Hexagonal thinking is a borrowed concept. And while no theorists have talked about the idea and its implication, a curriculum developer, Betsy Potash, has been credited with its adaptation to classroom settings. Suitable for both physical and virtual classrooms, hexagonal thinking is a great way to help the class open up on discussions.
But will it be helpful in mathematical lectures? That’s a big challenge because math isn’t just about discussions but more about practice. Nevertheless, using aspects of hexagonal thinking to teach mathematics depends on the teacher’s creativity.
Hence, examples of hexagonal thinking activities that are easily doable in class for an enriching mathematical lesson are given below.
Ways to employ hexagonal thinking in the math classroom
Hexagonal thinking has been adapted to match the requirements of a classroom. Below are concept-based examples of how teachers can use hexagonal thinking in a mathematics class.
1. Addition Hexagons
Addition hexagons can be a great way to teach children addition and the relationship between numbers. For instance, the number 7 can be broken down into several expressions that better explain how 7 is formed to the child. Examples of the expressions can be 5+2, 3+4, and 1+6. A teacher can also use more significant numbers to help the child develop hexagonal thinking in a mathematics class.
Math teachers can also employ further breakdown of numbers using these addition hexagons. For instance, the 5+2 can be further simplified into 3+2 or 4+1 and 1+1.
2. Multiplication Hexagons
Multiplication hexagons can also be very interesting to practice in class. A multiplication hexagon can be adjusted based on a child’s level of understanding. For instance, a child in 4th grade can be asked to think of all the multiplication examples that make up 200 (100×2, 50×4, 25×8). Another way to use them could be by breaking down the multiplication expressions into addition ones. For instance, 200 = 100+100 or 50+50+50+50. The addition and multiplication expressions can be used to explain the several numerical relationships between numbers.
3. Algebra
Algebra, calculus, and geometry might confuse a lot of individuals, but their differences make them unique in their own nitty-gritty way. Algebra uses alphabets to establish numerical relationships. Hence, through hexagons, several relationships are better explained visually. Binomial formulas like (a+b)2 can be expanded on hexagons. There can be several ways in which expansion can be done. For instance, hexagons with expressions like (a+b)(a+b), a(a+b)+b(a+b), and a2+ab+ab+b2 can be used sequentially or as different types of expansions. Algebraic expressions follow BODMAS’s rules but can also be a great representation of hexagonal thinking.
4. Geometrical Derivations
Geometrical derivations are based on specific rules. One such area of mathematical rules belongs to trigonometry. Trigonometry is all about finding if a figure is a triangle and is based on the regulations of Sine, Cos, and Tan. Almost all derivations are means to find the relationship between Sin, Cos, and Tan. Hence, hexagonal relationships can help students in the class to use activity-based learning to remember the relationship between sin, cosine, tangent, cotangent, secant, and cosecant, with the help of the table initially and without it, post the hexagonal thinking exercise.
5. Mensuration
The hexagon is a geometric shape; however, it is not studied like other shapes in the elementary years. However, for measurement, the hexagonal activity of making a web of hexagons, including figures similar in shape like a rhombus, parallelogram, and trapezium with daily life objects, can be great exercise. Similarly, creating hexagons for different 2D and 3D shapes can also help better memorize the other names and types of figures.
Hexagonal thinking: Mix of creative and critical thinking skills
Hexagonal thinking bridges the gap between critical and creative thinking. On the one hand, it allows individuals to consider novel thinking patterns. Conversely, it will enable students to test pre-conceived notions by elaborating on their beliefs and discussing them among people. As critical thinking involves careful consideration of a view, hexagonal thinking can provide means to tangibly represent the evidence that supports the belief.
Critical thinking has five stages; through hexagonal thinking, individuals can tangibly represent all of these. For instance:
- In the 1st stage of critical thinking, individuals can take suggestions and represent them on hexagons once a belief has been evaluated. Post that, a web of related or completely unrelated suggestions or solutions is made.
- In the 2nd stage – turning the problem into a question- individuals in groups can brainstorm questions that manifest the belief for which answers need to be found. These questions lead to intellectual debates and discussions to arrive at enlightening questions.
- In the 3rd stage– hypothesizing, individuals can together find tentative answers to the questions they decided. Hypothesizing can be through what is already known, for instance, facts and figures, or using a completely subjective approach. Hence, in a classroom or organizational setting, the 3rd stage of critical thinking, when matched with the hexagonal system, can reach different kinds of answers and theories that will only add to the knowledge and variety of information one has access to.
- In the 4th stage – logical expansion, elaboration on several hypotheses is presented in front of the class or individuals. This elaboration must have analytical support and explanation so that a group can decide whether to accept or refute the solutions.
- In the 5th stage – testing hypothesis – after the thesis with the most logical explanation has been selected; individuals can easily choose what is interesting enough to try out in reality.
All these hexagons represent each stage of critical thinking in a physical form, hence, helping individuals to use them as a stimulation for further expansion of logical reasoning. Since each hexagonal relationship is categorized in stages, individuals can easily maintain and indulge in regular consideration of the conclusion without putting much mental effort into recalling what has been discussed earlier.
Conclusion
Mathematics, critical thinking, logical reasoning, and now hexagonal thinking can all be practiced together. At the same time, all of these have quite a few real-life examples too. There is some common link binding these forms of mental operation, and the same link would help in the success of hexagonal thinking activities in a mathematics classroom. While the article mentioned above mentions algebra, trigonometry, and measurement to help students learn maths through hexagonal thinking, other concepts can also use the hexagonal relationships for more enlightening classroom learning.
An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,