analysis of a teacher education project “unpacking mathematical practice’ through the lens of a...

Running head: Myths in the theory of cultural relevant pedagogy 1

Analysis of a Teacher Education Project “unpacking mathematical practice’ through the Lens

of a Recent Development in the Culturally Responsive Teaching Literature

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Abstract

This paper presents an analysis of an exemplary teaching approach of pre-service

elementary mathematics teachers -‘unpacking mathematical practice’ through the lens of a

recent discourse in culturally relevant pedagogy literature called ‘teaching for vision’. The

author starts with providing a brief historical account of the pro and against cultural relevant

pedagogy literature with due emphasis to recent developments in the literature that changes the

traditional discourse into a more productive and workable framework. Unlike the traditional

approaches of the culturally relevant pedagogy literature that advocates for particular kinds of

pedagogies for ‘Others’ because they are ‘Different’; this framework attests that ‘best

practices’ in the teaching and learning fields like Mathematics and sciences can be used in any

school setting for any group of students as long as lessons are organized around meaningful

practices. ‘Unpacking mathematical practice’ was one of such practices used in mathematics

teacher education program at University of California, Los Angeles.

Background

Concerns about low academic performance of students from low-socio economic

background in urban schools mainly in mathematics and sciences has a long history, and it

persists as perennial problem in education (Ladson-Billings, 1995; Lankford et al., 2002). This

issue has been at the centerpiece of political, public and academic discourse for long time.

http://gallery.carnegiefoundation.org/collections/quest/collections/sites/franke_megan/


Researchers have also approached the problem from different perspectives and identified various

factors responsible for the academic plight of urban schools.

Some researchers argued that the problem is one of the manifestations of the existing

social-structural inequalities within the American society in which urban schools are victims of

discriminatory educational philosophies, policies, and practices (Aguirre & Turner, 2004; Feagin

& Feagin, 2003; Skrla & Scheurich, 2001). For example, in the year ‘2007–08, about 25 percent

of secondary mathematics teachers who taught in schools with at least half Black enrollment

had neither a certification nor a college major in mathematics, compared to 8 percent of

secondary mathematics teachers who taught in schools with at least half White

enrollment’ (Aud, Fox & KewalRamani, 2010). In addition, it is also documented that these

schools that serve historically marginalized groups of students receive fewer resources. For

example, at the national level, the discrepancy in spending per pupil in the most rich and high

poverty schools was for example $27, 240.00 for a class of 30 students and the percentage of

teachers without adequate credentials in science was 5 per cent in rich schools and 16 percent in

high-poverty schools (National Center for Educational Statistics, 2009). This chronic problem of

imbalance in resource allocation is more exacerbated since children who are attending the high-

poverty schools are also coming from low socio-economic status. For example, according to the

2007 National census report, the percentage of racial groups living in poverty is 8% in European

American, 10% for Asian Americans, 20% for Hispanic Americans, and 24% for African

Americans (U.S. Bureau of the Census, 2007).

Another discourse, on the other hand, takes the issue of low performance of students in

the urban school attributable to cultural mismatch, cultural illiteracy & lack of culturally

responsive practices in schools (Lewis W., et al., 2008). In response to this assumption, one


popularly known pedagogical approach that often cited as potential panacea to the problem is

Cultural Relevant Pedagogy (CRP).

In the literature, a number of names has been used interchangeably with little semantic

differences such as cultural responsive teaching (Gay, 2000), cultural adaptive teaching (Nicole

K. Grimes, 2010), cultural congruent teaching (Gay, 2002) to mention the few. But they all

attune to the notion of the ways that cultural dispositions, values, and traditions can be adopted in

the classroom and positively affect the educational experiences of students of color (Hyland,

2009).

To this effect, advocates of CRP argue that teachers of students of color must not only

be able to help these students achieve academically but also be able to incorporate and respect

cultural practices and values in their instruction, and be able to understand and critique the

oppressive relationship between the mainstream culture and the students’ culture and eventually

help students to be conscious of this relationship themselves (Beauboeuf-Lafontant, 1999). With

these premises, CRP since the 1990s has been promoted by scholars and practitioners alike as an

effective pedagogical approach to support the education of historically disadvantaged students

and students with diversified cultural backgrounds (Gay, 2002).

The impact of CRP around its major tenet areas such as increasing academic

achievement of students (Ladson Billings, 1995), heightening students’ socio-political awareness

(Ladson Billings, 1995; Gutstein, 2003), and helping students think critically about how social

injustices affected their lives (Ladson Billings, 1995; Esposito and Swain, 2009) are well

documented in the literature.

Despite its popularity, however, there are only few studies showing its positive effect

in practice. A meta-analysis of 45 classroom-based research studies from 1995 to 2008 reveals


that less than one third of the classroom teachers in the studies that they reviewed utilized

culturally relevant pedagogy as a way to promote academic success, cultural competence, and

sociopolitical consciousness which are the three pillars of CRP envisioned by Ladson Billings

and her colleagues (Morrison, Robbins, and Rose, 2008).

Moreover, Young (2010) documented that a number of studies have discussed the

difficulties that preservice and in-service teachers have in implementing culturally relevant

pedagogy in their classroom teaching. Young’s own research findings revealed that there were

“deep structural issues related to teachers’ cultural bias, the nature of racism in school settings,

and the lack of support” to implement the theory of CRP in practice (pp. 248). That means CRP

has been more at the level of discourse than the evidences available to support it. For example,

Villegas (1988) argued that promotion and acceptance of cultural difference alone perpetuates

the problem. Villegas believed that there is a need for teachers to have the capacity “to analyze

the sociopolitical system that gives rise to those differences” (p. 261) which otherwise, culturally

sensitive remedies to the educational problems of oppressed minority students that ignore this

political aspect of school are doomed to failure and “worse still, they give the illusion of progress

while perpetuating the academic problem” (p. 263).

Other writers even move to the extent of discrediting the very idea of CRP’s effort to

support students of color in their education. Popkewitz & Schmeichel are among this group.

Schmeichel (2011) argued that seeing children of color as having cultural skills and academic

predilections worthy of recognizing and responding to are linked to the discourses of deficit

through a shared reliance upon ‘difference’ as a system of reason (pp. 12). In doing so,

Popkewitz (2009) also argued culturally relevant teaching may have become “a reform impuls[e]

for equity [which] embodies and produces inequities and exclusions” (p. 303).


Schmeichel extended his argument saying that the reasoning behind culturally

relevant teaching not only re-inscribes students of color as culturally different from their white

counterparts, but also that attempts to “validate those differences as valuable resources that can

be accessed to help children of color to become as successful, presumably, as white children”

(p.13). As such, discourse around culturally different children ‘fixes cultural identity upon

students of color, and, in effect, governs the practices that order children, structuring what it is

possible for us to think about them and for them to think about themselves, determining what

they can and cannot become’ (Popkewitz, 2009). Schmeichel (2011, p.13) highlighting what

previous research studies have described African American children as ‘responsive to movement

and verve’ (Carter et al. 2008; Cole and Boykin 2008, cited in Schmeichel), and African

American and Hispanic children as more ‘successful in group activities than individual

assignments’ (Waxman et al. 2007; Hurley et al. 2009 cited in Schmeichel), may not necessarily

be true for all children in these groups, and there could be some African American and Hispanic

children who may not ‘respond positively to these pedagogies’. Then Schmeichel raised an

interesting question to challenge the very premises of CRP:

What happens, then, when an African American student fails to respond to

strategies which have been designed to complement her culture? Does this make

her less than African American? Has she been, to use a familiar term, culturally

deprived, if she doesn’t share an interest in classroom activities planned with her

cultural group in mind? (pp.14)

Schmeichel contends that by fixing an identity upon the students, a kind of systematic

change of discourse that positioned students of color as ‘culturally deficit’ and shifted overtime

to frame them as ‘culturally different’, culturally relevant discourses are another source of a

potential mismatch between the student and the strategies used in the classroom through the

imposition of ‘a single, drastically simplified group identity that denies the complexity of


people’s lives, the multiplicity of their identifications and the cross pulls of their various

affiliations’ (p.14).

Though Schmeichel and Popkewitz’s critiques of CRP do make sense, they however

failed to provide alternative solution to the problem.

A recent work by Django Paris (2012), on the other hand, calls for a need for changing

terminologies and stance around the discourse of cultural relevance pedagogy or cultural

responsive teaching. Paris argued that terminologies like “Relevance and responsiveness do not

guarantee in stance or meaning that one goal of an educational program is to maintain heritage

ways and to value cultural and linguistic sharing across difference, to sustain and support bi- and

multilingualism and bi- and multiculturalism” (p. 95). Paris’s point is that previous works using

the ‘relevance’ and ‘responsive’ language is with the premise that classroom practices that use

the language and culture of students to teach them part of the ‘acceptable’ curricular cannon .

Paris then provided an alternative terminology what he called it ‘culturally sustaining pedagogy’

which he believes is a pedagogy that is “more than responsive or o relevant to the cultural

experiences and practices of young people-it requires that they support young people in

sustaining the cultural and linguistic competence of their communities while simultaneously

offering access to dominant cultural competence” (p.95).

Though the proposal of changing the stance and terminologies of cultural relevance or

responsive pedagogy into ‘culturally sustaining pedagogy’ by Paris may sound an alternative

discourse, but, inherently it is not a new ‘productive’ approach to solve the problem of low

performance of urban students particularly in mathematics and the sciences. It is not a change in

terminologies that I think matters a lot here. What we need rather is how we can improve the

existing practices so that all students irrespective of their cultural background can perform well


in these fields. I also think that we may need to look at the Sciences, Technology, Engineering

and Mathematics (STEM) fields in a different lens than other fields such as history or literature

when we think of culturally responsive or relevant pedagogy. I argue that the STEM fields,

unlike any other cultural manifestations of humans such as various forms of traditions, music,

arts, etc., are relatively commonly shared knowledge domains across all human races in history.

I would argue that the knowledge and practices in the STEM fields couldn’t be reduced to a

given culture when it comes to ownership. In one way or another, the knowledge and practices of

the STEM fields is the product of collective contribution of all human races. Hence, learning

these fields shouldn’t be considered as gaining ‘access to dominant cultural competence’. I

would also argue that the ‘best practices’ of learning or teaching the STEM fields such as

‘accountable talk’ in mathematics or ‘inquiry-based’ approaches in the Sciences could work fine

across all groups of students irrespective of cultural differences. It would be a matter of building

on students’ prior understandings and experiences by drawing context-based examples,

situations, etc when we are employing ‘best practices’ rather than suggesting a new form of

pedagogy for [one] group and another pedagogy for [another] group just because they are

culturally different.

Therefore, in responses to the conflicting arguments in the literature and to move the

CRP conversation forward, we may need a productive and generative discourse rather than a

change in terminology for example. One potential discourse recently introduced to the literature

by Sleeter & Cornbleth (2011) is I think a response to the changing demographics of the US

student population and carefully avoids a discourse of rescuing the minorities unlike the majority

of prior discourse of CRP. It rather promotes a pedagogy that works for a 21st century dynamic

and fluid multicultural society in general. Sleeter & Cornbleth’s (2011) work in ‘teaching with


vision’ extended the earlier works on cultural relevant pedagogy mainly by citing the works of

Ladson Billings (1994, 1995) and Gay (2000) and argued that ‘culturally responsive teaching is

not just to students of color, but to everyone’ (p.2). They also highlighted that what popularly

known as “best practices” or “good teaching” in the literature can be ‘culturally responsive’ by

aligning these practices to specific situations. So, extending on the tents of cultural responsive

teaching or cultural relevant pedagogy (Sleeter & Cornbleth used these two phrases

interchangeably), Sleeter & Cornbleth (2011) added two more genres in their ‘teaching for

vision’ model- ‘intellectually engaging teaching’ and ‘socially aware teaching’. Sleeter and

Cornbleth argue that a teacher under the philosophy of ‘teaching for vision’ is required to learn

and practice the attributes of culturally responsive, intellectually engaging, and socially aware

teaching.

According to Sleeter & Cornbleth (2011), ‘intellectually engaging teaching’ and

‘culturally responsive teaching’ should be mutually supporting, but they highlighted that one is

not a guarantee of the other. A given teaching could be culturally responsive but may not be

intellectually engaging. Sleeter & Cornbleth (2011) defines the term ‘engaging’ or ‘engagement’

to refer to:

…active student involvement that is “minds-on,” not simply hands-on. Students are not

merely listening or watching or completing a rote drill and practice worksheet. They are

thinking about something intriguing or puzzling or otherwise challenging that they want

to figure out’ (p.5).

Sleeter & Cornbleth (2011) make a point that intellectually engaging teaching is not

only for those students who are traditionally in the advanced placement programs. It rather is for

all students ‘meeting them wherever they are, and building on whatever they already know or

understand. Just about all students can handle intellectual work if they understand the language,

examples and questions’ (p.6). Even more importantly, Sleeter & Cornbleth contend that


‘students of color, English language learners, students with learning disabilities or students who

come from low-socio economic status families do benefit from more, not less of intellectually

engaging teaching (p.6)

This idea of intellectually engaging teaching could be much more meaningful and

practical in the teaching of mathematics and sciences in a cultural responsive approach. Teachers

may use ‘best practices’ such as reform-based strategies in teaching math, and science by

designing learning tasks that are relevant and meaningful to students’ experiences and life. Since

the content or subject matter in math and science are relatively more generic and universal than

one finds in history, language studies or in the social sciences, a culturally responsive teaching

would less wrestle with issues of whose history or language has to be negotiated. Drawing

examples and building learning tasks around students’ experiences would easily suffice for an

intellectually engaging teaching to happen.

The third element in Sleeter & Cornbleth’s teaching for vision model is ‘socially

aware teaching’. Informed by the work of John Dewey (1944), they claim that socially aware

teaching is based on the idea that ‘education is a resource for the public good…,a socially aware

education is grounded in a value for human rights…and recognizes and grapples with the

political ideology that is inherent in education’(p. 7-8). Sleeter & Cornbleth extended their

argument that educating youth for ‘democratic participation’ in a continuously diversified

society like the United States entails fostering habits that enable them to hear and engage with

diverse perspectives. For Sleeter & Cornbleth, teacher education programs with the goal of

supporting visionary teaching would interweave these three themes-culturally responsive,

intellectually engaging and socially aware teaching.


Grounding on the works of Sleeter & Cornbleth’s idea of intellectually engaging

teaching, therefore, this paper is aimed at analyzing an ‘exemplar’ project presented at the

Carnegie foundation website targeting pre-service teachers titled “Unpacking Mathematical

Practice” by Megan Franke for a Mathematics Methods course at the University of California,

Los Angeles.

Analysis of “Unpacking Mathematical Practice”

Context

Unpacking Mathematics Practice (UMP) is an exemplary mathematics teaching

practice for pre-service elementary mathematics teachers archived in the Carnegie Foundation

for the Advancement of Teaching website. It was developed by Professor Megan Franke,

currently a chairperson of the Department of Education at UCLA Graduate School of Education

and Information Studies. Franke headed UCLA’s teacher education program and became

involved with the Goldman-Carnegie Quest Project, an effort that aims to explore and design

“signature pedagogies” for the education of teachers.

The rationale behind choosing UMP as object of analysis for this paper is twofold.

One is the fact that UMP focuses on preparing teachers for low-income urban setting, which is

also the major focus area in the cultural responsive teaching literature. The second reason is its

focus on ‘practice’. UMP was actually part of Goldman-Carnegie Quest Project-an effort to

explore and design ‘signature pedagogies’-which is becoming a center of attention in defining

‘pedagogy of practice’ in teacher education in general, and mainly in reform-based mathematics

education literature (Lampert, Beasley, Ghousseini, Kazemi, & Franke, 2010). One of the three

descriptors of ‘signature pedagogy’ proposed by Lee Shulman (2005) is ‘pedagogy of

engagement’ which attests that a reasonable degree of engagement is a prerequisite for any form


of effective learning to happen. Likewise, Sleeter & Cornbleth’s (2011) idea of ‘intellectual

engaging teaching’ is indeed a form of pedagogy of engagement. Sleeter & Cornbleth have also

argued that ‘best practices’ can be used in any school setting as long as lessons are organized

around meaningful practices. UMP’s central focus around the tents of ‘learning for practice’ is

also a focus on preparing teachers who would enact classroom instruction that focuses on

students’ meaningful engagement in the learning practice.

The UMP website, therefore, documents one of Franke’s practices while teaching

Mathematics Methods course during the ‘winter quarter’ for elementary mathematics pre-service

teachers to do the work of mathematics teaching at the urban setting focusing on learning from

‘practice in 2005. This project is designed with the intention of preparing these teachers to teach

in low-income urban schools. One generic question that I raised to analyze the goals, resources

employed, the process and practice of the UMP is, therefore, what aspects of the themes in

‘teaching with vision’ promoted by Sleeter & Cornbleth are incorporated in this practice.

Goals

The underlying philosophy of UMP was to ‘learn about and from practice’. Guided by

this principle, Megan Franke incorporated two Quest practices to help students ‘learn to learn

from their own practice and to help them learn how to unpack practice’. Franke described that

the main objectives of the UMP is to create opportunities:

(1) for preservice teachers' learning to become generative - where teachers learn to

learn from their practice, where they learn to experiment systematically; (2) to begin

to develop specific and detailed knowledge about the trajectories of students'

mathematical thinking; (3) to challenge (in ongoing ways) the assumptions they bring

about students, about culture about diversity and how those play out in their

interactions with students to support student understanding and identities and (4) to

make sense of the above ideas in relation to their work in urban schools - the reality

and other aspects of the work that influence how the above ideas they develop will

play out for them.


The four opportunities that Franke wanted to create for her students are in one way or

another related to the three themes that Sleeter & Cornbleth are advancing about the notion of

cultural responsive teaching. Learning to become generative requires teachers’ skills in setting

meaningful tasks so that students would engage in sense making practice. The first two

opportunities that she wanted to create for her students are focusing on how teachers could learn

about teaching practice from practicing it, and through their practice they would engage in

eliciting their students’ mathematical thinking. This experience in turn would help the would-be

teachers to conduct intellectually engaging teaching for their students. The last two opportunities

identified by Franke are related to what a socially aware teacher does-challenging his/her prior

assumptions about students’ cultural background and would then be able to set the appropriate

conditions for meaningful learning to happen whoever that child is in his/her class.

Resources/Materials

One of the most important ingredients of “visionary teaching” espoused by Sleeter &

Cornbleth in their discussion of cultural responsive teaching in standard-based classrooms is the

selection and use of appropriate learning and/or teaching materials/resources. A visionary teacher

who aspires to create a culturally responsive, intellectually engaging and socially aware teaching

to her/his students needs to equip with the knowledge, skill set and resources, and the capacity to

judge when, where, and how to use those skills and knowledge that will enable different kinds of

students across ethnic, racial, class, and gender categories to perform competently in complex

domains of learning.

In the UMP project, Franke had carefully crafted appropriate toolkits such as ‘Initial

Assessment sheet’ to document what students think about ‘practice’, ‘Mathematics Teaching

Practice Framework Sheet’ where preservice teachers reflect on the sample classroom video


lesson of exemplary teachers and their own trials of the sample video in their teaching practices,

and ‘discussion board’ for preservice teachers to discuss each other’s experiences in unpacking

the sample video lessons and their own practices.

Inspired by the experience of a Stanford University teacher educator (an experienced

and a National Board certified high school English teacher leading a very engaged discussion

around text for her preservice teachers who had successfully benefited from incorporating

sample video of classroom teaching from the Quest website); Franke decided to incorporate an

exemplary sample video of Mathematics teaching for her Mathematics Methods course for a

cohort of preservice mathematics teachers in her teacher education program. Franke described

that she selected one of her favorite video clips of Lilliam Paetzold teaching second grade

mathematics who poses a multi-digit addition problem. According to Franke, Paetzold in this

multi-digit addition problem asks her students to describe what the problem is asking and pulls

together the students' ideas. Then, she asks students to solve the problem in whatever way make

sense and she elicits students multiple strategies in a whole group discussion.

After the preservice teachers watched Paetzold’s video clip, Franke asked her

preservice teachers to generate the different practices they noticed Paetzold and her students

were engaged in. Then, Franke selected two other exemplary mathematics teaching classroom

video clips by Mary Hurley and Sue Lampkin from the Quest website for her preservice teachers

to unpack the practices and try out for themselves in their teaching practice. Franke described

that she selected these two sample video clips since they provide opportunities to examine

‘posing problems’ and ‘eliciting student thinking’. But she shared on her Quest website only

focusing on ‘problem posing’ on Mary Hurley’s “Horse Problem”. Franke argued that she

focused on problem posing because:


problem posing practice exists in every classroom; there are many ways to get better at

problem posing; it is critical to the ongoing lesson development; it involves content,

students, issues of participation and equity; even at the beginning teachers will see

"results", can see student willingness and knowledge; important for English language

learners, and research base for its importance to student understanding.

As explained the reasons for focusing on this particular problem, she highlighted its

appropriateness for English language learners, and issues of participation and equity which in

fact aligning lessons to contexts is one of the key aspects of culturally responsive teaching

practice as advocated by Sleeter & Cornbleth.

The “Horse problem” by Mary Hurley from Redwood Heights Elementary School

Oakland, California is one of the two Quest video clips used in Franke’s practice. As described

in the Quest website, adhering to a district's strict curriculum pacing guide with the individual

needs of her fourth and fifth grade students, Hurley focuses upon a process of reflecting and

revising her math instruction on a weekly, daily, hourly, and moment-by-moment basis. The

following is what Hurley has to say about her practice:

Sometimes the hardest work I do in the class is to really hone in on what I'm hearing -

what it is that they're really saying that captures their math thinking. Then taking that to

the next step, I have to think hard about what is going to be a really deep but

compassionate question that is going to move them further and at the same time open it

up to another group of kids who possibly didn't understand it. Listening is intense

because you don't know what is going to happen next. And of course, I make all kinds of

assumptions about what I think they understand that they may not. I try to figure out what

works. My approach is to spend a chunk of time sorting out what I think is important and

having that as my set of goals. Then I need to figure out what works given the context

I’m in, meaning mostly who the kids are that I’m working with this year.

As the above excerpt explains, what Hurley most importantly focus on was honing to

what students already understand and build on that depending on the contexts both in time and

space, like capturing what students have said and push that to the next level.

Based on the evidences on the sample classroom video clips that she had selected and

the sample excerpts of how her students were engaged in reflecting on these video clips and their


own try outs using the Initial Assessment sheet and Mathematics Teaching Practice Framework

Sheet’, I think that Franke has selected the appropriate resources and tools to meet the objectives

she has set for this project.

The Process

Franke’s ‘unpacking mathematical practice’ project was a three phase process cycle

which begins with her teacher education students watching Lilliam Paetzold’s multi-digit

addition problem classroom video clip as a common start up video for all. Then, she asked her

students to fill out the ‘Initial Assessment sheet’ asking them the following question:

As you consider your own teaching of mathematics, what 3 aspects of your practice do

you most want to make sure you include in your teaching of mathematics? If this is

unclear consider what we saw Lilliam do in the two second grade lessons. Are there

aspects of her practice that you want to make sure you include in your practice?

From this assessment, Franke came to realize that her students generate a list of what

they noticed about one class session - the focus was not on problem posing. She said that the

students ‘generated quite a range, some detailed and some very general, some pertaining to

mathematics and some not’. As she wanted them to understand ‘problem posing’ and the

strategies used in the process, she and the students re-watched the same common video together

this time focusing on problem posing. Unlike the initial assessment, Franke described that in re-

watching, her students noticed how Lilliam Paetzold focuses on a key mathematical idea in

unpacking the problem.


In the second phase, they together watched two quest sites (Hurley and Lampkin).

They created a list of what they noticed. Just like what happened in the common video of the

initial phase, Franke noticed that the students had little to say here too. Hence, she had to work

hard to get them to talk about the problem posing they watched. She asked many questions and

prompted them using specifics from what she knew was in what they had watched. This was the

students’ first engagement with the sites and it was in pairs in the computer lab. Then, she asked

them revisit the Quest sites at home and filled out ‘Mathematics Teaching Practice Framework

Sheet’ for one QUEST teacher of their choice but focus on problem posing. In this worksheet,

Franke asked the students, questions like “What did you notice about what the teacher did/said?

What was the most critical detail within this practice? What did you notice about student

participation? What did you notice about the mathematics? What did you notice about issues of

equity? What worked well in relation to this particular practice? What adjustments might

support student learning and participation?”


They then discussed the framework responses in class together. Franke described that

here students had much to say during the discussion. The conversation was lively and involved

multiple participants engaging with each other. The students did provide details but wanted to

move to general ideas quickly. She used her prompting to push for unpacking of the details of

practice. They organized the conversation after they had all of what was said all over the

discussion board.

In the third phase, they tried problem posing in their student teaching assignments.

They were then asked to fill out the Mathematics Teaching Practice Framework Sheet for their

problem posing in their teaching assignments. They discussed their response with colleagues in

the class. With the feedback they get from the instructor and their colleagues, they then tried

again in student teaching. Finally, they filled out the Mathematics Teaching Practice Framework

Sheet again but this time as a final reflection of the whole process of problem posing exercise-

“what I believe about how children learn mathematics ... and what I will do in my classroom...”

Conclusion

This experiment on unpacking mathematical practice by Megan Franke clearly

demonstrated that the learning process of unpacking ‘problem posing’ was not a linear process.

Rather the student teachers have been struggling particularly in the beginning such as difficulty

of detailing practice, choosing practices that were difficult to implement, lack of persistence to

elicit student thinking, and taking on simpler practices. But through Franke’s persistent probing

and challenging her teacher education students, they were finally able to unpack both their own

practices as well as exemplary mathematics teachers’ practices. This, however, doesn’t guarantee

that these would-be teachers could be able to apply what they have cultivated at their program

into their actual teaching assignment when they become teachers and start to run their own


classrooms. This requires further study on the actual practices of these teachers and the impact

they will have on their students learning.

Moreover, despite the fact that one of Franke’s objectives of this project was to

challenge (in ongoing ways) the assumptions they bring about students, about culture about

diversity and how those play out in their interactions with students to support their understanding

and identities, none of the evidences in her quest website indicated such explicit attempts have

been made. Rather, she was focusing on problem posing and pushing the teacher education

students to have intellectual engagement in understanding their students’ mathematical thinking.


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Appendices

I) Initial Mathematics Practice Assessment Worksheet

As you consider your own teaching of mathematics, what 3 aspects of your practice do you

most want to make sure you include in your teaching of mathematics? If this is unclear

consider what we saw Lilliam do in the two second grade lessons. Are there aspects of her

practice that you want to make sure you include in your practice?

Describe each aspect of practice and tell why you want to include it in your mathematics

teaching.

1.

2.

3.


If you had to choose one aspect of practice as the most central, which would you choose and

why?

II) Mathematics Teaching Practice Framework

Watch how the teacher ________________________.

What did you notice about what the teacher did/said?

What was the most critical detail within this practice?

What did you notice about student participation?


What did you notice about the mathematics?

What did you notice about issues of equity?

What worked well in relation to this particular practice? What adjustments might support

student learning and participation?

analysis of a teacher education project “unpacking mathematical practice’ through the lens of a...

Documents