“We remember 10% of what we read, 20% of what we hear, 30% of what we see, 50% of what we see and hear, 70% of what we discuss with others, 80% of what we personally experience, and 95% of what we teach others.”
– Edgar Dale
Introduction:
As both a Geography specialist, and an employee at a school where experiential learning activities is at the forefront of their learning model, one of my personal wondering’s is how to incorporate rich, experiential learning opportunities into the mathematics classroom. Geography as a subject lends itself to experiential learning as it is easy to utilise the out of classroom setting, and relate new learning to real world phenomena. Conversely, mathematics is not often a subject associated with experiential learning opportunities. In the Intermediate Math Course, Modules 7 (Problem-Based Learning), 8 (Learning for All) and 9 (Rich Mathematical Tasks) were of particular interest to me because of the connections they made between mathematics, contextualising the topics taught, and effective learning. As a student, both at present, and in the past, I definitely can relate to the importance of experiential learning. I learn more through doing. I also learn more when I can contextualise a problem. One of the main weaknesses in my own learning journey is that I cannot relate well to abstract concepts. Mathematics can be very abstract, and without context; students, like myself, can find it particularly difficult to understand.
Learning Outcomes:
1. Deepen our understanding of why experiential learning is important in the mathematics classroom.
2. Assess the impact that experiential learning strategies can have on learner progression.
3. Explore ways of incorporating experiential learning strategies into the classroom.
4. Connect experiential learning ideas to the key themes and concepts learnt on the course.
BIG Ideas:
I wanted to create my own Big Idea that related directly to the focus of this learning station. However, I also added one from Charles (2005), which I thought was most applicable to the topic chosen.
My BIG IDEA
CONTEXT: All mathematical concepts need to be connected to the real world to give context; allowing for deeper understanding.
BIG IDEA #5 (taken from Charles; 2005)
OPERATION MEANINGS & RELATIONSHIPS: The same number sentence (e.g. 12-4 = 8) can be associated with different concrete or real-world situations, AND different number sentences can be associated with the same concrete or real-world situation.
What is Experiential Learning?
“Experiential learning is the practice of learning through doing. It encourages the student to have first-hand experiences with the materials, rather than learning through someone else’s experiences in textbook or lecture.”
McGrann; 2016 discusses in his article; Learning by Doing: The Case for Experiential Education, how learning is intrinsically linked to doing. He makes the case for this type of learning with three key points:
a. Students will want to know more when they need to know more.
b. You never know what problems will need to be solved.
c. Give students the space and they will find the learning.
Activity: Watch the video above.
Q. What does experiential learning mean to you?
Kolb’s Experiential Learning Cycle
Kolb’s Experiential Learning Cycle outlines how a learner should progress when encountering a new experience. The first stage is concrete learning, where there is encounter of a new experience or a reinterpretation of an existing experience. This is followed by next stage, reflective observation, where one reflects on the experience on a personal basis. After this, abstract conceptualisation, allows the learner to form new ideas based on the reflection. Lastly, the active experimentation stage is where a learner will apply the ideas to his surroundings. All this will lead to the next concrete experience, and the thus the cycle continues.
How does experiential learning support the teaching and learning of mathematics?
The educational implications of experiential learning in math are multidimensional. They also help to promote the seven mathematical thinking skills, needed to develop our students into mathematical thinkers. Five key learning implications are outlined below:
1. Ability to immediately apply knowledge
Experiential learning is an opportunity for learners to apply what they’ve been taught to solve real-world challenges. Learners test their understanding of underlying principles, processes and procedures and can experiment and adapt their practice to achieve best outcomes.
Link to mathematical thinking skill: Representing, connecting, problem solving and selecting strategies.
2. Access to real-time coaching and feedback
Achieving expertise requires practice and focused coaching based on what is observed during practice. Every experiential learning activity should include a debriefing session where learners receive feedback and coaching from experts and fellow team members.
Link to mathematical thinking skill: Reflecting
3. Promotion of teamwork and communication skills
Most errors in health care involve a breakdown in communication and teamwork. Because the care of patients is provided in a team, we should learn and practice in teams. Reading a book or listening to a lecture does not provide the same experience.
Link to mathematical thinking skill: Communicating
4. Development of reflective practice habits
The gold standard in education is the person who can self-monitor the effectiveness of his plan, anticipate outcomes and develop contingency plans. We often refer to these people as “experts.” They are expert because they have had more experiences and have received more coaching than a non-expert and have incorporated certain thinking disciplines into everyday practice. Experiential learning helps accelerate the journey from novice to expert.
Link to mathematical thinking skill: Reflecting, reasoning and proving
5. Accomplishments are obvious
Learners can improve, and know they have improved, in as little as an hour because of the feedback loop created by problem solving, feedback and practicing again. In a traditional classroom setting, learners often do not know if they are on the path to success until they take an exam and get a score.
Link to mathematical thinking skill: Connecting and reflecting
How does experiential learning support a high teacher efficacy?
a. It helps the teacher to develop more appropriate learning opportunities for the target learners.
b. Teachers will have to design activities that will give opportunities to all the learners to learn in the best way that suits them.
c. The activities carried out will enable the learner to go through the whole process of the experiential learning cycle.
Challenges to Consider:
a. Limited class time. A major factor limiting the use of experiential learning activities is the limited class time. When most classes are subject to an hour time constraint, how can we ensure that we allow enough time for all the element of Kolb’s Learning Cycle to be fulfilled? At my current school, our lessons are two hours long to try to account for this problem. However, this then adds another problem concerning the attention span of our students.
b. Limited access to resources. Some schools do not have adequate access to the resources needed for experiential learning to take place. How could this be addressed?
c. Curriculum Constraints. One of the aspects of this topic that I find most challenging to deal with, is trying to plan for experiential learning activities for all areas of the curriculum. This is a time-consuming process, as not all concepts being taught typically lend themselves to this type of learning. Is it necessary to adopt experiential learning strategies all of the time?
d. Inadequate group work skills: Students who are new to this type of learning may not possess the necessary skills needed to work effectively in team work situations. Schools should try to encourage experiential learning tasks to be implemented at an early age so that students are familiar with this type of learning. What strategies do you find most effective for encouraging peer collaboration?
e. Overwhelming for the teacher: Experiential learning opportunities require a great deal of time and effort to prepare. In an ideal world, we would try to incorporate these into our daily teachings, but in reality, this is not the case. My school currently enforces a rule that states teachers should try to aim to implement an experiential learning activity at least three times per course. This helps to reduce the burden on teachers’ workloads. How else could we prevent teachers from feeling overwhelmed?
How does experiential learning support leadership in mathematics?
Throughout the course, we have learnt a number of key pedagogy related to successful 21st math teaching. All of which are designed to help new math educators to become leaders in this field. Experiential learning helps to facilitate these teachings in a number of ways.
1. The Growth Mindset – Promoting a growth mindset involves teachers facilitating the need for students to ask questions and be curious to find out more. Experiential learning allows this to happen naturally through bringing the math into real-world contexts.
2. Mathematical Thinking Skills – It has been identified that in order to be successful in the subject we need to be teaching students on how to become mathematical thinkers. As aforementioned, experiential learning helps to develop this skills in our young learners.
3. Rich Tasks – Current emphasis in maths pedagogy is on the need for rich tasks to be available to our learners. Experiential learning in its very nature is ‘rich.’ It provides opportunities for open ended questions, through sparking a natural curiosity about the math in the world around us.
4. 21stCentury learning skills – the skills outlined below, as identified in Module 4, are key to contemporary maths instruction.
*Creativity, Innovation and Entrepreneurship
*Critical Thinking
*Collaboration
*Communication
*Character
*Culture and Ethical Citizenship
*Computer and Digital Technologies – the TEDexEdU video below begins to address the importance experiential learning in today’s digital age.
Experiential learning subconsciously utilises these skills into everyday learning through students ‘doing the math’ for themselves.
A number of these skills are demonstrated through the video below, which shows experiential learning in Morocco.
Math in Morocco | Where Math Grows on Trees
Activity: Watch the video above.
Q. How are students demonstrating both 21st Century learning skills, and mathematical thinking skills, in their lesson?
Experiential learning: An example…
After watching the Math in Morocco video, I decided to conduct some research into experiential learning ideas, both in the math curriculum, and cross curricular. I came across this interesting article: We Can Do It: Experiential Learning Activities in Mathematics Courses for Liberal Arts Undergraduates; Stogsdill; 2014. Not only did it allow me to develop some ideas on how to incorporate experiential learning tasks into my own classroom practice, but it also conveyed the value that students place on these tasks.
I am taking some students on an extracurricular school skiing trip to Vorlage, Gatineau, on Tuesday this week. I got to thinking: why couldn’t I take students on a ski trip as part of their math learning? The following are some ideas of how an experiential learning ski trip could be incorporated into various stages of the math curriculum. I have linked these ideas to the EduGains Continuum and Connections documents.
Examples of ‘experiencing the maths’ for a ski trip:
1) Integers: Number Sense and Numeration:
Grade 8 Learning Goals:
a. Use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
b. Represent the multiplication and division of integers, using a variety of tools;
c. Solve problems involving operations with integers, using a variety of tools;
d. Evaluate expressions that involve integers, including expressions that contain brackets and exponents, using order of operations;
e. Solve and verify linear equations involving a one variable term
Tasks:
a. How much money do we need to make as a class to go on the trip?
b. How much money will each individual have to raise?
c. Write an equation that describes your rate of earning. Solve your equation showing all your work.
d. Make a graph showing the money you made per minute, per hour, per items sold. Show all appropriate labels and a title.
2) Fractions: Number Sense and Algebra:
Grade 9 Learning Goal:
a. Solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate and proportion;
Task:
a. Survey people at the ski field to determine whether they are staying at the resort or just using the ski field. Calculate a ratio that would describe the number of people staying at the resort vs the number visiting daily. Show the ratio in another form.
3) Proportional Reasoning: Measurement:
Grade 7, 8 and 9 Learning Goal:
a. Solve problems involving rates.
Tasks:
a. We estimate the distance of a ski slope to be 500m. With a partner, take turns skiing down the slope and record your time. Find your rate in meters per second.
b. Graph your rate of meters per second for skiing down the slope.
c. Determine the angle of the stairs that lead to the ski chalet. Develop a hypothesis of your findings.
4) Perimeter, Area, Volume: Geometry and Spatial Sense, Measurement:
Grade 7 Learning Goal:
a. Determine relationships among area, perimeter, corresponding side lengths, and corresponding angles of similar shapes
Tasks:
a. Find two similar figures of different sizes and draw them.
b. Give the scale factor from one to the next.
c. Give the area of the smaller figure and the area of the larger figure.
Grade 9 Learning Goals:
a. Solve problems that require maximizing the area of a rectangle for a fixed perimeter or minimizing the perimeter of a rectangle for a fixed area;
b. Solve problems involving the volumes of prisms, pyramids, cylinders, cones, and spheres.
Tasks:
a. Find the volume of the snow truck by estimating the height and width. Show your equations and work. Use appropriate labels.
b. The snow truck takes nine minutes to fill up with snow before it dumps into the snow pile. What would be the amount of snow needed to fill the snow truck per second in meters cubed?
Activity: Think of a topic within the math curriculum that you would like to develop an experiential learning task for.
Q. What is your idea for an experiential learning task?
Q. Which grades and strands in the math curriculum does it link to?
Q. Have you taken into account the fives challenges of implementing experiential learning tasks posed earlier in this blog?
a. Is there enough time for all stages of Kolb’s Learning Cycle?
b. Are your resources appropriate, and sufficient, for the task?
c. Does the task allow for rich learning opportunities?
d. Does your task require the learners to have prior skill-sets?
e. Does your task match your, or the educator’s, capabilities?
Closing Thoughts…