This document discusses using locally available experts in mathematics to promote inquiry-based learning. It defines experts as not just mathematicians, but also teachers, teaching assistants, advanced peers, and parents who are trained to ask thoughtful questions and guide student exploration. The experts model problem-solving strategies and coach students through the process, similar to an apprenticeship. This sociocultural approach encourages social interaction and guided participation to establish important mathematical traditions. While traditional instruction emphasizes memorization, research shows reform-based teaching that incorporates investigation, communication, and collaboration is more effective at developing students' mathematical understanding.

1. BADHIRIYA B.Ed
TRAINING COLLEGE
VELICHIKKALA, KOLLAM.
ONLINE ASSIGNMENT
Name of the trainee : SAMBHU RAJ P .R
Year : 2014-2015
Reg.No :
HUMAN RESOURCES LOCALLY AVAILABLE
EXPERTS IN MATHEMATICS
Checked by
jisha p vahab

2. This work is part of our B.Ed curriculum. I have select topic for online
assignment was “human resources locally available experts in
mathematics”

3. INTRODUCTION
In mathematics, studies have shown that instruction, especially at the high school
level, remains overwhelmingly teacher-centered, with greater emphasis placed on lecturing than
on helping students to think critically and apply their knowledge to real-world situations (Cobb,
Wood, Yackel, & McNeal, 1992). According to Stodolsky and Grossman most high school
mathematics teachers see mathematics as a rigid and fixed body of knowledge, and think that
their responsibility is to transmit this knowledge to their students (1995, as cited in Staples, 2007,
p. 165).Cuban (1984)delineated the features of such teacher-centered instruction as favoring
teacher-talk over student-talk and include situations in which the teacher directs instruction to the
whole class rather than working with small groups of students or with individual students. In
contrast to this approach, the National Council of Teachers of Mathematics (NCTM) advocates
for the development of an inquiry-based mathematics tradition. In an inquiry-based environment,
learning is viewed as an active, constructive activity in which students are encouraged to explore,
develop conjectures, and problem solves. Students are also encouraged to discuss and
communicate their ideas and results, often within small, cooperative groups as well as with their
teachers. NCTM authenticates the value of inquiry-based mathematics instruction by calling for
efforts aimed at creating collaborative and student-centered environments, where students have
opportunities to reason and construct their understanding as part of a community of learners
(NCTM, 1989, 1991, 2000). Mathematics instruction should provide students opportunities to
engage in mathematical inquiry and meaning making through discourse, and teachers should
encourage this process by remaining flexible and responsive to students 'response and
feedback(NCTM, 2000)

4. HUMAN RESOURCES– locally available experts in
mathematics
Particularly relevant to mathematics education is the notion that “learning is the
initiation into a social tradition [of mathematical inquiry, mathematical discovery, mathematical
argument, and so on]” (Solomon, 1989, p. 150).With enculturation as the emphasis, a teacher
who employs the sociocultural approach to teach mathematics would design a learning task
through which students can interact with experts. Simply put, it is a process of guided
participation and interaction of learning by solving problems just beyond a student's current
capability with the help of a more expert other via scaffolding. Experts do not necessarily imply
mathematicians. Teachers are most often the experts in real classrooms, and continuing
professional development strengthens their expertise in mathematics. In addition, teaching
assistants, advanced peers, and even parents can all be trained to become mathematics experts in
real classrooms. For the theorem that the sum of the three inner angles of a triangle is 180
degrees, experts would ask well-thought questions around the main idea of creating equal angles
in different places so that the three angles can be pulled together to examine the sum. These
questions prepare students for the demonstration of experts who would show students how to
move one angle (both physically and mathematically), would have students comment on the
move, and would ask students to move the other angles following a similar strategy. Observing
students closely, experts would alert students of wrong moves, would point out reasons for
wrong moves, and would demonstrate correct moves repeatedly. This modeling and coaching
process between experts and students, often considered apprenticeship in nature, is the very
foundation of the sociocultural approach that requires social participation and interaction of the
whole classroom community. Finally, experts would evaluate with students on different
strategies of moving angles and would reason with them on the best way to move angles. The
whole interaction between experts and students would end up with the establishment (or
enculturation) of an important mathematical tradition (or practice) on the use of auxiliary lines
for geometric proof. As a result, experts would have trained students on geometric proof in a way
very similar to how masters would have trained apprentices in, say, furniture building.

5. Conclusion
Although in recent years there has been significant objection to the type of reform-
based mathematics proposed by the NCTM, ample research has shown that the repetition and
memorization emphasized by traditional mathematical teaching practices, superficially addresses
these concerns (Manouchehri, 2007). In this study, we examined the pedagogical strategies used
by the IC teacher to foster mathematical discourse and promote in students the use of
mathematics language to communicate their thinking. The four teaching strategies utilized in this
study represent the teacher’s role during the discursive process (first and second strategy), and
the process by which the student’s ability to implement these discursive practices developed over
time (third and fourth strategy). The findings of the study suggest that students’ mathematical
dispositions can be transformed over time by a teacher’s pedagogical practices. This process of
transformation may not be perceived as linear and sequential. In addition, not all students would
accept this pedagogy as viable and useful for them. Some may extremely resist this change.
However as noted by Sfard (2003), there is substantial evidence to show that instruction focused
on meaning that emphasizes investigation, conjectures, communication and collaborative
conclusion, is more effective than those that try to circumvent it (as cited in Sanchez, 2006).This
research recommends that high school mathematics teachers adopt some of the more recent
reform-based instructional strategies that have been underutilized in these classrooms
REFERENCES
1. Human resources – Manmohan joshiy
2. Bae j.s (2004) paper presented of 10th international congress on mathematics education,
Copenhagen
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