Biker traversing mountainous terrain during MPS? (Melissa)

I imagine myself as a student in this class. I felt like the biker shown in the picture trying to traverse the mountainous terrain. Though the journey is full of hurdles, when I arrive at the destination, the sense of achievement is “Wow!”. By the end of the lesson, as how the teacher puts it, they were mentally exhausted and were looking forward to the recess break. Though I am just viewing the lesson, I could feel a very high press for thinking. I was mentally challenged throughout the lesson. There was no chance to be passive as there were very interesting questions posed by the teacher and students. There were rich interactions between the teacher and students. I saw in this lesson what Kazemi and Stipek (1997) meant when they talked about “press” students to think conceptually about mathematics.

Kazemi and Stipek (1997) did a study that demonstrated what it meant to “press” students to think conceptually about mathematics. He measured “press for learning” by the degree to which teachers emphasized students’ efforts, focused on learning and understanding, supported students’ autonomy and emphasized reasoning more than producing correct answers. His article on “Discourse that promotes conceptual understanding” delineates two important norms in classroom discourse and they are the social and sociomathematical norms. Social norms refer to practices such as explaining thinking, sharing strategies and collaborating. Sociomathematical norms are classified into four categories. Firstly, they are explanations that consisted of mathematical arguments, not simply procedural summaries of the steps taken to solve the problem. Secondly, the errors made by pupils offered opportunities to reconceptualize a problem and explore contradictions and alternative strategies. Thirdly, mathematical thinking involved understanding relations among multiple strategies. Fourthly, collaborative work involved individual accounting and reaching consensus through mathematical argumentation.

My proposed research questions are as follow:

1) What are the practices that establish the social and sociomathematical norms in this lesson?
2) How are these practices associated with the cognitive demand (Bloom’s Taxonomy) of our pupils?
3) Classify the questions generated during teacher to student and student to student interactions according to Bloom’s Taxonomy.

In this lesson, the teacher was providing opportunities for students to be engaged in conceptual understanding. These were some of the interesting questions or points raised by the teacher during facilitation of pupils’ learning:

1) What is the quickest way or shortest way to calculate?

2) I am not interested in the pattern but I want to know how you get to this.

3) How can you get these values in a quicker way. Maybe yours is quicker.

4) Now you are describing to me the pattern which is very interesting way but how to get these numbers?

5) Zi yuan has an idea. Think about his idea.

6) Who else wants to say some more about the method? How can we be sure that it works?

7) Teacher links pupil’s response to concept on area and perimeter.

8) Let’s say if your friend Siu Pah is not in school and you show her your working and she is able to understand.


The teacher does not teach. She uses pupils’ responses to alter her instruction to match pupils’ development of problem-solving strategies. She is not quick to give correct answers but she emphasizes on the process, explanation and presentation of the working. She got them into pairs and group to work out the strategies together. She emphasized on the process of creating a shared understanding.

In 1956, Benjamin Bloom headed a group of educational psychologists who developed a classification of levels of intellectual behavior important in learning. Bloom found that over 95 % of the test questions which students encounter require them to think only at the lowest possible level. Bloom identified six levels within the cognitive domain, from the simple recall or recognition of facts, as the lowest level, through increasingly more complex and abstract mental levels, to the highest order which is classified as evaluation.

Her approach has provided her pupils with opportunities with a high press for learning. They are operating mainly at Bloom’s Synthesis and Evaluation levels. At the Synthesis level, they are always trying to create easier and alternative methods and suggesting solutions during their interactions with the teacher and friends. At the Evaluation level, they listen to their friends’ explanations and provide their opinions and suggestions. There were some differences in opinions and methods and they have to learn to resolve these differences. In this way they learn to develop their own opinions, judgement and decisions on the strategies to use.

What is lacking in the photo posted on the biker is his companions? If only he has a few other companions to encourage him to press on, I am sure his mountainous journey would have been a much smoother and easier one uphill.


References:

Bloom, B. (Ed). (1959). Taxonomy of educational objectives: the classification of educational goals. New York: D. McKay Co.


Confrey, J. (1990). What constructivism implies for teaching (Pt 3, chap.8). Journal for Research in Mathematics Education Monograph, Vol 4, Constructivist views on the teaching and learning of mathematics (pp.107-124).



Kazemi, E. (2002). Discourse that promotes conceptual understanding. Putting
research into practice in the elementary grades: readings from journals of the National Council of Teachers of Mathematics, 44-49. NCTM.


Lane, A. (2007). Comparison of Teacher Educators’ Instructional Methods With the Constructivist Ideal. The Teacher Educator; Winter 2007; 42, 3; ProQuest Education Journals, 157.


Libby K., Bharath S., & Irv J. The Mathematics Educator (2008). A morphology of
Teacher Discourse in the Mathematics Classroom. Association of Mathematics Educators.

Theories and Practices for Teaching and Learning. A Quick Guide. SEED Resource Book. Singapore.


Vygotsky, L.S.: 1978, Mind in Society: The Development of Higher Psychological
Processes, Harvard University Press, Cambridge, MA.