Parent engagement in algebra learning and mathematics understanding

Mathematics Teaching

Learners Studying Basic Mathematics To Enable Helping Their Children With Their Education

The work of Jackson and Ginsburg (2008) reports on a series of algebra classes involving a group of African-American mother and elementary-aged children, who are low income and who "had limited and negative formal experiences with algebra." (p. 10) The women in the study who arrived to the algebra classes are reported to have had "well-informed view of what algebra was -- a disconnected body of knowledge that they did not understand -- and corresponding views of who could 'do' algebra." (Jackson and Ginsburg, 2008, p. 11) The study resulted in the women's views of who could 'do' algebra being changed "through genuine, intellectual inquiry into the mathematics of algebra." (Jackson and Ginsburg, 2008, p. 11) It is reported that questioning "is recognized as a critical instructional tool in the teaching of mathematics for understanding." (Jackson and Ginsburg, 2008, p. 18) Solomon, Lawson and Croft (2008) relate that while many learners "may be successful in mathematics" that they "nevertheless see themselves as existing only on the margins of the practice, or as lacking stability in it -- in this sense, they have what is called a fragile identity." (p. 1) Swan reports that research has shown that "many students view mathematics as a series of unrelated procedures and techniques that have to be committed to memory. Instead, we want them to engage in discussing and explaining ideas, challenging and teaching one another, creating and solving each other's questions and working collaboratively to share methods and results." (2006, p.162) Reported as the second aim is the development of more "challenging, connected, collaborative orientations towards their teaching." (Swan, p. 162) Jackson and Ginsberg reports that the women in the study in their role as parents were striving to "support their children's mathematics learning" and that the women held the view that the "algebra they explored grew out of their children's assignments and in turn would feed back into the children's work as they felt better able to support that work." (p. 26) As the women persisted with their learning of algebra the subject is reported to have become "intellectually challenging, accessible and pleasurable." (2008, p. 26) Two implications are stated from the research: (1) the role of the elementary mathematics curriculum was central to the academic and social accomplishments of the algebra sessions; (2) the importance of framing parents as learners. (Jackson and Ginsburg, 2008, p. 26-27) Wiley (2008) reports on Latina mother's participation in a community mathematization project and not only this but also participating as curriculum designers in a collaborative project with university researchers. It is reported that "the crux of this study lies in the process through which the mothers moved from one level of mathematical understanding to a more advanced level that could be communicated mathematically." (Wiley, 2008, p. 35) There were reported to be three critical components that "facilitated this process to varying degrees" including: (1) social networks; (2) agency; and (3) mathematical sense-making. (Wiley, 2008, p. 35) It is reported that the attitudes of parents and perceptions about mathematics education are reported "in the context of a community mathematics program designed to provide an opportunity for parents and children to learn together. Within the venue of this program, Mexican immigrant parents' voices revealed the importance of their own experiences as learners and how these experiences shape their perceptions of mathematics education in the U.S." (Allexsaht-Snider and Marshall, 2008, p. 9) It is reported that the attitudes of parents are revealing of the types of knowledge in mathematical practices which are valued and how the value of thee practices is differed across contexts. Specifically stated is "for these parents, whose formal mathematics experiences in Mexico valued memorization and the application of algorithms, conversations with researchers showed the importance of mutual respect and a shared understanding in building bridges between formal and informal networks of support." (Allexsaht-Snider and Marshall, 2008, p. 9)

III. CRITIQUE OF TEACHING APPROACHES

Ernest reports that a recent position "in the philosophy of mathematics is fallibilism which emphasizes the practice of mathematics and the human side of mathematics." (1991, p. 1) Fallibilism is reported to view mathematics as "the outcome of social processes." (Ernest, 1991, p. 1) The absolutist view of mathematics is one that is "an objective, absolute, certain and incorrigible body of knowledge, which rests on the firm foundations of deductive logic." (Ernest, 1991, p.1) According to Ernest the practice of teaching mathematics is dependent on certain elements including the "mental contents or schemas" of the teacher as well as the "social context of the teaching situation" and the "teacher's level of thought processes and reflection." (p. 1) The teacher as an instructor has the intended outcome for students of "skills mastery with correct performance." (Ernest, 1991. p. 1) Whereas the role of the teacher as an explainer has the intended outcome of "conceptual understanding with unified knowledge." (Ernest,, p. 1) Finally, the teacher as a facilitator has the intended outcome of "confident problem posing and solving." (Ernest, 1991, p. 1) Swan (2006) speaks of the traditional method of teaching mathematics and states that when it is reversed it is "builds on the knowledge that students already have" and additionally "exposes and discusses common misconceptions" and "uses higher-order questions." (p. 169) Swan additionally reports that traditionally teaching utilizes small group work and encourages "reasoning rather than 'answer getting' and uses rich collaborative tasks [while creating] connections between topics [and] uses technology in appropriate ways." (Swan, 2006, p. 169)