"The Real World As We Have Seen It": Latino/a Parents' Voices on Teaching Mathematics for Social Justice.

Author: Eric Gutstein

Source: Mathematical Thinking and Learning , 8.3 (2006):331-358.

  Gutstein, the author, explores and clarifies the opinions toward to mathematics programs for social justice from the view of Latino/a parents. He implemented four “real world” projects which invite the students to use mathematics and think/analyze the real problems in the world such as product cost of weapons, poverty and wealth, and discrimination of mortgage. His school district holds the high proportion of Latino/s and most of the parents are low income and their mother tongue is Spanish. In this article, he conducted the interviews with 10 Latino/s parents and summarized their voices.

  In short, the Latino/a parents want their children to understand, through education (including mathematics), about the discrimination, injustice and disadvantage which they faced and experienced in the society. Furthermore, the parents believe their children need to know that people who belong to the marginalized community have to defend them by themselves in the above society. In terms of mathematics, the parents see “mathematics as an integrated part of life” (p.352) and have a flexible idea to understand the role of mathematics in life such as different interest rates among races. The purpose of education for the Latino/a students, their parents think, should be preparation for the above injustice world while the parents agree with the conventional purpose of education. Finally, the parents advocate the educational programs that the author provided to their children, and they do not believe those programs are propagandized.

  As I see the voices of the Latino/a parents in this article, their voices seem to be premised on their marginalization. They emphasis on the way how marginalized community members survive in the suppressed society rather they try to solve this inequity circumstance. I suppose, to reduce this problem, the majority groups should learn social justice from the perspective of the minority groups to change the unbalanced society.

  Although the voices involve little mathematics contents in this article, his programs are very interesting to me. These programs enable all students, even who do not like mathematics or are not good at mathematics, to participate the mathematical activities. Therefore, they can feel mathematics as a part of life, can recover their confidence toward to mathematics, and can find the own motivation to study mathematics. As I mentioned above, participation of dominant groups is necessary to reduce the problem of inequity, thus the participants in those programs should be mixture of all groups. In this case, I am curious about the responses to the program for social justice that both majority groups and minority groups have, and balance between their power: majority vs minority.

Question:

Considering several reasons: increasing teachers’ burden, national curriculum, limitation of time etc., do you think it is possible to involve social justice contents in regular mathematics class realistically?  How can we include them in mathematics class?

Hedges in Mathematics Talk: Linguistic Pointers to Uncertainty

Author: Tim Rowland

Source: Educational Studies in Mathematics, 29(4), 327-353, 1995.

  The author, Tim Rowland, conducted the interviews with 10-12 years old children to linguistically analyze their uncertainty (hedges) in their predictions, generalizations, and explanations within the mathematical discourses. He utilizes the hedge model of Prince et al. (See the image below), and describes several cases of the hedges by both the students and the teacher (the author) that were extracted from the interviews.

(Rowland,1995, p.337)

 

• Ex)
• Plausibility Shield: I think…, maybe, probably
• Attribution Shield: According to N…
• Rounders: about, around, approximately
• Adaptor: a little bit, somewhat, fairly

  In the interview, the participated children often use Rounders and Plausibility Shields to express their proposition and to move their understanding from uncertainty to certainty. He addresses many children use the hedges to protect from being “wrong” since school-culture leads students to believe mathematics is evaluated by only binary: right or wrong. However, he suggests that using of the hedges in students’ conversations can inform their anxiety, fear, or lack of confidence for their understanding. Therefore, it makes teacher to be able to support their development from vagueness to conviction.

  I agree with the idea that school-culture forces students to provide high quality (accurate) opinions and instills fear in them to be “wrong” in mathematics classes, and agree with that the words and phrases of the hedges could help teachers to know their students’ understandings toward to mathematics contents. It might be difficult for teachers to know whether their students certainly understand what they have learned by tests which only have very small spaces to fill students’ explanations, and to know what they are exactly thinking. The interactions in the classroom, regardless of among students or between teacher and student, hold a lot of information about students’ attainments and idea, thus teachers need to be sensitive for their conversations in addition to their answers.

  In this article, Rowland mentions the zone between students’ proposition and conviction. If I could talk to him, I would ask him if there are any zones between nothing and proposition. After they confront prediction, generalization, and explanation in mathematics class, I believe, students might have something or nothing in their mind before they reach to uncertainly phase. In this case, I wonder if they use the hedges as well or use other words and phrases in their conversations.

  Something that was not included in this paper but actually I am interested, is about students who learn mathematics in additional language. Because of their language limitation, their usage of the hedges would be different from other students and other findings might be observed.

Questions:

When you hear prediction/explanation/generalization/ from your students in mathematical discourse, what point do you watch? i.e. facial expressions, voices, other student’s reactions etc.

 

Problem Posing in Mathematics Education

In this article, Brown and Walter describe five sensitivities that should be embedded to mathematics experiences when teachers introduce problem posing, focusing on pedagogical perspective.

1: An irresistible solving drive:

According to the authors, in some cases, students try to find out answers or solutions that are given without much thought. But it is important for students to think and understand what a problem is, what alternative mathematical entities are, what mathematical view is as problem-solving when they pose their own problems.

2: Problems and their educational potential

The authors question what we can do for a given problem other than coming up with the solutions. They believe students can create the new problems into the situation, and this variation/creativity enriches to understand original problem and enable to pose other possible educational problems aside from problem-solving.

3: The interconnectedness of posing and solving

The authors claim that there might be unexpected logical connections in which problem-posing and problem-solving.

4: Coming up with problems

The authors categorize problem-posing into two types: accepting and challenging. For challenging the given, they suggest “What if not?” strategy to be heuristics problems as following: (p.23)

1. Make a selection
2. Notice the attributes of the object
3. Vary the attributes
4. Ask a question about the new form
5. Analyse the questions

5: The social context of learning

The authors address importance of social context of learning in problem posing environments which are relationship of the individual and the group. They show the readers several ways to create problems for group interaction such as the case of using editorial boards.

 

Response:

  I agree with the authors’ idea of the sensitivities to problem posing in mathematics. As per my teaching experience for immigrant students in Japan, they tend to answer the mathematics problems by utilizing their assumption from parts of the sentence (some words), pictures and figures within the question because they have little Japanese language proficiency to understand the given problems. However, although not always, they surprisingly correctly answered those problems. This fact supports the idea in the first sensitivity. Therefore, problems in textbooks and drills in mathematics have common features across different countries, and I suppose some students who are familiar with it might be able to answer the questions in different languages.

  However, I have never seen the cases that the above immigrant students challenge problem posing. In addition to their limitation of language, there are no contents intend to problem posing in mathematics textbooks and drills and are a lot of the repeated problems instead. I suppose there might be no developments about problem posing in terms of textbooks and drills, thus the mathematics class used those problems might have no chance of heuristic learning for the students including non-immigrant students.

Questions:

Do you think the mathematics textbooks and drills are containing enough contents for the problem posing process? If so, has it been changed over the past years?

My Topic for Assignment

Mathematics learning for English Language Learners (ELLs) focusing on their obstacles of studying in additional language

I am thinking to explore how ELLs are(were) learning mathematics in English or how native teachers teach(taught) mathematics to ELLs. It might be not easy for them to learn mathematics in their additional language, especially for word problems and their participation in the class. Because ELLs consist of variety of people, I will focus on the people with some specific ethnic background such as Asian or Hispanic. I also would like to emphasize how their learning/teaching shifted and developed by the times.