EDUCATION, DIDACTICS
Programming minds: Strategies
June 2020
June 2020
Introduction
Programming minds is a complex and delicate process. As math teachers, we are equipped with a rich background and specialized training, but it is crucial to practice self-criticism and reconsider our methods to adapt to the needs of our students. Drawing from my exceptional experience with Gabrielle Chammaa, an author of school textbooks, I wish to share proven tips to improve the effectiveness of our teaching. Here is a structured approach to achieve 100 % success in teaching mathematics.
Strengthening prerequisites and reflective activities
It is essential to work on prerequisites (diagnostics) and to offer reflective activities to introduce concepts and revisit them from year to year. This method restores meaning to mathematical techniques (automatic skills). The student must understand the origin of what they are applying to do so with certainty. An uncertain student will never fully succeed in mathematics.
Emphasizing mathematical understanding and mental calculation
Mental calculation must be at the core of our teaching. Explain to students that they will become human calculators, highlighting the benefits of this practice: research shows that mental calculation maintains brain sharpness and enhances learning abilities. Although math skills are often associated with the left hemisphere, mental calculation also stimulates the right hemisphere. A fully active brain is much more efficient.
Enhancing mathematical vocabulary
Regularly working on mathematical vocabulary is crucial. Many students struggle to express themselves fluently in mathematics due to a lack of vocabulary. To address this, frequently offer vocabulary exercises, both oral and written. Linking linguistics and mathematics is beneficial. Use grammatical analogies to explain mathematical concepts and explore the etymology of terms to reinforce understanding. This will lead to a better dissection of elements in algebra and geometry. For example, in algebra, composing numbers with units, tens, and hundreds is like composing sentences with subjects, verbs, and complements. In geometry, the word "bisector" comes from the Latin roots "bi" and "sector". "Bi" is a prefix meaning "two" or "twice," derived from the Latin word bis. "Sector" comes from the Latin word sectus, which is the past participle of secare, meaning "to cut". Thus, "bisector" literally means "something that cuts into two." The perpendicular bisector of a line segment is the perpendicular line that divides the line segment into two equal parts; the perpendicular bisector is unique, meaning there is exactly one such bisector for any given line segment and that must be explained precisely. We use the definite article "the" with the expression "perpendicular bisector", which must always be followed by a noun complement "of the line segment …".
Developing translation between different mathematical languages
The ability to switch between different mathematical languages—graphic, symbolic, and verbal—leads to a better understanding of algebra and geometry concepts, thus reducing errors. Encourage students with humor, comparing their brains to Google Translate, explaining that they will become human translation apps, surpassing even Google.
Prioritizing oral learning before writing
Start by working on mathematics orally before moving on to writing to maximize the assimilation of learning steps and problem-solving power. Oral work is lighter since it involves fewer sensory organs than writing. It allows for immediate and developed reflection, complementing mental calculation and the verbalization of calculations. Middle and high school students often lose these skills. Show them the importance of these techniques in forming and developing reflective intelligence.
Using analogies with daily life and other subjects
Bring mathematics closer to students by making analogies with everyday life situations or concepts from other subjects. For example, solving a math problem can be compared to cause/effect reasoning in biology, physics, and chemistry. Similarly, the conditions for the existence of a mathematical expression can be compared to the living conditions of an organism. Simplify mathematical concepts with concrete analogies, such as comparing 7√3 − 2√3 to 7 apples minus 2 apples, to get 5√3. You can count tenths, eighths, thirds... just like you count apples, tables, notebooks... The members of an equation seem like the balanced trays of a scale; to maintain balance, you need to add or subtract the same mass to both trays... This approach makes mathematics more accessible and understandable.
Using simulations, manipulations, and modeling
Don't hesitate to integrate more simulations, manipulations, and modeling into lessons. For example, teaching probabilities by simulating events or triangles by manipulating concrete objects greatly facilitates students' understanding.
Encouraging extensions and the creation of exercises
At the end of each concept, encourage students to reinvest their knowledge and skills by creating their own math exercises, adapting them to make them simpler or more complex. This activity allows them to understand how problems are constructed and to detect hidden steps since they will be acting from the perspective of a teacher.
Structuring learning in steps
Divide learning into steps, from the simplest to the most complex. Each concept must be worked on in distinct phases. Never work on more than one objective per session and complete all relevant exercises for each objective before moving on to the next. Juggling between objectives can disrupt the learning mechanism.
Allocating time for understanding
Give students the necessary time to better understand multiple concepts and the different perspectives of a concept. A week is the minimum time needed to assimilate any new information. Do not evaluate students if the objective is not achieved or if the skill is not acquired.
Rethinking curriculums
Some concepts, although fundamental, are sometimes placed at the end of the yearly curriculum or not addressed in previous classes. The order of sequences must be justifiable. Rethinking curriculums is crucial for a complete understanding of concepts.
Conclusion
The aforementioned points have been tested and proven successful in forming a complete and broad mathematical intelligence in students. Another secret lies in the use of rich and well-structured books. I recommend "Thema" by Hachette-Antoine for the Lebanese curriculum at the middle school level and "Math Masters" by Hachette-Antoine for elementary school. For the French curriculum, "Hyperbole" by Nathan for high school and "Transmath" by Nathan for middle school. These books are written to perfection and contain prerequisites, reflective activities, lessons, applications, oral exercises, vocabulary exercises, error exercises, training, and well-chosen in-depth activities. Everything is in your hands, so let the math party begin!
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