school mathematics teacher, resource person for RÉCIT at the Hautes-Rivières School Service Center

Text presented as part of the consensus conference on the use of digital technology in education organized by the CTREQ, of which we presented an overview.

Mathematics teaching in primary and secondary school, and particularly in college, has difficulty adapting to the integration of digital resources and tools that we have seen appearing for more than thirty years (Assude, 2007).

Digital is transforming the ways of doing mathematics. However, we still teach the same calculation methods, ask to draw freehand graphs and work the geometry in the same way as when these tools did not exist!

## A little history

50 years ago this year, the company Texas Instruments launched its first calculator, the Datamath. In the 1970s, the first calculators from Texas Instruments (SR-50 in 1974) and Hewlett Packard (HP-35 in 1972) making it possible to perform trigonometric ratios appeared

The first graphic display calculators appeared in 1985 with the Casio fx-7000G, but the most popular are those from Texas Instruments, which appeared in 1990 with the TI-81. With them, the possibility of coordinating and quickly converting different semiotic representations (lists of numbers, table, ruler, graph) is increased. For example, the study of the influence of the value of the parameters of the functions is facilitated, since the tool quickly offers feedback to the student through the graph produced.

The first dynamic geometry software that will be used in schools in Quebec is Cabri-geometer (1986) and several other software have appeared subsequently. With them, the exploration of geometric properties or relations is favored and the proof activity is modified (Laborde & Capponi, 1994).

The work of generalization is also reinforced since the tool makes it possible to study multiple cases by simply moving free points. In these microworlds, the student learns to construct objects by questioning their properties and their preservation (Arzarello, Olivero, Paola & Robutti, 2002).

In recent years, we have seen suites of tools like Geogebra (2001-2002) and Desmos (2011) allowing the teacher to create, share and modify activities that integrate dynamic geometry, spreadsheet and graphical representation.

Similarly, tools like Photomath (2014) and Symbolab (2011) allow students to see the complete steps of mathematical calculation techniques. Finally, block programming has experienced a meteoric rise in recent years with in particular the Scratch tool from MIT which was released in 2007.

Programming allows a problem-solving approach where the student is led to produce creative solutions. Combined with robotics, it's a winning combination.

## The use of technology in the math classroom

However, the integration of technology in mathematics courses has been variable geometry for several years and it is not unrelated to teaching methods which have not evolved much either.

The traditional model of the mathematics course where the teacher explains the theory to the students who must apply it through various exercises is still very much present. Most of the time the technology (if there is any) is used by the math teacher in front of the class, probably on a digital board but the student remains passive in using the technology.

The debate is not on the usefulness of these high-performance technological tools, but on how to use them in the classroom and integrate them into our pedagogy.

Who would still agree to extract a square root by hand? To make an accurate graph with grid paper? Or to explore the properties of a geometric transformation after taking fifteen minutes to perform it with compasses, squares and straightedges?

The central idea is not to evacuate all these tools and techniques, but to apprehend them as technologies located at a given time. They were, at that time, the best tools available. Demonstrating their uses certainly remains relevant, but a broader reflection is necessary in terms of digital integration which makes it possible to approach new problems from primary and secondary school and to learn how to solve them with tools whose apprenticeship would prove necessary to ensure a more solid scientific training.

The teacher must find the added value of technology in his teaching:

- When should I use the technology? Which?
- When will students use technology? Which?
- What does technology allow students to do that paper and pencil cannot?
- Is introducing or deepening mathematical concepts using technology-integrated situations better than lecturing these concepts?
- Can technology allow my students to discover mathematical concepts? To make conjectures? To solve problems?
- Why would I use this technological tool rather than another?
- What mathematical activities are possible or perceived differently through the use of ICT?
- Etc.

We can go further and ask ourselves if our current mathematics programs are adapted to the use of technology. The answer is obvious: no. Let's take a secondary fourth mathematics content, the linear correlation and the regression line.

It is clearly indicated in the progression of learning that*if necessary, the value of the correlation coefficient for the models under study is determined using technological tools. *However, in the field, we know very well that this learning is not done with technology. Why ? Ministerial examination requires, because this content is never verified with a question requiring technology.

## Ministerial ordeal influences use of technology

The ministerial secondary four mathematics examination has been paper-and-pencil since its implementation. The use of technology in testing has evolved over time.

However, it seems that one element has not changed: we do not question whether the wording of the questions remains adapted and relevant to the technologies present and accessible to students.

A quick analysis of the tests and the various information documents that precede the moments of handover rather gives the impression that one checks after the development of the test if the technology would make it possible to answer certain questions more easily. And if so, options are specified that cannot be used.

If we continue to proceed in this way, it will be impossible to develop both the learning activities carried out in class and the evaluation activities which should prepare the citizen of tomorrow who wishes to do mathematics or who needs these mathematics in professions in different fields.

With a results-based approach, teachers feel pressure to present and have students work with ministerial-type questions. And because of this, as these are more traditional questions (multiple-choice, short-answer questions to assess mastery of mathematical concepts and processes, and application situations), the use of technology is still first side of the learning process.

What good will it do for the teacher and the students to use the technology if it is not available during the ministerial test?

And this does not influence only the teachers of the fourth secondary, but a large majority of the teachers of the lower and higher levels. By giving the impression that the use of technology does not transform teaching, learning and evaluation activities, we close our eyes to the inequities that are present in the various classes in Quebec.

For students learning in classrooms that integrate technology through problem solving, returning to challenges that ignore techniques learned with technology is like asking them to use a circular saw all day long. year and that they were entitled to a handsaw for the ministerial test. This technological debate also exists in secondary 1 where we can see several models of use of the scientific calculator: it is allowed, it is not allowed, it is allowed from the month of May, etc.

## The impact of the choices made in the ministerial examinations has an impact on the evaluation in general.

In 2015, the Group of Leaders in Mathematics in Secondary (GRMS) surveyed more than 500 teachers and educational advisers on assessment using ICT. Here are some findings from this survey:

1) there is a desire (even a concern) to ensure fairness in the use of ICT in evaluation;

2) participants recognize that the only technologies used in evaluation (and not in all cases) are calculators;

3) it seems that the “technological level” differs greatly from one teacher to another, as does their openness to using ICT;

4) the participants affirm that the structures currently in place do not allow the use of ICT in mathematics assessment in an equitable manner for all.

The GRMS was of the opinion that students who had access to graphing calculators since 2001 during these tests had an advantage over those who did not.

In the document available here, several examples are provided based on test questions.

## The necessary reflection on the place of technology in mathematics assessment

When will there be a real reflection on the place of technologies in the evaluation of mathematics in the context of a ministerial test?

Two interesting avenues in the 2018 Higher Council for Education report, Assessing so it really matters, were:

By seeing the test as a lever to improve evaluation practices, the integration of technologies would no longer be seen at all in the same way.

This text forces the observation that reflection on the integration of digital technologies in the classroom cannot be left to the discretion of each teacher, nor even to that of a school team, a team from a school services.

The Minister, through his Ministry of Education, must engage his teams responsible for learning, evaluation and certification in a clear mandate for the digital shift that we want Quebec to take. A systemic reflection carried out by each individual interested or intervening directly or indirectly in the teaching of mathematics seems more than necessary.

The following questions could then fuel this reflection:

- Is our current mathematics education adapted to the technological world in which we live?
- What is the place of calculation (mental and written) in a technological context?
- Is it normal for a student to finish high school without ever having used certain technological tools such as a spreadsheet for example?
- How technology allows to be creative in mathematics?
- Do technology activities allow students to have mathematical conversations with each other and with the teacher?
- Are the proposed technology activities only with immediate feedback, i.e. right or wrong answer?
- How is feedback given in your math technology activities? Does it give meaning to the students' reasoning?
- Do the proposed technological activities create an intellectual need for new mathematical skills?
- Do technological activities in mathematics make it possible to make estimations before calculations? Guess before proof? Sketches before graphics? Explanations in words before the algebraic rules? Everyday language before mathematical language?
- Do the proposed technological activities allow students to be right and/or wrong in different ways?
- Do the proposed mathematical activities allow students to use a variety of technological tools?
- What are the mathematical concepts that can be deepened with technology? (Tracks: Financial Mathematics, Statistics, Probability, etc.)
- How could technology be used in a mathematical assessment context?

BIBLIOGRAPHIC REFERENCES

Arzarello, F., Olivero, F., Paola, D. et al. A cognitive analysis of dragging practices in Cabri environments. Zentralblatt für Didaktik der Mathematik 34, 66–72 (2002).

Assude, T. (2007). Changes and resistances regarding the integration of new technologies in mathematics education at primary level, Researchgate.

Superior Council of Education (2019). Evaluate to make it really count. Report on the state and needs of education 2016-2018. Quebec.

Laborde, C. & Capponi, B. (1994). Cabri-geometer constituting a medium for learning the notion of geometric figure, Research in didactics of mathematics, 14 (1-2), 165-210.