“If you present math the way it really is, this fantastic expression of human creativity and ingenuity, people do want to read that!” – Steven Strogatz, professor at Cornell University
We all know how important it is that children experience mathematical activities across a range of contexts and locations and by using direct sensory experience – and that outdoor learning is just as important as ‘desk work’. Connecting Maths to every-day life and to our real environment gives Maths topics a purpose and a meaning. Remember that question that students ask: “Why do we have to study this?”? In order to avoid it, we can try to show them how Maths can be applied to other sciences, such as Biology studies, but also how one can use it in every-day tasks such as cooking, cost-effective packaging, gardening, in order to make difficult situations simpler and above all getting to know more about each other. Task such as treasure hunts, origami, paper folding, and construction projects can combine modeling, object manipulation, problem solving, performing, movement and collaboration into a rich learning experience.
Of course, there is no “one size fits all” teaching strategy. The teacher still needs to determine if hands-on activities are suitable for a certain lesson as well as students’ level and age. Unless these activities bring an added value to a lesson, they are useless. Having the learning outcome in mind and considering the child(ren) when planning the lesson will help in selecting the best strategy. Students’ explanations could be a good way to assess the value of a tool. Clear rules and explanations are always required and sometimes, creating the teaching materials can be a Math lesson in itself.
These types of activities are especially beneficial to students with dominant kinesthetic intelligence. This is “the ability to use one’s mental abilities to coordinate one’s own bodily movements”. The main elements of the kinesthetic intelligence are control of one’s bodily motions and the capacity to handle objects skillfully, as well as the ability to process information through the sensations in the bodies. These students enjoy all types of sports and physical activities, they need to be touching, moving and manipulating objects, moving around and acting. For these learners, performing physical actions can lead to learning mental actions and operations, so the mathematical notions are represented by actions. They often express themselves through dance. These pupils would use solid or pictorial models wherever possible and act on these, by moving parts around, while sometimes talking to themselves during this process. When they are remembering ideas, they can think of the actions that they did or do the actions with their hands, for example a student could run his finger along the sides of a triangle as a help to remember a theorem or formula. When they hear things they can focus on the actions that are being done and try to anticipate the outcomes of actions. As far as their difficulties, they may find it hard to remember the names and would need time to translate their action knowledge into alternative forms of expression, such as symbols or words.
The methods to empower this type of intelligence would be the use of touching, feeling, movement, improvising, “hands-on” activities, using mime and facial expressions and physical relaxation exercises. Moreover, the types of activities we will be focusing on benefit and empower an important and often neglected skill: the spatial creativity. Here you have an article on the importance of spatial skills for future STEM careers and ways to develop it.
Here are just a few types of hands-on Math activities that can be used to enrich teaching and learning.
“What really drives education is curiosity, trying to fill gaps in our understanding. And the world around us is a tremendous resource to stimulate that curiosity.” (Sir Ken Robinson)
Learning math outside the classroom walls offers students the wonderful, powerful experience of finding the Math that is hiding in plain sight.
In November 2006 the UK Department for Education and Skills published its manifesto ‘Learning Outside the Classroom’. The Manifesto opens with the statement, “We believe that every young person should experience the world beyond the classroom as an essential part of learning and personal development, whatever their age, ability or circumstances.” Such experiences “help us to make sense of the world around us by making links between feelings and learning. They stay with us into adulthood and affect our behaviour, lifestyle and work. They influence our values and the decisions we make. They allow us to transfer learning experienced outside to the classroom and vice versa”. The document offers an insight on the benefits, strategies, aims and supporting actions connected to outdoor learning.
Here are some activity examples for taking Math outdoors:
- Take part in the Erathosthenes’ experiment, that takes place each year, in March and September
- Treasure hunts are complex activities that can have many forms. You can use QR codes for creating the tasks, such as in this one, which took part in an open-air museum.
- Try some “Messy Outdoor Math” like these Scottish teachers and students
- Make sure to take a look at the brochure created in the project “Path of Innovation through Europe”, that aimed to introduce orienteering activities in school. There are a lot of mathematical activities and ideas there!
- Measuring the height of a tree or building using a simple theodolite in this activity from Mathisfun
- Six examples of #StreetMath adventures suitable for elementary students too.
Tips: As the activities take place outside the classroom or even outside the school premises, the tools for such activities have to be easily portable: for example measuring tools and cameras are very useful. Tablets or smartphones can offer a wide range of apps: sketching and annotation tools (such as Sketch Box or Skitch), Geogebra, mind mapping tools (such as Mindomo), QR readers (such as ScanLife), photo editors (such as Pixlr or PicsArt), sound recording and sharing (such as Soundcloud), screenshot tools (such as Screenshot), doodling tools (such as You Doodle or Sketch for Keep), or even astronomy tools (such as SkyView).
Activities using paper or string
The false idea that Math is “only about numbers” can take out the enjoyment and the curiosity, especially for students who lack numeric abilities. They will label the subject as boring and therefore miss the beauty of the patterns, shapes, visual proofs and possibilities that could be explored in classrooms and connect Math to reality and creativity.
Paper and string are cheap and easy to use anywhere, which makes them valuable materials in any class. Students can be encouraged to use their kinesthetic intelligence to play with tangram, create tessellations, make geometrical paper objects, such as platonic solids and carry out simple proofs of their geometrical properties through paper folding or origami, create drawing techniques etc. Students will also use measurement and manipulation and investigation, for example to study the area/perimeter connection or “discover” the number PI. Some other mathematical concepts that can be studied with paper and/or string activities include sequences, symmetry, fractions, sums and combinatorics, geometric constructions and many more. In this way, they will understand relations, rules and theorems in a kinesthetic way.
Some example activities:
- In this activity, children create an origami star. They are introduced to both geometry and analytical skills in a creative way.
- A fold-and-cut activity (with a story too!) You can find more examples here. If you need some templates for such activities, they can be found at http://howtofoldit.org/
- The Math in a simple A4 paper! . Here you have the second part of the activity.
- Resources for origamihttp://artcuratorforkids.com/origami-for-kids/ also suitable for younger students.
Construction and/or modeling activities
Math teachers who have only paper and pencil at their disposal, find some of the curriculum contents very difficult to illustrate. A lot more objects and materials besides string and paper can be used for modeling mathematical knowledge, from Lego pieces to cakes. This approach stimulates children to learn, helping them to understand and use math in totally new ways, so that geometrical rules, axioms and operations are „physically” elaborated and stimulate kinesthetic learning. Activities such as object manipulation, movement, measuring, mime, crochet can also be turned into an opportunity to learn Math.
More example activities:
Students can prove theorems and properties in a practical way, based on object manipulation, self-made models, experiments and observations, using different materials and auxiliary tools, such as in this practical lesson on volumes where making the shapes, physically measuring them and turning them round in their hands helped the students understand what they were doing far more than simply working from a textbook would have done.
As another example, they can build and use a wooden device to prove the theorem of Thales or build a vehicle propelled by a balloon and studying its movement.
Turning the Math class into a workshopis certainly not easy and it cannot be a day-to-day practice maybe, but trying it from time to time can bring calculations to life.
A seventh grade group of students used a community project- building benches for a veterans’ home- to apply and grasp Math concepts. The benches were created in a first time class called “carpentry math.” It’s designed to teach kids that measuring, ratios, proportions, angles and fractions are all things that can be applied to real life jobs.
Rocket Science-Working in teams, students design and build rockets powered by water and pressurized air. Using what they learn about the fundamentals of force and motion, they build a fully functional rocket including: payload compartment, propulsion system, recovery system and guidance system.
Building a geodesic domewith straw- in a combined math and engineering activity
Tips: Building activities are often used in the flipped classroom – a very popular teaching strategy nowadays. This blog post includes a list of 12 tools that can be used in such an activity. Many of them have tutorials or suggestions for educational use.
Even if the outdoors and hands-on activities are so involving and enjoyable, they should include opportunities for reflective thinking. To support learning, it is important to encourage children to communicate their explorations and findings. In order to support this, teachers can offer reflection prompts as a way to encourage students to think about what happened, to discuss and think deeply about the purpose and implications of the activity, reinforcing what was learned. Students can be encouraged to analyze the new approaches and compare them to their preferred method, finding new ways to study mathematics. It is also an opportunity for the educator to understand better what he/she expected students to learn, what they actually learned, and what they still needed to learn.
Article written by: Irina Vasilescu, Secondary school Math teacher and Scientix Ambassador.