chapter 10: Ability Grouping

The students at Amber Hill and Phoenix Park are taught using two very different classroom make ups.  Amber Hill students are placed in classes that are set by ability and Phoenix Park students are in classes that are mixed.  There were many complaints from students at Amber Hill but the Phoenix park students made little or no comment about their groupings.  The sets in the UK limit the grade that can be achieved by students in their GCSEs, so a student in bottom set will write a different exam than someone in top set and the maximum grade they can attain is a D (which is not recognized as a pass for university entry).  As Boaler (2002) points out “many of the students suggested that the limits placed on their attainment had caused them to give up on mathematics” (p. 165). 

“[I]f students are not exposed to high-level content, they cannot learn it” (p. 174).  Boaler (2002) makes this comment in reference to the unfairness of student from Amber Hill.  However, there is an entirely different picture at Phoenix Park where “the students were given activities to work on alongside the higher attaining students, and they were constantly encouraged to think about mathematics and learn” (p. 168).  Students at Phoenix Park were given equal opportunities to improve their math work if they so desired, despite previous results, abilities, and behaviour.

Boaler (2002) suggests through this chapter that the ability groups were determined by other factors than ability.  She discussed the fact that many students in bottom sets felt that they were placed there based on their behaviour.  In addition, she claims that social class determines the success of the students in set classes whereas it doesn’t appear to be a factor for success in mixed ability groups.  In fact, in this case there were more students from working class families that performed above their expectations in comparison to middle class students (p. 171-172).  Boaler makes the bold statement that the sorting of students by ability “ensures that students are never exposed to high-level content, particularly in mathematics” (p. 174).   Since working class students tend to perform worse in ability set groups, it can be concluded that this type of grouping is disadvantaging these students because of their social class.  This is an example of disempowerment of the disadvantaged and a direct replication of society (Davis, Sumara and Luce-Kapler, 2008).

Ability grouping also doesn’t promote an inclusive learning environment.  Inclusion has a basic premise that has all students receive full access to an education and the equality of rights.  This may require adjustments to be made to teaching, programs and even physical environments (Savvidou, 2011).  The government of Newfoundland and Labrador promotes “the basic right of all students to attend their neighbourhood schools with their peers, and receive appropriate and quality programming in inclusive school environments” (2011). 

References:

Boaler, J.  (2002). Experiencing School Mathematics.  New York: Routledge.

 Davis, B., Sumara, D., & Luce-Kapler, R. (2008). Engaging Minds. New York: Routledge. 

Savvidou, C. (2011). Exploring teachers’ narratives of inclusive practice in higher education. Teacher Development, 15(1), 53-67.

Learning Styles

Students always discuss teachers and describe their favourite ones as the teachers that encouraged their learning the best, teachers that were helpful and teachers that were fun.  Perhaps, it is not so much the teachers themselves that make them great as it is their teaching style and the match to the learning style of their students.  Boaler (2002) states that “different pedagogies are not just vehicles for more or less knowledge, they shape the nature of the knowledge produced...” (p. 132).  In other words students may be able to learn more and grasp a deeper understanding if the teaching style is effective. 

 

The Amber Hill students were very clear in their displeasure of the way they were being taught, especially the girls.  They enjoyed classes that were more collaborative, open and non-competitive.  When faced with everyday mathematics problems the Amber Hill students would “abandon the mathematics they had learned in school and were forces to rely on their own invented methods. (Boaler, 2002, p. 130).  Whereas, the Phoenix Park students found that their “project-based work was useful in new and different situations” (p. 125).  

Burton (1999) discusses research and classroom teaching with a number of mathematicians and finds that the competitive style is very predominant in most mathematics classrooms and that researchers have spoken of the difficulties in “persuading teachers that a collaborative style is appropriate in classrooms” (p. 132).  In Burton’s research, she found there to be differences in learning styles of lecturers.  A female lecturer stated that, “most of the work that I do is collaborative” while a male lecturer claims that “mathematicians as a whole don’t seem to work together” he also claimed to prefer to work alone and that he doesn’t like working with others (Burton, 1999, p. 129).  This is also mirrored by Boaler’s discoveries of the top set students from Amber Hill.  The females preferred to work collaboratively with other students because it gave them “access to a depth of understanding that textbook work denied them” (Boaler, 2002, p. 142).  However, the boys “disliked working in groups because they felt that it slowed them down” (Boaler, 2002, p. 143).

References:

Boaler, J.  (2002). Experiencing School Mathematics.  New York: Routledge.

Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know      mathematics? Educational Studies in Mathematics, 37, 121–143.

Chapter 7: Real Life Appliation and Skills Retention

One of the main differences noted by Boaler(2002) in terms of the mathematics learning of the students from Amber Hill and Phoenix Park  is the transfer of knowledge from the school setting to real life situations.  The students from Amber Hill “indicated that they saw little use for the mathematics they learned in school in out-of-school situations” (Boaler, 2002, p. 120).  Whereas the Phoenix Park students “did not regard the mathematics they learned in school as inherently different from the mathematics of the real world” (Boaler, 2002, p. 118).  This would lead us to believe that the project based approach used by the Phoenix Park teachers allows math to become more relevant for the students in real world applications.

A study on problem-based learning by Miller (2004) also yielded a similar result.  Her students reported a new found confidence in their abilities to be able to solve a problem independently after completing the projects provided by the teacher.  In addition, she found that students were able to apply solutions to different problems that could occur in the workplace (Miller, 2004, p. 586).

Another conclusion that Boaler (2002) found from her investigation was the length of time that the students retained their mathematical skills and knowledge.  The students at Amber Hill were reported to have forgotten their procedures over a short period of time.  Whereas, Phoenix Park students were reported to “answer questions correctly 6 months after their lessons” (Boaler, 2002, p.114).  Without a doubt this is due to the method of learning that these students experienced.  Cherry (2011) reported that “by establishing relationships between new ideas and previously existing memories, you can dramatically increase the likelihood of recalling the recently learned information.”  When school problems are related to students’ lives they are more likely to remember new techniques they have learned.  Miller (2004) also states that problem-based learning achieves one of Dewey’s outcomes; the student is able to apply the knowledge long after it has been learned for the class. 

References:

Boaler, J.  (2002). Experiencing School Mathematics.  New York: Routledge.

Cherry, K. (2011). Top 10 Memory Improvement Tips: Improve Your Memory With These Great Tips. Retrieved, Nov. 7, 2011 from http://psychology.about.com/od/cognitivepsychology/tp/memory_tips.htm

Miller, J. S. (2004). Problem-Based Learning in Organizational Behavior Class: Solving Students' Real Problems, Journal of Management Education, 28, 578-590.

Digging into student behaviour and teacher strictness and academic performance

After researching into the effects of student  behaviour on academic performance, I was faced with a lot of evidence supporting the typical expected results that the better the behaviour of a student in the classroom the better they perform academically.  Zettler (2011) discusses the factor of self-control  on academic performance and makes the claim that “high self-control indicates better students’ performance” (p. 121). In a study conducted by Elias and Leverett (2011) the school district focused on improving moral and attitudes of students.  They found that by restoring morale and moving students towards positive behaviour, academic performance was improved (p. 28).  This is in direct conflict with Boaler’s (2002) claim that student behaviour and motivation does not make their academic successes any different than other students from Phoenix Park.

However, research backs up Boaler’s (2002) statements about the strictness of teachers.  She claims that the teacher that gave the students more freedom actually achieved the highest results on the GCSE exams that the other stricter teachers’ classes.  Students that have more positive and supportive relationships from their teachers are shown to have higher levels of academic achievement than those students that are faced with conflicting relationships with their teachers (Rimm-Kaufman, 2011).  This may explain why the students in the stricter teachers’ classes did not perform as well.

References:

Boaler, J.  (2002). Experiencing School Mathematics.  New York: Routledge.

Elias, M., Leverett, L.  (2011). Consultation to urban schools for improvements in academics and     behavior: No alibis. No excuses. No exceptions. Journal of Educational and Psychological Consultation, 21(1), 28-45.

Rimm-Kaufman, S. (2011). Improving students' relationships with teachers to provide essential supports for learning. American Psychological Association. Retrieved from http://www.apa.org/education/k12/relationships.aspx 

Zettler, I. (2011). Self-control and academic performance: Two field studies on university citizenship behavior and counterproductive academic behaviour. Learning and Individual Differences.  21, 119–123.

Does Student Behaviour and Teacher Discipline Style Affect Learning?

While reading through chapter 6, one of the most alarming finds by Boaler for me was the fact that the badly behaved and unmotivated students did not under achieve on their examination results in comparison to other students at Phoenix Park.  Does this mean that the more free learning style actually works for these students? Or does it mean that these students may still be learning despite acting out in lessons?  

In addition, Boaler (2002) suggests that a stricter teacher does not yield better results than a teacher that gives students a lot more freedom (p.103).  This also seems to conflict with popular belief of what should work better in a group setting for ample learning.  

Both of these claims have me wondering how much of an impact teachers actually have on the learning of students or is the style of learning more important?  I am so intrigued that I plan to do some research on both topics!