W1_Reading

Here is my week one reading post.

Article summary:

Motivation in elementary mathematics

In this article, we are considering how computers may be enough cause for motivation on both the part of teachers and students to improve practice and achievement in an elementary mathematics classroom.

Some of the barriers to integrating technology are described.  Teachers may not use technology in the classroom because they simply don't know how, and aren't willing to learn.  Teachers who might integrate technology may not do so due to lack of appropriate equipment and access to technical and administrative support.

Many benefits are described for both teachers and students, when technology is integrated into the classroom.  For teachers, student engagement and achievement generally increase with technology integration.  This is demonstrated through improved time on task and improved learning.  Students can benefit from technology use through tutorial programs.  These programs help students gain practice in skills while allowing them to work at their own pace. Their confidence builds through the use of learning games.  They are learning while "at play".

Suggested uses of technology include Integrated Learning Systems (ILS).  An ILS can track and report student progress. Teachers are encouraged to use technology because when they do, students perceive themselves as being more successful.

The authors conclude that teachers need to develop and maintain their computer literacy skills.  Meaningful technology use in the classroom is still a far reach for many educators and their mathematics classrooms.

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Article summary:

“Are you really challenging your children to think during their math lessons?”

A math program, Primary Cognitive Acceleration in Mathematics Education (PCAME), is being used to improve opportunities for discussion and collaboration in elementary mathematics classes.  A national report in London, England found that “teaching is still unsatisfactory in one in eight lessons” in spite of national literacy and numeracy initiatives (Bell, 2003).  The shortcomings are said to be due to teachers’ lack of subject area knowledge, and students not having adequate opportunities to discuss their learning amongst themselves.

The approach of the PCAME program is to provide training to teachers in which they experience collaborative environments themselves.  They work to develop curriculum, and reflect on their classroom experiences.  The program is based on interventions drawn from Piaget and Vygotsky.  The goal is to have children thinking about mathematics in challenging ways, with a focus on effective questioning and making cognitive leaps.

Lessons are presented as “Thinking Maths” once a month.  The lessons are sequenced to allow for integration of math topics within a rising level of cognitive demand.  They are presented in two episodes: first to motivate and engage students, second to handle higher order concepts and reasoning.  The lesson investigations are meant to provoke cognitive conflict.  Students work collaboratively to strategize and discover solutions.

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Article summary:

Using student interviews to guide classroom instruction: An action research project

Teachers at Jefferson Elementary in Jefferson, Oregon investigate how student interviews can influence the way that teachers present mathematics in the classroom.  Teachers were struggling with implementing problem solving, and trying to utilize more effective questioning techniques in their classrooms.  They lacked sufficient knowledge about their students’ mathematical understanding.

Two questions are developed to research:

Do student interviews provide teachers with a more detailed, accurate, and complete picture of children’s mathematical understanding?

Does this knowledge help teachers to improve the way that they teach mathematics? (Buschman, 2001)

Interviews were conducted in the Fall and Spring.  Qualitative data collection techniques were utilized.  School-wide scheduling changes were required in order to equitably collect interview data and provide educational programming to students. 

The student interviews directly supported two instructional approaches used by Jefferson teachers.  One approach is cognitively guided instruction.  This model builds on a child’s prior experience, and new knowledge is linked to something the child already knows.  A second approach is based on the theory of constructivism.  The interviews provided teachers with opportunities to observe student’s attempts at solving problems in ways that made sense to the student.

Teachers reported that their focus during instruction became more student centered.  They worked to meet individual student needs.  Teachers felt that they were better able to pose questions to aid struggling students or to challenge students to further engage them in the problem solving process.

Teachers found that students benefitted from sharing multiple ways of solving problems, and being able to work cooperatively with others.  Students gained facility in creating their own strategies for solving problems.

Interviews can go beyond traditional forms of assessment to provide teachers with greater insights “into how students think and reason, how they demonstrate their creative abilities and talents, and how they apply and use problem solving strategies in mathematics.” (Buschman, 2001)

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Article Summary:

A Four-Point Instructional Model

In this article, an instructional model is presented that promotes mathematical thinking.  Mathematical thinking is defined in what mathematicians do.  “Mathematicians observe phenomena, look for patterns, formulate questions about what they observe, and try to answer those questions.” (Manouchehri, 2001)

Students in most classrooms are not asked to make observations and pose questions.  The model proposed here focuses on problem posing.  Students experience math lessons in four phases: 1) large-group problem posing, 2) small-group problem solving, 3) large-group discussion about findings and discoveries, and 4) extended assignments and projects.  Using this model, a teacher can help students make connections socially and mathematically. 

The teacher’s role in this model is to facilitate group interactions.  The teacher must model appropriate questioning techniques and problem solving strategies.  The teacher facilitates student discussion and interaction and works to clarify points and further engage students in higher order thinking. 

Peer collaboration allows social interaction and active engagement with the math topics.  Students learn new thinking strategies and varied approaches from one another.

“Teachers foster mathematical thinking and discourse that is in line with the work of mathematicians.” (Manouchehri, 2001)

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References

Buschman, L. (2001). Using student interviews to guide classroom instruction: an action research project. Teaching Children Mathematics, 8(4), 222-7. Retrieved from Science Full Text Select database

Coombes, P. (2004). “Are you really challenging your children to think during their maths lessons?”. Mathematics in School, 33(3), 12-13. Retrieved from Science Full Text Select database

Guha, S., & Leonard, J. (2002). Motivation in elementary mathematics: how students and teachers benefit from computers. TechTrends, 46(1), 40-3. doi: 10.1007/BF02772036

Manouchehri, A. (2001). A four-point instructional model. Teaching Children Mathematics, 8(3), 180-6. Retrieved from Science Full Text Select database