Ann Anderson


Relevant Thesis-Based Degree Programs


Graduate Student Supervision

Doctoral Student Supervision

Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.

Understanding African immigrant families' support for their children's mathematics learning in Canada (2021)

This research investigates African immigrant families' experiences and perspectives of their children's (10-15-year-old) mathematics learning in the home, community and school settings within the Greater Vancouver area. The study employs the concept of cultural capital framework and Afrocentric worldviews to understand how African immigrant parents support their children’s mathematics learning at the upper elementary and middle grade levels (Grades 4 - 8) in Canada. Specifically, the study addressed the following questions: i) which socio-cultural strategies and understandings do African immigrant families living in a large metropolis draw upon to support their children’s mathematics learning? ii) what are African immigrant families’ experiences and perspectives with respect to their (10–15-year olds) children’s mathematics learning in the home, community and school settings, within the Greater Vancouver Area? The study’s findings indicate that, African immigrant parents 1) were aware of the gatekeeping function of mathematics and its role in reproducing or disrupting race or class hierarchies and 2) perceived their support for their children’s mathematics fluency as a sure way for securing a status for counterbalancing their social exclusion and positioning themselves as people of education and intellect. The study’s findings also indicate that immigrant families leveraged various forms of capital in support of their children’s mathematics learning: Cultural, linguistic, aspirational, technological/digital and navigational capital. These forms of capital extend the narrowly conceived definitions of capital as accumulated wealth, resources, and experiences of white middle-class families. The results of the study are significant in that they provide much- needed insights into ways to build culturally responsive mathematics education informed by African immigrant students’ and families’ funds of knowledge.

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Tertiary mathematics and content connections in the development of mathematical knowledge for teaching (2020)

Emphasis on the importance of subject matter expertise in teaching secondary mathematics is found in the research literature and in policy. In the United States, for instance, the No Child Left Behind Act, calls for secondary teachers to be certified in a subject specialization. In Canada, admission to secondary teacher education programs requires extensive subject-specific university coursework. However, it is unclear if or how extensive subject matter expertise impacts the practices of teachers in a secondary classroom.This study aims to explore how advanced coursework in mathematics, beyond the scope of the high school curriculum, impacts the ways prospective teachers understand and teach secondary content. Using a qualitative case study methodology, five prospective secondary mathematics teachers participated, with data obtained through document analysis and semi-structured task-based interviews. Participants engaged with classroom-relevant tasks and were explicitly asked how they could draw upon advanced mathematics to inform their teaching. Participants also detailed their perceptions of the role advanced mathematics plays in their development as teachers.Results from this study reveal that participants saw little value in the content of advanced mathematics to their teaching, but expressed value towards the beliefs and values gained through advanced mathematics, such as problem solving and rigour. Some participants demonstrated misconceptions at the secondary level, which had direct connections to content from their post-secondary mathematics coursework. For example, all participants made the false claim that a real-valued polynomial can be factored if and only if it has a root.Results extend the literature through rich empirical data which illuminates how prospective secondary mathematics teachers perceive and use advanced mathematics in understanding the secondary curriculum. While participants held content knowledge beyond the secondary curriculum, this knowledge was not integrated in a way that impacted their understanding of secondary mathematics. An understanding of post-secondary mathematics has the potential to be of value to secondary teachers in the classroom, but this potential needs a space to be unlocked. I argue that mathematicians and teacher educators need to work together to build opportunities for prospective teachers to build connections between the mathematics they know and the mathematics they need to teach.

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Teachers' practices in kindergarten classrooms within the Cape Cast metropolis, Ghana (2017)

Even though previous research points to the significance of kindergarten teachers’ practices, that take into consideration the nature of children and how they learn, there is limited research regarding developmentally appropriate practices in various socio-cultural contexts. To address this gap in the literature, a qualitative multi-case study into the perceptions and classroom practices of four kindergarten teachers in two Ghanaian schools, Tata and Kariba, was carried out over a six-month period. Four research questions guided the study, namely: How do teachers interpret and apply DAP in kindergarten classrooms within the Ghanaian sociocultural context?; With what kind of learning activities do teachers engage kindergarten children?; Which instructional strategies do teachers use in a kindergarten classroom?; and What factors and beliefs influence teachers’ instructional decision-making in a kindergarten classroom? Cognitive constructivist theory (Piaget, 1951) and sociocultural theory (Vygotsky,1978) informed the research. Data used were semi-structured individual interviews and pair-based interviews and fieldnotes of classroom observations. Both within and across case interpretative analysis, as outlined by Stake (2006), was used.The findings of this study revealed these teachers’ practices were developmentally appropriate and they interpreted DAP within the Ghanaian socio-cultural context through contextually relevant language of instruction (English language, Nfante language), age- and culturally- appropriate learning materials, and the use of storytelling, traditional songs, and traditional rhymes. Moreover, teachers in both the urban and rural setting, described a variety of learning activities they believed impacted children’s development in different ways; they pointed to play-based instruction and integration as well as specific strategies such as picture-walk and think-pair-share that they believed promoted effective DAP; and discussed their explicit and implicit theories of teaching involved in their instructional decision-making processes. These findings are discussed in light of current research in early childhood education to provide insights into how DAP, as interpreted and applied in the Ghanaian socio-cultural context, can inform teaching and learning in kindergarten classrooms, globally. Implications for future research and practice both within Ghana and elsewhere are established.

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How Young Children Negotiate Sociomathematical Norms during Inquiry-Based Learning in Mathematics: A Discursive Psychological Perspective (2014)

This dissertation uses a discursive psychological perspective to investigate how young children use the structure of spoken language to support their participation in mathematical discussion. There is a general consensus that participation in the practice of collective argumentation not only promotes, but actually constitutes the learning of mathematics (Cobb, Yackel & Wood, 1992a; Krummheuer, 2007). However, given the wide variety of forms that mathematical communication might take (Barwell, Leung, Morgan & Street, 2005), how to fruitfully define and document the practices of communication involved, especially for young learners, remains an open question. Through a series of related discourse analyses (three linked studies carried out on a common data set), I explore some of the discursive practices 5- to 7-year-olds use as they negotiate what will become a taken-as-shared understanding regarding mathematical validity: a sociomathematical norm regarding what it means to know in mathematics. Discursive psychology (Edwards, 1997) affords an examination of how participants treat notions of knowing and understanding during interaction. Using corpus linguistic analysis in the first study here allows me to elaborate features of this group’s culture of negotiation by illuminating patterns in the interactional sequences involving doing knowing. Conversation analysis in the second study affords an examination of the practices by which young children incorporate mathematical content within the social act of negotiation: doing mathematical understanding. Further analysis attending to multimodal aspects of communication in the third study shows how the participants used those previously noted discursive practices to develop and sustain a six week long investigation into the meaning of the square root symbol: doing algebraic reasoning. These analyses show how the children are able to draw upon a range of sociomathematical norms as resources that enable them to participate in ways that co-ordinate with each other. The findings suggest that expanding our expectations for what mathematical knowing looks like with young children affords the development of learning environments that support all children’s sustained, successful engagement with mathematics.

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Listening to Students: A Study of Elementary Students' Engagement in Mathematics Through the Lens of Imaginative Education (2014)

This dissertation investigates the problem of student engagement in elementary mathematics through the particular theoretical framework of imaginative education (IE) (Egan, 1997, 2005). The question at the centre of this study is what the use of IE and imaginative lesson planning frameworks means to children and for their engagement in elementary mathematics. For this study, five intermediate-aged elementary students were tracked through a unit of shape and space (geometry). The unit, framed with the binary opposites of vision and blindness, asked students how they might come to understand shape and space as a sighted and as a visually impaired person. Thus a humanized perspective was brought to the learning of mathematics. After the unit the five focus students took part in an individual and a whole-group semi-structured interview with the teacher/researcher. The study used qualitative instrumental case study methods; data sources included students’ mathematics journals, activity pages, transcripts of audio- and videotaped semi-structured individual and group interviews, a teacher/researcher diary, and a detailed unit overview and lesson plans. The study gathered rich descriptive data focused on bringing out the students’ perspective of their experience. Results indicate that the students demonstrated positive engagement with mathematics and that the IE theory, which utilized the students’ imaginations and affective responses, allowed multiple access points through which to connect with the mathematical concepts. Three conclusions of the study were that the students expanded their mathematical awareness through making a variety of connections, they were able to develop self-confidence in their learning of mathematics by using emotions and imagination, and they were able to use cognitive tools, particularly a sense of wonder, to engage with mathematics. The dissertation concludes with a discussion of implications and recommendations in four areas, including the need for further research in different educational contexts, in the interaction of imagination and affective responses, and into characteristics of mathematical engagement such as self-confidence. Recommendations for how future pedagogical practice might use the IE theory and embrace the expansion of students’ perspectives in classroom practice bring the dissertation to a close.

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Problem posing as storyline: Collective authoring of mathematics by small groups of middle school students (2013)

This dissertation investigates the problem posing patterns that emerge as small groups of students work collectively on a mathematics task, and describes the characteristics of problem posing that result. This case study is a naturalistic inquiry about four small groups of Grade 8 students in the Lower Mainland of British Columbia who are working in a classroom setting, with the researcher acting as participant/observer and videographer. The concept of author/ity is used to highlight human agency in mathematics. Small groups, as learning systems, are being considered to be “authors” of their discourse, and the improvisational nature of authoring is discussed. A parallel is drawn between the storyline of a literary work and the storyline that emerges as a group poses problems in order to work its way through a mathematical task. The metaphor of a tapestry is used as a way of describing how the threads of group discourse weave together. To address the challenge of documenting collective behavior at the group level, a method of data analysis is introduced that “blurs” the data in order to capture patterns that emerge over time – transcripts are color-coded and then shrunk to create tapestries that provide visual evidence of collective problem posing patterns. This dissertation finds that collective problem posing is an emergent process. Each group poses its own set of problems, and the number of problems posed and their frequency also vary, resulting in individual tapestries for each group. The tapestry patterns are then used to compare characteristics of the groups’ discussions. Problem posing appears to be an activity that these groups are able to do without receiving formal instruction or direction. The reposing of problems helps to structure each group’s discussion, with the role that each problem plays in the conversation evolving as it reemerges. The concept of groups working as bricoleurs is also explored, with bricolage in mathematics being characterized as a creative and generative process. The dissertation concludes with a discussion of expertise in school mathematics and what implications an “aesthetic of imperfection” might have in the mathematics classroom.

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Master's Student Supervision

Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.

Young children, parents and technology:a case study exploring how the play choices of a 3 year old child relate to parental attitudes and behaviours around technology (2019)

Today’s digital landscape is evolving more quickly than existing research about the effects of digital technology on the development, learning and family life of young children, particularly those under the age of five. As research suggests, there is a causal relationship between use of digital technology and the health and well-being of individuals. It is therefore important to come to an understanding of how digital behaviours are developed in the early years, a time of radical growth and learning with long term implications for the young child. Research suggests that the child’s development of attitudes and behaviours related to digital technology may be influenced by parental use of and attitudes about digital media as well as the structuring of the child’s experiences and environment. The purpose of this qualitative case study was to explore the question of how the play choices of a 3 year old boy relate to the behaviours and beliefs parents demonstrate in the home in regards to digital technology. Data collection included parent and child questionnaires as well as observations and documentation of the child’s play preferences when offered choices from traditional as well as digital materials. Results were examined using a thematic analysis to determine if a relationship between child choices and parental beliefs and practices is indicated.

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Parental involvement in children's mathematics learning: A case of a rural community, Ghana (2015)

Although emergent literature and anecdotal experience indicate the importance of parental involvement in their children’s mathematics learning, there is still a void in literature with regard to involvement of parents with low formal education in their children’s mathematics learning in culturally diverse contexts. In an attempt to address this void, a study that employed socio cultural learning and social constructivist theories investigated how parents with low formal education are involved in their children’s mathematics learning in a rural Community, Ghana. Data was collected from six parents with low formal education, their 8-9 year old children as well as the children’s class teachers through semi-structured individual face to face interviews and home visit observations. Analysis of the data corpus revealed that 1) parents’ mentorship and engagement in local business transactions, were used as learning and evaluation contexts for a child’s mathematics competence; 2) parents perceived giving and receiving correct change as a key indicator of one’s moral standing and mediated children’s mathematics accordingly; 3) parents, teachers and children consider mathematics as a hallmark of future success; 4) parents’ belief that increasing time spent on academic activities improved children’s success, within the examination culture of the context;5) teachers see low formal education as a handicap of parental involvement in children’s mathematics learning; 6) children typically corroborate their parents’ perceived ways of supporting their mathematics learning. These findings are significant and offer insight into how parents with low formal education from a different cultural context are involved in their older children’s mathematics learning. The study adds to the literature on the topic of parental involvement from a non-western context.

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Understandings of emotional salience in a preschool classroom (2015)

The purpose of this research was to examine the ways in which preschoolers use artistic, kinaesthetic and linguistic modes of expression to recognize, label and understand feeling words of varied salience within a classroom environment. The ways in which a multi-modal approach towards emotional literacy in the classroom supported emotional literacy is examined. The research site was an urban preschool classroom in the lower mainland of British Columbia. Seventeen three-and-four-year-old children created drawings, kinaesthetically posed, and discussed feeling words of varied salience: ‘calm’, ‘happy’, and ‘ecstatic’, which served as the primary data source, supplemented with teacher observation notes. Analysis found that each mode offered unique insights into how young children recognize, understand and label feeling words of varied salience. Limitations of this study are discussed and suggestions for further research are offered.

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Utilizing the empty number line to facilitate sense making in the mental math classroom (2014)

The purpose of this study was to explore the possibilities of the Empty Number Line to further develop and strengthen students’ numeracy skills, specific to addition and subtraction. The Empty Number Line (ENL) is a Dutch approach to developing numeracy and mental math skills in the elementary classroom. Internationally acknowledged, the Empty Number Line (ENL) boasts to solving computational tasks in a manner that builds on users intuitive understanding of number. Typically, this model is introduced in the primary years to support early numeracy development. However, this study set out to determine if the tool could be utilized to strengthen the computational skills and fundamental numerical understanding of a sample of 28 Grade 4 students, having no prior exposure to this model. Specifically, the researcher sought to determine what the ENL could reveal about students' sense of number, while utilizing the tool in a manner that supported sense making and self generated strategies. Central to this study was to establish student opinion of this tool, in regards to its effectiveness and ease of use. Over a four week period, students were asked to commit to eight one hour blocks focusing on the exploration of this tool. Three strategies, stringing, bridging and splitting were presented. Via whole class lessons, independent tasks and group activities, students completed a variety of tasks by applying a presented strategy. Student samples and journals were analyzed to determine students performance and opinions over the four week period. Overall students responded very favourably to this tool, and the majority of students developed a good understanding of how to utilize the ENL. However, data unveiled much about students’ numerical capabilities, and in many cases highlighted gaps in children’s number sense. In addition, data analysis highlighted some important future considerations for those considering using this tool, including the delivery of solutions as well as the challenge of applying splitting to subtraction tasks. To conclude, this study highlights advantages and disadvantages when using the ENL to solve 2 and 3 digit computation tasks, as well as considerations to educators intending to present this approach in future teaching endeavours.

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Defining math disability: the impact of using different cut offs when assessing the cognative characteristics of math disabled participants (2012)

Mathematics disabilities (MD) can cause serious difficulties for children throughout their education. However, there is a lack of consensus in the literature regarding how MD should be defined. This makes it difficult to compare results across studies and to determine the overall cognitive profile of MD. The present study investigated the cognitive profiles of participants with MD defined using various cut off criteria and using different assessment measures. Further, this study endeavoured to investigate the differences between those who have MD at one time point and those who have MD at two time points (MD persistent). Over 700 participants were recruited from the North Vancouver school district to participate in this study. Participants were evaluated over two years (grades 2 and 3). Performance was measured using 16 different cognitive measures and 4 achievement tests. Scores on the achievement tests were used to assign MD status. A series of t-tests were conducted to determine whether there are differences between the cognitive profiles of those defined as MD using a 10th percentile cut off (MD10), a 25th percentile cut off (MD25), and a low achieving score between the 11th and 25th percentiles MD(11-25) when compared to typically achieving students (TA). Cut offs were based on performance on two separate math achievement tests: the Woodcock-Johnson Third Edition (WJ III) Calculation test and the Woodcock-Johnson Third Edition Applied Problems test. This study concludes that MD10, MD25, and MD(11-25) all represent similar enough cognitive profiles when compared to the TA group that using a 25% cut off to define MD will suffice for future research. Furthermore, the results suggest that the MD persistent group has a similar enough profile to the terminus point group that additional caution should be used when studying MD persistent in the future. The cognitive profiles of the MD groups are described and implications for research and practice are discussed.

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Life through a mathematical lens: building parental awareness of home numeracy practices through photography (2011)

The home is a rich site for mathematics exploration, communication and discovery and parents play an invaluable role as their children’s first math teachers. However, literature suggests that parents do not often realize the mathematics in which their children engage at home (Beningno & Ellis, 2008; Tudge & Doucet, 2004; Warren & Young, 2002; Winter, Salway, Lee, & Huges, 2004). Pound (1999) highlights that unless children’s everyday activities are viewed with a mathematical lens the mathematics may go unnoticed. This study, grounded in the theoretical framework of numeracy as a social practice, examines the ways in which parental awareness of home numeracy experiences may be enhanced through photography and the photo interview. These methods have been frequently used in examining literacy practices and it seems reasonable that photographs may provide a language of inquiry for numeracy practices.Four parent dyads of prekindergarten to kindergarten aged children participated in two photo assignments where they were invited to capture events where their children were engaged in mathematics. Each assignment was followed up by a photo interview where parents were invited to discuss the mathematics being portrayed in photographs. An exit interview was conducted to allow parents to share what they learned from the experience. All parents pointed to an increased awareness of mathematics in the home. These results suggest that strategies such as used here foreground math for the parents and heighten their sensitivity to it.

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Collaborative assessment in middle school mathematics (2010)

This study examined the mathematical learning that grade 8 students demonstrated when they were given the opportunity to work collaboratively, with a teacher-assigned partner, on an in-class assessment. In addition to topic-specific concepts, skills, and procedures, mathematical learning also included more general abilities such as selecting strategies, developing plans, communicating ideas, and evaluating solutions. The primary sources of data for this study were the conversations and written papers of four “equal status” dyads as they worked on a problemsolving assessment in which they were encouraged to discuss their ideas and submit a joint solution. Analysis indicated that most dyads worked collaboratively throughout the task and that both students were relatively equal contributors to the joint solution. Therefore, while collaborative assessment reduced the ability to hold individual students accountable for what they had learned, it appeared to be an accurate reflection of most students’ mathematical knowledge and ability. One dyad, however, remained committed to working independently; the partners rarely discussed their ideas with each other and both students created their own solutions. During their discussions, students who collaborated were more likely to discuss various calculations related to the problem, rather than discuss potential strategies or solutions. Students interacted comfortably and informally with each other and asked questions if they did not understand, but did not often critically challenge their partner’s suggestions or provide justification for their own ideas. As a result, students did not always make reasoned choices when approaching the problem or evaluate the appropriateness of their strategy or solution.

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Views of Young Second Language Learners on Building Relationships with Peers in an English Classroom Setting (2010)

School communities are becoming more diverse in many countries around the world and are including children who are learning in a language that is not their first (2LL). Little is known about the experiences young 2LLs have when they enter early childhood settings for the first time. The aim of this study was to investigate in what ways being a 2LL may impact peer relationships according to the views of young children who learned or are learning English as a second language. The participants of this study were five children, ages 5-8, from an Arabic community near a large urban center in western Canada. The children‟s parents responded to an advertisement on an Islamic school‟s communication board. Data collection included two individual interviews held in each child‟s home and one group interview carried out at the children‟s school. All interviews involved a persona doll and were audio recorded and transcribed. The interview data were analyzed for reoccurring themes throughout the children‟s responses. The findings were organized under the headings: the children‟s feelings on their first day of school, the children‟s thoughts on the persona doll‟s (a 2LL) feelings on her first day of school, and the children‟s suggestions to help the doll learn English and socialize in the classroom. Overall, this study indicates that young children point to support from bilingual peers and/or teachers as valuable for the second language learner‟s acquisition of the new language. In addition, results of this study support previous research that has explored effective strategies for teaching young 2LLs.

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