Participation in campus leisure and recreation programmes can provide university students with various benefits, but the provision of effective leisure programmes are complicated by the changes that have taken place in the demographic composition of the student population attending South African universities. Increases in the proportion of black students attending university, and decreases in the proportion of white students means that current students possibly exhibit leisure behaviours that differ from those of their predecessors. With eleven official languages in South Africa, the language diversity among students is a further issue with which leisure professionals have to contend. Students also come from different economic backgrounds, posing additional challenges to universities’ leisure service providers. Since demographic factors, including culturally based perceptions and values, ethnic identity, language, religious beliefs and family structure (Outley & Witt, 2006:112) may influence leisure behaviour and preferences, it is important for leisure professionals to understand how these factors influence the perceptions students have of leisure. For purposes of this study, leisure perceptions are conceptualised to include leisure meanings, leisure experiences and leisure constraints. Due to the lack of research regarding leisure within a South African context (Goslin, 2003:39; Wegner et al. 2006:249) the purpose of this study was to determine the relationship between demographic variables and leisure perceptions of selected South African first-year university students. The study utilised a once off crosssectional research design, using three research instruments, the Leisure Meanings Inventory (LMI), Leisure Experience Battery for Young Adults (LEBYA) and the leisure constraint questionnaire by Raymore et al. (1993:104). An availability sample was used that comprised 344 first-year students in academic programmes related to sport, leisure and recreation studies from six South African universities. Data analysis included confirmatory factor analyses, t-tests, ANOVA and 2-way ANOVA. For leisure meanings, results indicate that female students are more likely to see leisure as Exercising Choice and Achieving Fulfilment than are male students. Home language also influences leisure meanings, with Afrikaans students seeing leisure as Escaping Pressure, whereas English-speaking students associate it with Passing Time. Students staying in private accommodation associated leisure more with Passing Time than those in university hostels. Furthermore, students that are in a relationship are less likely to see leisure as Achieving Fulfilment than those that are not. For leisure experiences, white students are more aware of leisure benefits and opportunities than are black students, and experience less boredom and distress during their leisure. Additionally, white students are more aware of leisure benefits and opportunities than are Coloured students. Seeing that a lack of awareness of leisure participation benefits and opportunities often are associated with boredom, which in turn is associated with delinquent behaviour, the possibility exists that increased awareness of leisure may assist in combating delinquent behaviour among students. In terms of language, Afrikaans-speaking students and students that speak African languages experienced more challenge in their leisure than their English-speaking counterparts. This result may be either because of ethnic factors, such as traditions or customs associated with specific languages or because of language, per se, as proposed by the Sapir-Whorf hypothesis. With regard to leisure constraints, black students experienced greater interpersonal constraints than did white students, while white students experienced greater structural constraints than did black students. Additionally, Indian students experienced more intrapersonal constraints than did black students. Students staying in university hostels experience less structural constraints than those in private accommodation. Lastly, students from rural areas/informal settlements experienced less intrapersonal and structural constraints than students that grew up in towns and cities. The study is the first of its kind in South Africa, providing a new insight into leisure, and addressing the paucity of research within the South African context. Recommendations include the implementation of comprehensive leisure education programmes to inform students of the benefits of leisure and the opportunities available to them. In so doing, students can be assisted in negotiating constraints and in developing more complex leisure meanings. In order to meet the challenges, leisure professionals need to know how student diversity affects leisure programming; hence training of current leisure practitioners in the form of short learning programmes is suggested. Future research should include: a) modifications to the research instruments to accommodate the South African population and to increase reliability, b) replicating the study on a broader student population to provide a more detailed picture of leisure perception at South African universities, and c) using a mixed-method research design, including both quantitative and qualitative methods for gathering data. / Thesis (PhD (Recreation Science))--North-West University, Potchefstroom Campus, 2013.

Participation in campus leisure and recreation programmes can provide university students with various benefits, but the provision of effective leisure programmes are complicated by the changes that have taken place in the demographic composition of the student population attending South African universities. Increases in the proportion of black students attending university, and decreases in the proportion of white students means that current students possibly exhibit leisure behaviours that differ from those of their predecessors. With eleven official languages in South Africa, the language diversity among students is a further issue with which leisure professionals have to contend. Students also come from different economic backgrounds, posing additional challenges to universities’ leisure service providers. Since demographic factors, including culturally based perceptions and values, ethnic identity, language, religious beliefs and family structure (Outley & Witt, 2006:112) may influence leisure behaviour and preferences, it is important for leisure professionals to understand how these factors influence the perceptions students have of leisure. For purposes of this study, leisure perceptions are conceptualised to include leisure meanings, leisure experiences and leisure constraints. Due to the lack of research regarding leisure within a South African context (Goslin, 2003:39; Wegner et al. 2006:249) the purpose of this study was to determine the relationship between demographic variables and leisure perceptions of selected South African first-year university students. The study utilised a once off crosssectional research design, using three research instruments, the Leisure Meanings Inventory (LMI), Leisure Experience Battery for Young Adults (LEBYA) and the leisure constraint questionnaire by Raymore et al. (1993:104). An availability sample was used that comprised 344 first-year students in academic programmes related to sport, leisure and recreation studies from six South African universities. Data analysis included confirmatory factor analyses, t-tests, ANOVA and 2-way ANOVA. For leisure meanings, results indicate that female students are more likely to see leisure as Exercising Choice and Achieving Fulfilment than are male students. Home language also influences leisure meanings, with Afrikaans students seeing leisure as Escaping Pressure, whereas English-speaking students associate it with Passing Time. Students staying in private accommodation associated leisure more with Passing Time than those in university hostels. Furthermore, students that are in a relationship are less likely to see leisure as Achieving Fulfilment than those that are not. For leisure experiences, white students are more aware of leisure benefits and opportunities than are black students, and experience less boredom and distress during their leisure. Additionally, white students are more aware of leisure benefits and opportunities than are Coloured students. Seeing that a lack of awareness of leisure participation benefits and opportunities often are associated with boredom, which in turn is associated with delinquent behaviour, the possibility exists that increased awareness of leisure may assist in combating delinquent behaviour among students. In terms of language, Afrikaans-speaking students and students that speak African languages experienced more challenge in their leisure than their English-speaking counterparts. This result may be either because of ethnic factors, such as traditions or customs associated with specific languages or because of language, per se, as proposed by the Sapir-Whorf hypothesis. With regard to leisure constraints, black students experienced greater interpersonal constraints than did white students, while white students experienced greater structural constraints than did black students. Additionally, Indian students experienced more intrapersonal constraints than did black students. Students staying in university hostels experience less structural constraints than those in private accommodation. Lastly, students from rural areas/informal settlements experienced less intrapersonal and structural constraints than students that grew up in towns and cities. The study is the first of its kind in South Africa, providing a new insight into leisure, and addressing the paucity of research within the South African context. Recommendations include the implementation of comprehensive leisure education programmes to inform students of the benefits of leisure and the opportunities available to them. In so doing, students can be assisted in negotiating constraints and in developing more complex leisure meanings. In order to meet the challenges, leisure professionals need to know how student diversity affects leisure programming; hence training of current leisure practitioners in the form of short learning programmes is suggested. Future research should include: a) modifications to the research instruments to accommodate the South African population and to increase reliability, b) replicating the study on a broader student population to provide a more detailed picture of leisure perception at South African universities, and c) using a mixed-method research design, including both quantitative and qualitative methods for gathering data. / Thesis (PhD (Recreation Science))--North-West University, Potchefstroom Campus, 2013.

Proteins have been optimized by evolution for billions of years to work on a nanometer scale. Therefore, they are extremely promising for nanotechnological applications. Cytoskeletal filaments propelled by surface-attached motor proteins have been recently established as versatile transport platforms for nano-sized cargo in molecular sorting and nano-assembly devices. However, in this gliding motility setup, cargo and motors share the filament lattice as a common substrate for their activity. Therefore, it is important to understand the influence of cargo-loading on transport properties. By performing single molecule stepping assays on biotinylated microtubules, it was shown that kinesin-1 motors first stop and then detach when they encounter a streptavidin obstacle on their path along the microtubule. Consequently, the deceleration of streptavidin coated microtubules in gliding assays could be attributed to an obstruction of kinesin-1's path on the microtubule rather than to "frictional" streptavidin-surface interactions. The insights gained by studying kinesin-1's behavior at obstacles were then used to demonstrate a novel sensing application: Using a mixture of two distinct microtubule populations that each bind a different kind of protein, the presence of these proteins was detected via speed changes in the respective microtubule populations. In future applications, this detection scheme could be combined with other recent advancements in the field, creating highly integrated lab-on-a-chip devices that use microtubule based transport to detect, sort and concentrate analytes. It has been envisioned that the kinesin-1-microtubule system could be used for even more complex appliances like nano-assembly lines. However, currently available control mechanisms for kinesin-1 based transport are not precise enough. Therefore, improved temporal control mechanisms for kinesin-1 were investigated: Using a polymer that changes its size in solution with temperature, starting and stopping of gliding microtubules was demonstrated. In combination with local heating by light, this effect could be used to control the gliding of single microtubules. Finally, a strategy to create photo-switchable kinesin-1 was developed and tested for feasibility using molecular modeling.

Proteins have been optimized by evolution for billions of years to work on a nanometer scale. Therefore, they are extremely promising for nanotechnological applications. Cytoskeletal filaments propelled by surface-attached motor proteins have been recently established as versatile transport platforms for nano-sized cargo in molecular sorting and nano-assembly devices. However, in this gliding motility setup, cargo and motors share the filament lattice as a common substrate for their activity. Therefore, it is important to understand the influence of cargo-loading on transport properties. By performing single molecule stepping assays on biotinylated microtubules, it was shown that kinesin-1 motors first stop and then detach when they encounter a streptavidin obstacle on their path along the microtubule. Consequently, the deceleration of streptavidin coated microtubules in gliding assays could be attributed to an obstruction of kinesin-1's path on the microtubule rather than to "frictional" streptavidin-surface interactions. The insights gained by studying kinesin-1's behavior at obstacles were then used to demonstrate a novel sensing application: Using a mixture of two distinct microtubule populations that each bind a different kind of protein, the presence of these proteins was detected via speed changes in the respective microtubule populations. In future applications, this detection scheme could be combined with other recent advancements in the field, creating highly integrated lab-on-a-chip devices that use microtubule based transport to detect, sort and concentrate analytes. It has been envisioned that the kinesin-1-microtubule system could be used for even more complex appliances like nano-assembly lines. However, currently available control mechanisms for kinesin-1 based transport are not precise enough. Therefore, improved temporal control mechanisms for kinesin-1 were investigated: Using a polymer that changes its size in solution with temperature, starting and stopping of gliding microtubules was demonstrated. In combination with local heating by light, this effect could be used to control the gliding of single microtubules. Finally, a strategy to create photo-switchable kinesin-1 was developed and tested for feasibility using molecular modeling.

Stumbo and Peterson (2004:9) argue that the participation in meaningful leisure activities may lead to the improvement of elderly people’s health, well-being and quality of life. Changes which are associated with old age, such as the increase in adverse health conditions; however has a significant impact on leisure participation of the elderly (Austin et al., 2006:49). For the purpose of this study, the following questions need to be answered: a) Are physical, social, spiritual and cognitive leisure activities part of the leisure profile of persons sixty years and older? b) Do structural, interpersonal and intrapersonal constraints play a role in limiting the leisure participation of persons sixty years and older? c) Does a relationship exist between participation in physical, social, spiritual and cognitive leisure activities and perceived well-being of people sixty years and older? d) Can a leisure activity paradigm be compiled to indicate the leisure participation of persons sixty years and older? To answer these questions, this study focused on using a phenomenological research design to enquire about the meaning of the leisure phenomenon in elderly people’s lives (Fouché, 2005:270). This study was developed in accordance with the mixed methodological approach referred to by De Vos (2005b:361) as a combination of quantitative and qualitative research used in a single study. For the purpose of this study, one hundred and ten elderly people (men and women), sixty years and older and members of the Potchefstroom Service Centre for the Aged, participated. An availability sample was used to identify the participants who completed the questionnaire and participated in the focus group interview. Seventy two participants (60 females and 12 males) completed the questionnaire, whereby eight participants (5 females and 3 males) participated in the focus group interview. According to the results, respondents 60-64 years old indicated that they participate more in social, creative and cultural, and general leisure activities. Although 60% of these respondents (60-64 years) experience low levels of health, 80% still participate in physical leisure activities. The results suggested that these respondents (60-64 years) also participate less in travelling and outdoor leisure activities than respondents 65-74 years old and 75 years and older. Regarding respondents 65-74 years old, the results indicated higher levels of participation in social leisure activities, followed by general leisure activities. These respondents (65-74 years) participate more in travelling and outdoor leisure activities than the other age groups (60-64; 75 and older). Compared to the respondents 60-64 years, the leisure participation in creative and cultural and physical activities of respondents 65-74 years is significantly lower, even if the results showed they have a healthier health profile than respondents 60-64 years. The results showed that respondents 75 years and older participate more in general leisure activities, followed by social leisure activities and creative and cultural leisure activities. In comparison with respondents 60-64 years, respondents 75 years and older participate more in travelling and outdoor leisure activities. Although respondents 75 years and older, according to the results, have a healthier health profile than respondents 60-64 years and 65-74 years, participation in physical leisure activities was still very low. Regarding the relation between the leisure profile and the different types of living arrangements, it showed that respondents living in retirement villages participate more in social, general and physical leisure activities whereas respondents living in their own homes, participate more in general, social and creative and cultural leisure activities. However, respondents living with their children or family, or in a communal home, participate more in social leisure activities. In terms of the importance of leisure participation in elderly people’s life, the results indicated that 60% respondents 60-64 years, acknowledge leisure participation as very important in their lives, whereas 6% respondents 65-74 years and 75 years and older (21%), indicated leisure participation as not important. According to the respondents’ health profile, in relation to living arrangements and gender, women respondents living in retirement villages experience lower health levels than those living with their children or family, or in communal homes as well as male respondents. The results indicated that most of the respondents who experience average to low health levels, participate in social leisure activities whereas those who participate in outdoor leisure activities experience average health levels. In terms of happiness, well-being and quality of life, the male respondents living in retirement villages experience higher levels of happiness, well-being and quality of life compared to those living with children or family, or in communal homes. Women respondents living in their own homes or with their children or family, or in communal homes experience the highest levels of happiness, well-being and quality of life. This study also suggests that elderly people’s leisure participation can be programmed and planned by using a leisure activity pyramid. This leisure activity pyramid place social activities at the foundation of the leisure program, from where general, creative and cultural, physical, outdoor and travelling leisure activities can develop. The results showed, elderly people have a need to experience leisure benefits; hence the leisure benefits respondents 65-74 years old experience, includes interaction with others, whereas respondents 75 years and older indicated that they experience personal growth as a leisure benefit. Respondents (male and female) 65-74 years old indicated that meeting other people was the biggest leisure benefit, whereas respondents 60-64 years indicated that they participate in leisure activities to experience physical challenges while respondents 75 years and older participate in leisure activities to experience relaxation. In terms of the constraints which can limit participants’ leisure participation or exclude them from it, the respondents experience financial shortages as the most important constraint. The results showed that constraints are experienced differently between gender and age groups. Hence, the male respondents 65-74 years old and female respondents 75 years and older, indicated a shortage of time as the most important constraint, while male respondents 75 years and older, as well as female respondents between 60 and 74 years, indicated financial shortages as the most important constraint. According to the results, it seemed that respondents 85 years and older experience time and security, economic and structural, personal and programming as constraints. Respondents living in a flat on the same premises as children or family, experience time and security as constraints in contrast to those living with children or family, who experience economic and personal constraints. According to this study it is clear that old age and the provision of leisure services to older people, is a very complex issue. In the light of this information it is necessary for tertiary institutions to provide specialized training for recreation students, in the field of providing leisure services to older people, to meet the complex leisure needs of the elderly. / Thesis (PhD (Recreation Science))--North-West University, Potchefstroom Campus, 2013

Stumbo and Peterson (2004:9) argue that the participation in meaningful leisure activities may lead to the improvement of elderly people’s health, well-being and quality of life. Changes which are associated with old age, such as the increase in adverse health conditions; however has a significant impact on leisure participation of the elderly (Austin et al., 2006:49). For the purpose of this study, the following questions need to be answered: a) Are physical, social, spiritual and cognitive leisure activities part of the leisure profile of persons sixty years and older? b) Do structural, interpersonal and intrapersonal constraints play a role in limiting the leisure participation of persons sixty years and older? c) Does a relationship exist between participation in physical, social, spiritual and cognitive leisure activities and perceived well-being of people sixty years and older? d) Can a leisure activity paradigm be compiled to indicate the leisure participation of persons sixty years and older? To answer these questions, this study focused on using a phenomenological research design to enquire about the meaning of the leisure phenomenon in elderly people’s lives (Fouché, 2005:270). This study was developed in accordance with the mixed methodological approach referred to by De Vos (2005b:361) as a combination of quantitative and qualitative research used in a single study. For the purpose of this study, one hundred and ten elderly people (men and women), sixty years and older and members of the Potchefstroom Service Centre for the Aged, participated. An availability sample was used to identify the participants who completed the questionnaire and participated in the focus group interview. Seventy two participants (60 females and 12 males) completed the questionnaire, whereby eight participants (5 females and 3 males) participated in the focus group interview. According to the results, respondents 60-64 years old indicated that they participate more in social, creative and cultural, and general leisure activities. Although 60% of these respondents (60-64 years) experience low levels of health, 80% still participate in physical leisure activities. The results suggested that these respondents (60-64 years) also participate less in travelling and outdoor leisure activities than respondents 65-74 years old and 75 years and older. Regarding respondents 65-74 years old, the results indicated higher levels of participation in social leisure activities, followed by general leisure activities. These respondents (65-74 years) participate more in travelling and outdoor leisure activities than the other age groups (60-64; 75 and older). Compared to the respondents 60-64 years, the leisure participation in creative and cultural and physical activities of respondents 65-74 years is significantly lower, even if the results showed they have a healthier health profile than respondents 60-64 years. The results showed that respondents 75 years and older participate more in general leisure activities, followed by social leisure activities and creative and cultural leisure activities. In comparison with respondents 60-64 years, respondents 75 years and older participate more in travelling and outdoor leisure activities. Although respondents 75 years and older, according to the results, have a healthier health profile than respondents 60-64 years and 65-74 years, participation in physical leisure activities was still very low. Regarding the relation between the leisure profile and the different types of living arrangements, it showed that respondents living in retirement villages participate more in social, general and physical leisure activities whereas respondents living in their own homes, participate more in general, social and creative and cultural leisure activities. However, respondents living with their children or family, or in a communal home, participate more in social leisure activities. In terms of the importance of leisure participation in elderly people’s life, the results indicated that 60% respondents 60-64 years, acknowledge leisure participation as very important in their lives, whereas 6% respondents 65-74 years and 75 years and older (21%), indicated leisure participation as not important. According to the respondents’ health profile, in relation to living arrangements and gender, women respondents living in retirement villages experience lower health levels than those living with their children or family, or in communal homes as well as male respondents. The results indicated that most of the respondents who experience average to low health levels, participate in social leisure activities whereas those who participate in outdoor leisure activities experience average health levels. In terms of happiness, well-being and quality of life, the male respondents living in retirement villages experience higher levels of happiness, well-being and quality of life compared to those living with children or family, or in communal homes. Women respondents living in their own homes or with their children or family, or in communal homes experience the highest levels of happiness, well-being and quality of life. This study also suggests that elderly people’s leisure participation can be programmed and planned by using a leisure activity pyramid. This leisure activity pyramid place social activities at the foundation of the leisure program, from where general, creative and cultural, physical, outdoor and travelling leisure activities can develop. The results showed, elderly people have a need to experience leisure benefits; hence the leisure benefits respondents 65-74 years old experience, includes interaction with others, whereas respondents 75 years and older indicated that they experience personal growth as a leisure benefit. Respondents (male and female) 65-74 years old indicated that meeting other people was the biggest leisure benefit, whereas respondents 60-64 years indicated that they participate in leisure activities to experience physical challenges while respondents 75 years and older participate in leisure activities to experience relaxation. In terms of the constraints which can limit participants’ leisure participation or exclude them from it, the respondents experience financial shortages as the most important constraint. The results showed that constraints are experienced differently between gender and age groups. Hence, the male respondents 65-74 years old and female respondents 75 years and older, indicated a shortage of time as the most important constraint, while male respondents 75 years and older, as well as female respondents between 60 and 74 years, indicated financial shortages as the most important constraint. According to the results, it seemed that respondents 85 years and older experience time and security, economic and structural, personal and programming as constraints. Respondents living in a flat on the same premises as children or family, experience time and security as constraints in contrast to those living with children or family, who experience economic and personal constraints. According to this study it is clear that old age and the provision of leisure services to older people, is a very complex issue. In the light of this information it is necessary for tertiary institutions to provide specialized training for recreation students, in the field of providing leisure services to older people, to meet the complex leisure needs of the elderly. / Thesis (PhD (Recreation Science))--North-West University, Potchefstroom Campus, 2013

This paper presents an innovat ive cons t ruct ion of a probabilistic model for predicting chance situations. It describes the construction of a four phase model, derived from an intense qualitative analysis of the written responses of 94 mathematically talented middle school students to the probabilistic compound event problem: “How many doubles are expected when rolling two dice fifty times?” We found that the students’ comprehension process of compound event situations can be broken down into a four phase model: beliefs, subjective estimations, chance estimations and probabilistic calculations. The paper focuses on the development of the model over the course of the experiment, identifying the process the students underwent as they attempted to answer the question. We explain each phase as it was reflected in the students\' rationalizations. All phases, including their definitions and students’ citations, will be presented in the paper. While not every student necessarily goes through all four phases, an awareness and understanding of them all allows for efficient, effective intervention during the learning process. We found that guidance and learning intervention helped shorten the preliminary phases, leading to more relative time spent on probabilistic calculations.

The purpose of this study was to investigate relationships in the asset-based approach. This study forms part of a longitudinal asset-based community intervention research project. A qualitative approach was followed, guided by a phemenological epistemology. Informed by theories on relationships, the systems theory and literature on the asset-based approach I constructed a conceptual framework on relationships in the asset-based approach. In this conceptual framework relationships within the asset-based approach were described in terms of personal needs of the individual, the influences of relationships, the nature of relationships and the context within which asset-based relationships occur. Purposeful sampling was applied to select eight educators from three schools in the communities of Soshanguve, Eersterust and Oshoek as participants. Data was collected by means of semi-structured phenomenographical interviews used together with observations (documented as visual data, field notes and personal reflections). Based on the literature review I conceptualised relationships in the asset-based approach, thus adding to the literature on relationships and on the asset-based approach. Five prominent categories of description emerged subsequent to the phenomenographic data analysis. These categories were visually presented in a phenomenographical outcome space. Teamwork emerged as the main category. The two categories care and support and communication were included in the teamwork category. The participants experienced barriers in the asset-based intervention process but overcame them in order to achieve positive changes due to relationships. This study contributed to the knowledge base of relationships in the asset-based approach. / Thesis (PhD)--University of Pretoria, 2009. / Educational Psychology / unrestricted

This paper presents an innovat ive cons t ruct ion of a probabilistic model for predicting chance situations. It describes the construction of a four phase model, derived from an intense qualitative analysis of the written responses of 94 mathematically talented middle school students to the probabilistic compound event problem: “How many doubles are expected when rolling two dice fifty times?” We found that the students’ comprehension process of compound event situations can be broken down into a four phase model: beliefs, subjective estimations, chance estimations and probabilistic calculations. The paper focuses on the development of the model over the course of the experiment, identifying the process the students underwent as they attempted to answer the question. We explain each phase as it was reflected in the students\'' rationalizations. All phases, including their definitions and students’ citations, will be presented in the paper. While not every student necessarily goes through all four phases, an awareness and understanding of them all allows for efficient, effective intervention during the learning process. We found that guidance and learning intervention helped shorten the preliminary phases, leading to more relative time spent on probabilistic calculations.

Educators strive to improve student learning outcomes and there are numerous theories suggesting how this is best achieved. However, application of these theories to the coal face of a classroom is often fraught with obstacles resulting in poor outcomes. Constraints imposed by educational policy, school systems, structures and the individual students themselves, realistically require adaptation of theoretical techniques if genuine learning is to be imparted to students. This paper discusses some of the issues surrounding the practical implementation of new methodologies into the classroom and identifies important factors that affect teenagers in their learning of mathematics. Working within the constraints, constantly confronted with obstacles, can be frustrating and demoralising. This paper reflects on twenty years of classroom teaching of mathematics to students with relatively poor socio-economic backgrounds and the lessons learnt from them that may assist teachers to remain enthusiastic and creative with the energy to truly improve mathematics education. Key issues explored in the paper include: ‘Realities of a teacher’s working day’, ‘The learning of mathematics within a government secondary system’, and ‘What can be done to ensure mathematical learning takes place?’