6. Reflective thinking to Susan Gerofsky’s article

Genre analysis as a way of understanding pedagogy in mathematics education
This is a paper regarding the application of genre analysis in mathematics education, focusing the lens on two topics: one is the genre features existing in word problems and the relationship between word problems, riddles and parables; the other one is the lecture genre of initial calculus at a university. After reading the whole paper, I want to propose some questions as below:
1. On pp38, you proposed a question for readers to think about: “What are word problems?” To be honest, when I arrived in Canada initially, I was confused about the concept of ‘word problems’. If we just talk about this concept from the view of mathematics, I have to admit that we have different notions between China and Canada. If I translate the words of ‘word problems’ into Chinese literally, ‘word problems’ means ‘wen zi ti’, which means that the problems only involve mathematical data and question without being embedded into a real or fictional story, for instance: 1 more than a number divided by 7 is 10. What is the number? . But with getting myself into the Canadian mathematics education, I realized that ‘word problems’ here is the same meaning as the problems that we call ‘ying yong ti’ in China (if I translate the Chinese words ‘ying yong ti’ into English literally, ‘ying yong ti’ refers to problems of application (applying mathematics to problems embedded into either life contexts or stories) So, here, I still need to clarify the question of ‘what are word problems?’. Are they the same as ‘ying yong ti’ or the combination of both ‘wen zi ti’ and ‘ying yong ti’? In terms of the features of word problems that you typified in the paper, a word problem is a three-component, sequenced rhetorical structure (a story element which can be disposable, data and question), I think that ‘word problems’ is the same as ‘ying yong ti’ in China. Then I’m not sure how to term the problem just like the one I illustrated above?
2. The use of verb tense in word problems is ‘tenseless and non-deictic’. Although I understand that the strange mixing of verb tenses in word problems may not disturb the understanding of English speaking students about the problems, I’m wondering if the mixing of verb tenses will confuse ESL students and to what extent it affects ESL students’ math thinking. From my perspective, I think that ESL students will generally have a long term obstacle of developing the English language register and genre. The English genre they have, to some extent, is more consistent with the genre of their mother tongue, different from the one that English speaking students hold. ESL students usually learn English in a very formal environment in which the use of verb tense in English is governed by norms of grammar, so if the word problems would be counterproductive to ESL students’ English learning?
3. The painting example (pp39) you illustrated in the paper is impressive. I have ever met the same situations in my previous teaching. What my students were more curious about was to explore the truth of the stories or the life contexts in which I embedded the problems rather than the math problems per se. So, if we have a number of stories that we can use to integrate the math problems, do we have any criteria that we can refer to when assigning an appropriate story to the problem and deciding the language we need to use in order to avoid distracting students’ attention?
4. In the second case study-initial calculus lectures as a genre, the features of the lecture genre evoke my resonance. You said: “The lecture genre, is already a mode of persuasive talk that tries to “sell” its audience on both of truth of the ideas presented, and the authority and status of both the lecturer and sponsoring institution as purveyors of truth and knowledge….In the lecture genre, tag questions, rhetorical questions (fake dialogue), non-standard use of ‘we’, hard sell persuasion techniques and ‘making encouraging noises’ can co-occur.” In my view, the features of the lecture genre can be shared by the genre of all teacher-centered environments in which there are no sufficient interactions, discussions, argumentations between the teacher and the students. I can see these features in my past teaching. However, in most cases, I feel that these features emerged spontaneously and unconsciously in my teaching. Even when I was explaining mathematics knowledge to one student rather than to all students in my big-size class, I realize that I would still use these tag questions, rhetorical questions, etc, such features belonging to the lecture genre naturally and unintentionally. So, I think that even in the student-centred learning environment, the same genre will still occur naturally. For example, when I invite students to enter into the communication, regardless of as a teacher or just as a facilitator (in student-centred environment), I will still say “Let’s look at…, Let’s do….” rather than “Let you look at…, or Let you do…”. If we always make explicit use of “we, us, our”, the communication between my students and me must sound weird. In this sense, I’m asking if the use of tag questions, rhetorical questions, the extensive use of the first personal plural pronouns sometimes are unconscious behaviors in a person’s speaking(including monologue and dialogue), and sometimes, if even the hard sell is also unconscious and spontaneous?