·         higher levels of motivation

·         almost limitless resources

·         an opportunity to see maths as cross-curricular

·         greater curiosity leading to more effective exploration

·         creative ideas driving investigations

·         meaningful application of problem solving strategies and thinking skills

·         a heightened sense of purpose and relevance

·         the all important bridge between theory and reality

·         greater independence and an improved attitude to learning

·         greater enjoyment and achievement 

·         a realisation that our environment offers opportunities for learning and enjoyment

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. 

 

Make sure to take a look at the brochure created in the project "Path of Innovation through Europe", that aimed to intruduce orienteering activities in school. There are a lot of mathematical activities and ideas there!

Another project you can find inspiration in is Math City Map. It offers weekly math tasks, an application to work with, a portal, math trails, tutorials and much more. Take a look!

-Treasure hunts are complex activities that can have many forms. You can use QR codes for creating the tasks, such as in this one, that took part in an open-air museum. 

- 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. In addition, take a look at the two documents below.

- Pre-primary activities examples and more fun activities for primary school students here, here and here

- Try some "Messy Outdoor Math" like these Scottish teachers and students such as in the video below.

-Take part in the Erathosthenes experiment, that takes place each year, in March and September

- Try some statistics study on leaves

 

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. Here are some examples.

 

Android apps: sketching and annotation tools (such as Sketch Box or Skitch), Geogebra, mindmapping 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). A very simple tool for creating QR codes treasure hunts is here or you can find ready-made (paid!) treasure hunts on this website. 

 

And a few useful iPad apps:  these tools for recording audio notes . A good tool can also be Educreations, for creating a lesson and sharing it. You can draw on a whiteboard or on photos while narrating what you are doing. The lesson can also be published on the Educreations website. I am not an iPad user, so if you need more STE(A)M apps, you can find them herehttps://ictevangelist.com/periodic-table-steam-ipad-apps/

According to Gardner, the author of the Multiple Intelligences theory, the aim of education “should be to develop intelligences and to help people reach vocational and avocational goals that are appropriate to their particular spectrum of intelligences. People who are helped to do so, he believes, feel more engaged and competent and therefore more inclined to serve society in a constructive way." Gardner states that anyone possesses different kinds of intelligence and therefore can learn, remember, perform, and understand in different ways. According to his ideas, "we are all able to know the world through language, logical-mathematical analysis, spatial representation, musical thinking, the use of the body to solve problems or to make things, an understanding of other individuals, and an understanding of ourselves. Where individuals differ is in the strength of these intelligences - the so-called profile of intelligences -and in the ways in which such intelligences are invoked and combined to carry out different tasks, solve diverse problems, and progress in various domains."

 The theory he proposed in his 1983 book Frames of Mind: The Theory of Multiple Intelligences differentiates intelligence into eight specific (primarily sensory) "modalities": verbal-linguistic, logical-mathematical, spatial-visual, bodily-kinesthetic, musical-rhythmic, interpersonal, intrapersonal and naturalistic, rather than seeing it as dominated by a single general ability.  (In more recent works, a ninth type, the existentialist intelligence, is added.) While all these types are present in any person, one or several are dominant for each of us.  They are located in different parts of the brain and can work together, as well as independently. All of them can be improved throughout our life, provided we have a growth mindset, not a fixed one. This theory explains why some pupils remember best what they have seen, while others are good with words, or at building things, some are very creative but find it hard to remember formulas or work in formal Mathematics. In order to get the best results, a teacher has to meet the learning needs of the students to examine methods for tracing and accommodating  these individual ways of learning in his/her teaching. 

  The Multiple Intelligences  theory states that pupils will benefit more from a broader vision of education, that would drive teachers to use different methodologies, exercises and activities to reach all students, not just those who excel at linguistic and logical intelligence and challenege them to discover "ways that will work for this student learning this topic" According to Gardner’s theory, students have different types of dominant intelligence and they can be reached more effectively by using a wider array of approaches. “Pupil engagement is a multi-faceted construct that includes affective, behavioral and cognitive dimensions” (Fredricks, Blumenfeld and Paris , 2004) More references on the MI theory here.

 

While the teacher can choose the approach used for presenting a certain notion or task, it’s important also that the students learn to understand and value their own approach to successful mathematics learning, to understand the conditions under which they learn best and to broaden their approach to learning. At the same time, this will help them learn to value their peers. Teachers can encourage students to reflect on how they grasp mathematical ideas the best, as well as understand that although students learn in different ways they can still be equally effective as learners and can learn the same ideas.

You can find out what is your intelligence profile with this test!

 

  Here is a list of six tips for nurturing a growth mindset from Carol Dweck and a longer talk she gave on this topic at EdWeek's  "Leaders to Learn From" event in Washington. You can read another article about her research. And here are some resources for teaching growth mindset from Edutopia, with a special section on Math. 

  Finally, you can test your own mindset here and learn how to develop your own growth mindset! You can also use this mindset quizz for students (it's free, but requires login, so you need to create an account).

Here is another interesting project or teaching unit on building bridges. 

 

 

Reflection and communication are not only parts but key aspects of hands-on learning, as we strive to facilitate and empower our students'reflective thinking. 

 

 In addition to offering materials to touch and explore, teachers can ask open-ended questions that promote problem solving and challenge children’s mathematical thinking and reasoning, as well as help them see things from a broader perspective. Such questions are not meant to elicit correct answers but rather to engage children in open-ended conversations that promote high-level thinking.  One of the foundations of play-based learning is that the teacher is active in the play, asking questions and adding knowledge and insight. The teacher learns together with children throughout the inquiry process. The building and manipulation must be followed by reflection and explanations, in order to help children maintain their focus on a particular topic, refine and expand their ideas, communicate their learning to others, and reflect on their experiences. To support learning, it is important to encourage children to communicate their explorations and findings. Teachers can establish a routine through which children share their experiences at group time. 

 Even if the outdoors and hands-on activities are so involving and enjoyable, they should include opportunities for reflective thinking. 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 prefered 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. The reflection activities could offer the educator  valuable information to help him/her adapt the class to the students’ needs, have a more dynamic approach to teaching in order to align better with students’ individual and collective needs, rather than adopt a “one size fits most” approach. The reflection prompts can ask students to take about 15 minutes to discuss in their groups and then respond in writing (on the worksheet) to  a few simple questions such as: 1. Describe several things that you learned from this activity? 2. How could you apply what you learned in your current class work?  

 

 

- Discovering the Art of Mathematics: 11 inquiry-based books freely available for classroom use. These texts can be used as semester-long content for themed courses (e.g. geometry, music and dance, the infinite, games and puzzles), or individual chapters can be used as modules to experiment with inquiry-based learning and to help supplement typical topics with classroom tested, inquiry based approaches (e.g. rules for exponents, large numbers, proof). Also, take a look at the document below.

- A whole blog of Math activities- here is the videos section

- Our project's Twinspace page for the bodily-kinaesthetic intelligence

- Kids STEM activities A-Z series (not just Math but also Science experiments for preschool to elementary school students)

- Math-on-a- Stick: more ideas for Math activities at early ages

- Another interesting collection of activities to browse

- And of course, we could not end this without some Christmas activities!