Professional knowledge
Know students and how they learn
Know the content and how to teach it
Know the content and how to teach it
The physical, social and cognitive characteristics of students affects learning and has implications for teaching. For example, students in the early years of school are beginning to understand ideas beyond first hand concrete experiences, are still developing control of small and large muscles, have short attention spans and can be egocentric. Students at this stage learn best when activities are short and hands-on with opportunity for movement. Encouragement to work co-operatively may also be required.
Understanding how students learn also has implications for teaching. For example, Piaget (1972) tells us knowledge is actively constructed by students rather than being passively received (as cited in Reys et al., 2012) and similarly Dienes (1960) believed that students construct new knowledge through reflection on their physical and cognitive actions (as cited by Reys et al., 2012). Further insight into how children learn was provided by Bruner (1986) who asserted that learning was a social process where students engage in dialogue with themselves and others (including teachers) (as cited by Reys et al., 2012).
To support the development of the mathematical concept of a number line I used my knowledge and understanding of the characteristics of students and of how students learn. I provided each student with a numbered card and encouraged them to work together to form themselves into a forward counting sequence. To help students to understand this idea beyond their first hand concrete experience, I then provided individual students with numbered train carriages which were sequenced from 1 - 20 to form a train.
To differentiate teaching I ensure instructions are delivered in multiple ways. For example, when teaching mental maths strategies I provide instructions to students verbally, in written form and through visual modelling. This assists students of different abilities to understand and participate in the task. Below is an example of a visual aid I used in combination with verbal examples to assist students practice the mental maths strategy of estimating.
To support the full participation of students with disability I work to develop my knowledge and understanding of specific learning needs. For example, one of my students could undertake a maths activity along with her same age peers if the questions were first read to her. It was important therefore for either myself or the teachers aide to work with this student to ensure she understood the written problem in order to complete the maths task.
Another student could similarly undertake the same maths activity as his same age peers if he were provided with hands on materials - for example, he was provide with notes and coins to assist him with addition and subtraction for a money maths activity. Another strategy I use to support full participation of students with disability includes allowing appropriate wait time when participating in class discussion, as some students will need more time than others to formulate their responses.
The strategies I used during my fractions maths lesson form another example of my ability to differentiate teaching to meet the specific learning needs of students across the full range of abilities. The whole class explored fractions as I guided them through a power point presentation I had prepared. Students were encouraged to participate by both asking and answering questions during this activity. To cater for different abilities I then set them to work individually on laptops to complete different fractions activities I had selected from Maths is Fun (i.e. different activities were selected for four ability levels). The classroom teacher and I moved around the class assisting students, prompting and extending where required.
I believe these examples support my philosophy of teaching that given the appropriate support every child has the right to be challenged and the ability to learn. Additionally, to support the development of the students' ability to be critical and reflective thinkers I leave time at the end of each session to allow students to reflect upon and share the details of what they have learnt and what they would like to learn in the future.
Teacher's comment - "You bought students together quickly, they responded well to your request for listening attentively. Getting students to look at a question they have difficulty with the previous day as a class was a positive strategy before sending them to continue. Great that you brought the students to the mat and went through their learning. You have more command of the class and you are using more strategies to gain their attention."
References
Reys, R. E., Lindquist, M. M., Lambdin, D. V., Smith, N. L., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics (1st Australia Edition). Milton, QLD: John Wiley & Sons Australia.
Reys, R. E., Lindquist, M. M., Lambdin, D. V., Smith, N. L., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics (1st Australia Edition). Milton, QLD: John Wiley & Sons Australia.