Project - Based Learning

The style of teaching at Phoenix Park (PP) certainly has its advantages and disadvantages.  However, it is a style of teaching that appears to lead to better learning for the students and isn’t that what schooling is all about?  The project based learning method has allowed these students to develop a deeper understanding of mathematical concepts.  Michel, Cater and Varela (2009) describe project (problem)-based learning  as  a course that is structured around solving real world problems. 

Comprehension tasks, such as the ones that the students at PP experienced, are accomplished by knowing what procedure to use and why to use it (Doyle, 1983, p. 165) .The students develop a deeper understanding of the methods of mathematics and can apply their knowledge to real life situations.  Doyle (1998) also points out that “[m]emory for information acquired by comprehension is more durable” (p.162).

 In addition the students of PP were more creative with their answers and much more eager to take risks than the students from Amber Hill (AH) (Boaler, 2002).   Isn’t that a great way of preparing these students for the futures?  Wouldn’t all employers want their employees to be creative and innovative?  

The major problem with this form of learning is that the skills students are learning do not match the requirements of the end of school math assessments, in this case the GCSE exam.  As Hosp (2010) emphasized teaching and assessments need to be closely matched.  This may explain why teachers at PP begin to teach using more traditional methods a semester before the GCSE exam begins.  It is very evident then that project-based learning is not fully adequate in preparing students for their final exam but does prepare them for real life math problems.  

References:

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

Doyle, W. (1983). Academic Work. Review of Educational Research, 53(2),

          159-99.  

Hosp, J.L. (2010). Linking Assessment and Instruction: Teacher Preparation and Professional                  Development. TQ Connection.

Michel, N., Cater, J.J., Varela, O. (2009). Active versus passive teaching styles: An empirical study of student learning outcomes. Human Resource Development Quarterly, 20(4), 397-418.

The Influence of Socioeconomic Status of Students of Teaching Practices

We often like to say that we don’t think about the socioeconomic status (SES) of our students any more than we consider their race, religion, or gender.  However, subconsciously and even at times consciously we do consider these factors when planning lessons, activities and assessments.  

Boaler (2002) describes the students at Amber Hill as being mostly from working class families.  She suggests that because of this the teachers have sought a more structured approach to their teaching (p. 28).  She also cites the findings of Anyon (1981) to show that schools in poorer neighbourhoods “discouraged personal assertiveness and intellectual inquisitiveness in students and assigned work that most often involved substantial amounts of rote activity” (p. 35).  This shows a form of prejudice against these students because of their family income and background.  It hardly seems to follow the idea of differentiation, which would take into account the learning styles of these students not how much money their families have.  To group all of these students into one category is not fair, “there is nothing so unequal as treating everyone the same way” (Davis, Sumara & Luce-Kapler, 2008, p. 178). 

I would argue that if students from a lower SES find mathematics concepts harder and are more likely to become a behavioural issue than the more open style of teaching would be a better option. 

Allowing students the choice to complete different activities and to take them to a level of difficulty that better suits their abilities, would give them a feeling of empowerment and provide them with the confidence they need to achieve well in math.  “Recent research shows that self-regulatory processes are teachable and can lead to increases in students’ motivation and achievement” (Zimmerman, 2002, p. 69).  

References:

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

Davis, B., Sumara, D., & Luce-Kapler, R. (2008). Engaging Minds. New York: Routledge. (Original work published 2000).

Zimmerman, B. J. (2002). Becoming a Self-Regulated Learner: An Overview. Theory into Practice, 41(2), 64-70.

When Good Teaching Leads to Bad Results: The Disasters of "Well Taught" Mathematics Courses

Schoenfeld (1988) makes some great points about one of the main problems with the learning of mathematics.  He makes the claim that if the lesson runs very smoothly (i.e. students are behaving, paying attention, doing their work and achieving the outcomes) there can still be major problems with their deep mathematical understandings.  As Boaler (2002) points out, the students of Amber Hill are well behaved and are working well but they are learning in a manner that allows them to understand only the surface of completing repetitive practices.  

As stated by Schoenfeld (1988, p.4) routine exercises do not lead to significant understanding of the subject matter and the students in his study showed to have attained the curriculum outcomes but not to have attained an overall connection of the subject to real life applications.  As Jeffery Wilhelm (1997, p. 16) emphasized in his book “You Gotta BE the Book”, in order for students to be successful, they need to have an interest in what they are learning and the subject must be relatable to their own experiences.  

Students are often led to believe that there is only one correct way of completing a mathematical problem and as Schoenfeld pointed out only the correct steps for constructions were correct and the method counted more than deriving the correct response.  We see this every day in our math classrooms.  Students are frequently taught “tricks” to solve problems without really understanding what they are doing.  For example, multiplying two binomials is often taught using the FOIL method.  Students just memorize the steps First Outside Inside Last without understanding that they are multiplying each term in the first bracket by each term in the second bracket.  This often results in many mistakes especially when integers are involved.  Additionally, students seem to find difficulty in completing word problems with fractions or decimals.  The questions may be written the exact same way as if there are whole numbers but once they see a fraction they don’t understand what operation to use or how to complete the question at all.  It shows that Schoenfeld is right, students memorize a method without a deep understanding of what is truly going on!

References:

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

Schoenfeld, A. H. (1988).  When good teaching leads to bad results:  The disasters of "well taught" mathematics courses.  Educational Psychologist, 23(2).

Wilhelm, J. (1997). You Gotta BE the Book: Teaching Engaged and Reflective Reading with            Adolescents.  New York: Teachers College Press.

Introduction and Chapter 2

Boaler uses these two chapters to introduce the investigation, the UK school system and the two schools that are being studied.  Throughout the rest of the book she will look at her findings and give direct accounts from students and teachers.  Boaler (2002) states that these accounts “give detailed insights into the ways that mathematics teaching affects mathematics learning” (p. 1).  There is no doubt that the style of teaching used in the classroom makes a difference in how well the students learn.  With mathematics learning and achievement becoming an increasing concern with parents, students, teachers and school districts, Boaler`s study could prove to be very informative for teachers of mathematics.

I am very interested to see what the resulting outcome is for the varying teaching styles at both schools.  Will the results prove to be any different in her investigation since her preliminary results showed no mathematics performance difference between the two schools’ NFER results.  Will she find any other influences on mathematics attainment based on other factors such as gender, ethnicity, class ability grouping, etc.?