Week 9: Response to Outdoor Mathematical Experiences: Constructivism, Connections, and Health

Summary:

Meg Moss (2009) believes that outdoor mathematics experiences could help teachers and children interact better with the world we live in, both in preservice teacher education and in elementary schools. Through such a natural curiosity they are able to build mathematical knowledge using both a constructivist psychological and socio-cultural viewpoint. Experiences in outdoor mathematics not only help students see the links between mathematics and other disciplines, but can also make learners feel more connected to their natural world. This paper describes outdoor mathematics and related theoretical framework, and then offers specific examples of outdoor mathematics tasks that can be used in primary teacher education.

Stop 1: How do we make math fun?

Children are natural adventurers and are born with curiosity and imagination. Nowadays, we see many students in our class say no to mathematics due to mathematics anxiety, losing confidence when failed frequently, and lacking interests when the teaching expectation are beyond or below their capacities etc. After reading this article, I was thinking, how do we create some mathematics activities that are fun and educational-orientated at the same time besides those conventional means?  When I first heard the idea of cooperating mathematics with outdoor activities, and teach with and within school garden, the sense of curiosity raised and I felt a willingness of participating in as an adult and teacher, thus not to mention students with full potential and curiosity at their age. We can make math discussions happen anywhere, for example in sidewalk chalk, outside in the sunshine, in the garden, instead of with pencil and paper and at a desk.

Stop 2: Constructivist Perspective

The theoretical support of constructivist learning is that outdoor math practices are a meaningful way of implementing constructivist learning through both a theory of analytical learning and a socio-cultural context. Aspects of constructivism in psychological learning theory include the idea that learners build new knowledge based on past experiences and understanding. Young children are very much connected to the world around them as much of their early learning is focused on their world experience. A socio-cultural interpretation of constructivism is that by engaging in activities and logical thinking within a group, learners build new knowledge. The outdoor activities mentioned that building community through collaborative activity outside classroom provides opportunities to share and interact on math. I found this is very interesting, as my dad once told me when he was young living in the countryside, his secondary school would normally have a ‘Seed Planting Break’ in early spring and a ‘Harvest Break’ in late autumn, not only all students but also teachers have their obligation to go back to their family farm and croplands, to do the farm work for their family. Thus, these students would obtain knowledge of agriculture in school and back home, and enhance their practices in the family yards straightaway. Students coming from families with farming history learnt about sowing, transplanting rice shoots, spreading insecticides by estimating crops and measuring areas, the importance of healthy eco-system and sustainability and much more… through constructivism.

Stop 3: Relate to My Experience in the Orchard Garden Workshops

In UBC, we had Orchard Garden Workshop running from 2007. With curiosity and interest, I participated three workshops this semester, we have done the England tradition of apple wassailing, hands-on workshops such as planting seeds for the coming spring and re-growing veggies from kitchen scraps for sustainability, as well as learning diverse means of collaborating math teaching with and in the garden. It was a great fun! I was impressed that every member participated in the workshop has something to share from their living and working experience, either from childhood memories to recent veggie planting and gardening practices etc. Thus, I guess it won’t be hard for preservice teachers to ground their teaching and spread ideas, since we humans as the living creatures who share the planet with other species, we all stand and start our life from this beautiful word. With the great hope of passing our knowledge in mathematics and our responsibility of teaching sustainability to our next generation, we will see more educators and practitioners join this practice.

In the previous workshop, my friend Amanda who is a PhD student from EDCP, and an experienced Grade 7 math teacher, led a participatory activity in the garden about measuring and estimating perimeter and area of things in the garden using our body part. For example, I used the extended distance between my thumb and my index finger (about 15 cm) to measure the perimeter of a bench, used my palm to measure the surface area of head of broccoli etc. I was inspired by this demonstrative, engaging and descriptive activity, and thought about including teaching fractions in the garden too. Similarly, Meg Moss (2009) suggests using leaves and rocks to help students better understand the concepts of perimeter, area and volume etc., and working in group would be wonderful to include Complex Instruction here too!

It was a great pleasure to be the blog author and official photographer of the UBC Orchard Garden, I had been taking pictures and writing blogs for the activities and memorable moments, as it was mentioned by Meg Moss (2009) as a good way to appreciate what was offered by the great nature and track what do we learn from them. Here is the link if you want to check it out: https://www.blogger.com/blogger.g?blogID=2127680076264956287#allposts/src=sidebar

Question 1:

Do you have experience connect outdoor activities with teaching subjects (not restricted to mathematics) and help students see that learning is not just something that happens only in the classroom and textbooks?

Question 2:

Have you incorporated school garden with teaching, not only in teaching mathematics but other subjects?

Reference:

Moss, M. (2009). Outdoor mathematical experiences: Constructivism, connections, and health. In Tasks in Primary Mathematics Teacher Education (pp. 263-273). Springer, Boston, MA.

Week 8: Response on Forcing Awareness by Dave Hewitt

Summary

 Whether it would be helpful and appropriate to force awareness in teaching, it has been a controversial topic among teachers. Dave Hewitt suggests that forcing awareness is a process involving deliberately planned tasks, usually with a standardized questioning line, where an instructor interacts with learners so that it is highly likely that the learners will develop a particular understanding of mathematics in this situation. The role of instructors is to bridge what students don’t know and what they are coming to know, to build upon their existed awareness so that they become aware of something new. From this view, teaching is seen as interacting with existing awareness of learners, rather than attempting to educate learners about the teacher's awareness.

Stop 1 Forcing Awareness

When I reflected on my teaching, I realized that the process of forcing awareness is likely to include stressing certain things while ignoring others, concentrating the attention of the learners on some issues, and arbitrarily guiding the questioning etc. However, the crucial aspect for instructor is to be sensitive to learners ' awareness and quickly adjust teaching strategies in that moment, so that existing awareness can be used, influenced, guided, challenged or appreciated. It would be beneficial for learners to use the power of their mind and not just sit and expect to be told. Thus, we should create a classroom culture where initiatives and motivations are welcomed and appreciated.

Question 1

In your teaching practice, did you notice the proportion of forcing awareness and student-centered learning? Which teaching pedagogy would you prefer and why?

Stop 2 Educating Awareness

When looking at the roles a teacher taken and questioning employed in educating awareness, only percentage success can be achieved by learners. There is a loss of sense of achievement and empowerment in learning, which discourage learners’ initiation and curiosity. On the other hand, student-centered learning includes students in the process of thinking, discovering, conjecturing, evaluating, and this means that what is new is related to what they learned as it evolved out of what was already there. It means that the new knowledge is not a specific piece of information that needs to be learned but is connected to what has already been known.

Question 2:

Can you think of any benefits of deliberately educating awareness in math class? Can you give an example?

Stop 3 the Benefit of Forcing Awareness v.s Rote memorization

According to the illustrated examples, barely talking the concepts doesn’t guaranteed listeners managed to transfer the words they heard into meaningful mathematical ideas. Furthermore, it is very likely for them to truly aware of the mathematical significance of the statement, or be able to apply this new knowledge in new situation.  It is too often the case that, instead of this, a learner tries to memorize this as ‘received wisdom’ from their teacher; trying to memorize someone else’s awareness rather than having educated their own.  It is too often the case that, a learner attempts to memorize 'received wisdom' fed by instructors, rather than generate their own. it is just a separate piece of information floating in someone’s mind. The difficulty with attempting to memorize something is that this is always followed by forgetting at a later date. Memory is distinct from sense of consciousness. Memory needs extra effort to preserve and retain this memory over time. This is because it can be unattached to the consciousnesses that a learner already has; it is only a single piece of knowledge that floats in someone’ mind.

Question 3

Would you recommend rote memorization in mathematics education?

Reference Hewitt, D. P. (2018). Forcing awareness.