- FAQ 1: NumberSense and the Curriculum and Assessment Policy Statement (CAPS): Is NumberSense CAPS aligned?
NumberSense and the Curriculum and Assessment Policy Statement (CAPS) (2012)
The NumberSense Mathematics Programme is a comprehensive mathematics programme. A question that is often asked is whether or not the NumberSense Mathematics Programme is CAPS aligned. The simple answer is yes! However, to better understand the answer requires an informed understanding of both CAPS and the NumberSense Mathematics Programme.
The Curriculum and Assessment Policy Statement (CAPS) (2012)
The Curriculum and Assessment Policy Statement (CAPS) (2012) is a single document that combines the National Curriculum Statements Grades R – 9 (2002) and the associated Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines. This means that CAPS has two important sections relevant to this discussion:
- Specification of content (aka the curriculum) (Section 3.2 of the Foundation Phase CAPS and Section 2.7 of the Intermediate Phase CAPS); and
- Clarification of content (Section 3.3 of the Foundation Phase document and Section 3 of the Intermediate Phase document)
- In the Foundation Phase, the section suggests “… sequencing of topics into terms … pacing of topics over the year …” and goes on to say that “some Content Areas require more time”… but “all Content Areas must be taught every term” … “The sequencing of topics into terms gives an idea of how topics can be spread and re-visited through the year. … Teachers may choose to sequence and pace the content differently from the recommendations in this section” i.e. teachers may change slightly the suggested amount of time allocated to topics. (Foundation Phase CAPS, 2012, pg. 31)
- In the Intermediate Phase, the section suggests “… a sequencing of topics per term … pacing of topics over the year … ” and goes on to say that “Each content area has been broken down into Topics. The sequencing of topics within terms provides an idea of how content areas can be spread and re-visited throughout the year. … Teachers may choose to sequence and pace the content differently from the recommendations in this section. However, cognisance should be taken of the relative weighting and number of teaching hours of the content areas for this phase.” (Intermediate Phase CAPS, 2012, pg. 31)
The NumberSense Programme and CAPS
In terms of the overview of CAPS provided in the previous section:
- The NumberSense Mathematics Programme is aligned with – and in many cases exceeds – the specified content in CAPS.
- A “content” mapping for all of the pages in the NumberSense Workbooks and NumberSense Companion programme can be found under the Resources tab.
- The NumberSense Mathematics Programme addresses all content areas every term.
- In the NumberSense Programme, mathematics is developed in an interrelated way. Content is not presented in blocks or topic units, but rather through activities that reveal the interrelated nature of the mathematics. On account of this, children are exposed to many of the content areas (topics) each week, not just once a term.
- The NumberSense Mathematics Programme develops mathematics guided by age, grade and number range appropriate developmental trajectories for each concept. That is, in the NumberSense Mathematics Programme learning opportunities are developmentally sequenced. CAPS also sequences learning opportunities developmentally. In short, the NumberSense Mathematics Programme and CAPS broadly sequence “content” in a similar way.
- The NumberSense Mathematics Programme workbook activities can be seen in the illustrative examples provided in the “Clarification of content” sections for each grade in CAPS. This is no small surprise as some of the contributors to the writing of CAPS were previously involved in the development of the NumberSense Mathematics Programme. The NumberSense Mathematics Programme was developed and published between 2009 and 2011 – before and during the development of CAPS – and was no doubt used as a resource by the authors of CAPS.
- The NumberSense Mathematics Programme advocates that the implementation of the programme is most effective in classes where the teacher works with smaller groups of children (arranged by developmental level) for short periods of time while the other children are working independently on written work or investigations (in the case of measurement, geometry and data handling). A careful reading of CAPS will reveal that CAPS advocates exactly the same classroom organisation (Foundation Phase CAPS, 2012, pages 8 to 10).
All the above noted, there is one very important distinction between the NumberSense Mathematics Programme and CAPS. CAPS is, as the title states, a policy statement. The NumberSense Mathematics Programme is a mathematics programme. The one describes what should be included in a mathematics programme the other is a mathematics programme. The workbooks and other elements of the NumberSense Mathematics Programme can be given to children and they can use these resources to learn about and do mathematics. CAPS cannot be used by students. CAPS is intended to support teachers and material developers to develop learning programmes.
In summary, although the NumberSense Mathematics Programme predates CAPS and is different in its purpose, the NumberSense Mathematics Programme and CAPS are well-aligned in terms of content, sequencing and philosophy.
- FAQ 2: Does the NumberSense Mathematics Programme provide a complete mathematics curriculum?
The NumberSense Mathematics Programme is aligned with the South African mathematics curriculum. That said, the way in which topics are addressed does not always coincide with the sequence of the current CAPS document. Concepts in the NumberSense and Companion Workbooks follow a developmental trajectory and are visited and revisited on a regular basis. With the completion of each workbook, a child ‘covers the curriculum’ and by completing the workbooks intended for each year, the child does so several times.
The NumberSense Workbooks cover Numbers, Operations and Relationships as well as Patterns, Functions and Algebra. The Companion Workbooks cover Space and Shape (Geometry) and Measurement and Data Handling. In the Foundation Phase, these concepts are developed through activities and are not worksheet-based. So the Companion Workbook for the Foundation Phase is in the form of a Teacher Guide of activities which we believe will reveal the concepts and mathematics that we want the children to learn.
The NumberSense and Companion Workbook Series has been created to support children’s development of a robust sense of number and deep understanding of mathematics. The series is responsive to the developmental needs of children, is informed by current research on how children learn mathematics and provides a comprehensive mathematics solution for Grades R to 7.
In the early workbooks, the development of number sense starts with foundational concepts and understandings in a low number range. As children progress through the series they are supported and encouraged to develop increasingly sophisticated strategies and a deeper understanding of higher number ranges. The NumberSense and Companion Workbook Series provide daily practice. Children should, if working in the correct book, be able to work independently from one page to the next, asking for help and guidance if needed. The richly-illustrated and engaging workbooks can be used in a wide range of different ways.
With the publication of the NumberSense Companion Workbooks, we complete the mathematics curriculum coverage for Grades 4 to 7. It is our hope that the NumberSense Companion Workbooks will provide children with the same challenges and enjoyment that they get from the NumberSense Workbooks and that it helps them to experience mathematics as a meaningful, sense-making, problem-solving activity.
Teacher Guides for the NumberSense Workbooks 1-24 and Companion Workbooks Grade R-7 are available for download at the Teacher Guides tab (under the Resources tab).
- FAQ 3: Which NumberSense Workbook should I use for my child?
Please see the discussion on Selecting the initial NumberSense Workbook for a child.
Please contact info@NumberSense.co.za for further assistance.
- FAQ 4: What support are users of the NumberSense Mathematics Programme offered?
The NumberSense Mathematics Programme has been developed to support children’s development of a robust sense of number and a deep understanding of mathematics. In order to make mathematics a meaningful, sense-making activity, the workbooks provide problems for the children that reveal what we want children to notice or learn.
It is therefore beneficial that a teacher, parent, facilitator, tutor or any user of the programme has an understanding of the philosophy behind the books. The workbooks should not be taught but rather worked through and patterns and strategies discussed. In order to support this philosophy, we provide the following support materials and activities:
- An overview of the research and literature on how children learn mathematics that has influenced the development of the NumberSense Mathematics Programme.
- Web-based user guides for NumberSense Workbooks 1-24, Companion Workbooks Gr R-7.
- Downloadable print masters of teaching aids and resources.
- Classroom resources (GeoGenius Construction Kit, GeoGenius Visualisation Kit, Number lines, Flard cards, Projection CD, NumberSense Companion Kit and resources).
- Regular teacher and parent workshops in major centres across the country.
In all applications, the programme allows for differentiated learning support, independent engagement by children and the opportunity to experience mathematics as a meaningful, sense-making activity. Teachers and parents play an important role in the success of the programme. Not only is there a need to ensure that children are working in the most appropriate workbook but teachers also need to monitor children’s progress for the identification of problems, misunderstanding and necessary interventions. Furthermore, it is critical that teachers and parents discuss the activities with the children. Ask the children to explain their answers, describe any patterns they may have observed and invite them to ask questions. This contributes to their development of a strong sense of number.
See NumberSense Workbooks for guidance and sample pages to get you started.
Please contact 021 706 3777 or mail info@NumberSense.co.za for further assistance.
- FAQ 5: Is there a memo or answer key for the NumberSense Workbooks?
The NumberSense Mathematics Programme has been developed to provide children with daily independent practice with foundational mathematics concepts that research has shown to be predictive of future success in mathematics.
Success in mathematics relies on having knowledge of a range of mathematical concepts and skills, being able to apply that knowledge and those skills in a range of contexts and situations that are both familiar and unfamiliar with an understanding of what you are doing and the ability to reason about what you are doing. Success in mathematics is so much more than “getting the right answer”!
We have resisted producing solution sets for the workbooks for fear that the focus of the work in the workbooks shifts from noticing and reflecting on the patterns and mathematical structure that the activities on each page are designed to reveal, to merely checking if the answers are correct or not. That said, as more and more teachers use the workbooks in their classes it is also important that they are confident in knowing the correct solutions to each of the questions on a page.
As you reflect on the work that learners have done on each page, be sure to ask questions such as:
- How did you do that?
- Why did you do that?
- What did you notice?
- Have you done this before? How is this different to what you did last time?
Our experience is that children benefit most when the teacher does the page themselves before the lesson. In so doing, the teacher gets a better sense of the purpose of the page and an understanding of what the page is seeking to develop. Again, our experience is that as teachers do more and more of the programme themselves, they gain a greater insight into the workbooks, insight into their own understanding of mathematics and of what it means to do mathematics.
The Solution sets can be found under the Resources tab, in the Teacher Guide section:
- Workbooks 00-12 (Foundation Phase)
- Workbooks 13-24 (Intermediate Phase)
- The solutions for the Companion Workbooks for Grades 4-7, can also be found here, as part of the Companion Workbook Teacher Guides.
Please email info@NumberSense.co.za should you have questions that the Solution Sets do not support and answer.Solution Sets (Workbooks 00-24)
- FAQ 6: Are supplementary worksheets available for the NumberSense Workbooks ?
We do not supply supplementary worksheets for our workbooks. The workbooks were designed to cover a page a day, a book a term. This means that you have 192 worksheets (pages) available to you for the year! We have, however, developed supplementary worksheets for Workbook 1, as many of the teachers felt that the workbook moved too quickly. For your support, we have developed User Guides for each of our workbooks and hope that the guidance these give will assist you in unpacking the pages to enable both remediation and extension.
Please contact info@NumberSense.co.za for further assistance.NumberSense Workbook 1 Supplementary Worksheets
- FAQ 7: How do I cope marking the NumberSense Workbooks?
The Workbooks present a tension – on the one hand we are trying to provide a fair amount of daily practice, consolidation and reinforcement opportunities for children, while on the other hand, we do not want to “kill” teachers. Our sense is that, in general, children do too little constructive mathematics practice per day. In some cases we find teachers limiting the amount of work they set children each day in an effort to manage their own marking loads and stresses. This has disastrous implications for children.
With marking a class’ work, we suggest that this should or could be done on an ‘impression basis’. Look at the page and make one of three decisions:
1. The child is getting most or all of the work right: Circle any glaring errors, initial the page and put the book on the “no problems” pile.
2. The child is making a number of consistent errors across the pages: Circle question(s) that the child should redo, initial the page and put the book on the “must talk with these children” pile. When next you get a chance you call this group of children together and talk about the typical errors that they are making.
3. The child is making a hash of things: Initial the page and put the book on the “must assign an easier book” pile. Assign these children an easier book that best suits their developmental state.
- FAQ 8: Is there a minimum order? How long will it take for my Workbook to get to me?
We accept orders of any size. You can order one book if you wish.
Our delivery turn-around time is 3-4 working days after confirmation of your order.
- FAQ 9: Is it possible to get an electronic version of the NumberSense Workbooks for projection?
Yes. We make our NumberSense projection files available to schools that use the NumberSense Mathematics Programme at a nominal charge.
The files have copies of the workbooks that the school has ordered in a format that allows teachers to project the workbooks onto a screen using a computer and data projector or smart board. This format enables the projection of the page or exercise that the class is busy with. Currently, these contain the English, Afrikaans, isiXhosa, isiZulu, Setswana and Sesotho versions of Workbooks 00-24, as well as the Companion Workbooks Grade 4-7 in English and Afrikaans.
Each file comes with software that enables you to open the files. You need to install the latest version of CopySafe before you can open the files. If you have noticed that last year’s files won’t play anymore, it is because the contents of each file expires at the end of December. We update our projection files each year. Please contact us if you would like to purchase these files. One purchase is sufficient for an entire school as the information may be shared within a school computer network.NumberSense Workbook Projection Files
- FAQ 10: Are the NumberSense Workbooks available for Android and iOS?
The NumberSense Mathematics Programme is available in app format for both Android and iOS devices. Without losing any of the rich pedagogical approaches that underpin the success of the paper version, the mobile version provides a range of additional benefits:
- Marking is automatic, providing children with instant feedback.
- Teachers and parents receive instantly accessible reports on the progress of children. Detailed and curriculum-linked feedback and analysis allow for remediation as and where required.
For further detail on the NumberSense App, please mail appsupport@NumberSense.co.zaNumberSense Mobile App
- FAQ 11: What other products does NumberSense offer?
The NumberSense Mathematics Programme offers the following products:
- NumberSense Workbooks 00-24 (Grade R – 7)
- NumberSense Companion Workbooks (Grade 4 – 7)
- NumberSense Companion Teacher Guides (Gr R – 3)
- NumberSense Companion Activity Kit and resources
- NumberSense Projection Files which have all the NumberSense Workbooks in English, Afrikaans, isiXhosa, isiZulu, Setswana and Sesotho, as well as the Companion Workbooks Gr 4-7 in English and Afrikaans
- Flard Cards
- GeoGenius Construction Kit and GeoGenius Visualisation Kit
- NumberSense Number line
- NumberSense Device Stamp Set
- NumberSense App (Android and Apple)
Please call the office 021 706 3777 or email info@NumberSense.co.za to find out more.
- FAQ 12: How should children count the fingers on the hands in Workbooks 1-10?
We want children to treat the ‘hands and fingers’ situations as follows:
- All hands have five fingers. This is true even if a hand’s fingers are folded over.
- For example, if there are 12 hands then there are 60 fingers; whether the fingers are upright or not, they are still part of the hand.
- The reason for including activities that involve counting fingers is that we are trying to encourage children to see the efficiency of counting in fives.
- Fingers provide a natural collection of five.
- FAQ 13: How should children count the eyes on the faces in Workbooks 0-10?
We want children to treat the ‘eyes and faces’ situations as follows:
- All faces have two eyes. This is true even if an eye is not visible because it is covered by hair.
- The reason for including activities that involve counting eyes is that we are trying to encourage children to see the efficiency of counting in twos.
- Eyes provide a natural collection of two.
- FAQ 14: When are the 'times tables' introduced in the NumberSense Workbooks?
We do not encourage the memorisation and rote reciting of multiplication tables. The reciting of multiplication tables in no way means that learners understand the multiplication facts that they are singing; are able to apply them with understanding and/or reason with them. That said, we do believe that learners should know a range of “multiplication facts” and their interrelationships. These facts become facts not because the learner can recite them but rather because they perform the multiplications so often that they reach a point where they know the calculation as a fact without having to resort to the calculation that produced it.
We start developing multiplicative thinking from as early as Workbook 2 (second term of Grade 1) through the use of tables that record the number of objects in a collection of such objects. For example we use tables to show that one hand has five fingers, two hands have ten fingers and three hands, fifteen fingers. In so doing we are laying the foundation for what will become one, two and three groups of five which in turn becomes 1 × 5; 2 × 5; and 3 × 5 etc.
The multiplication symbol is introduced in Workbook 6 (second term of Grade 2).
- Testimonials: What our User Group has to say about the NumberSense Mathematics Programme
Feedback from the fourth term workshops:
“By writing this tiny note I want to express gratitude for the helping hand that the NumberSense Mathematics Programme has been for me and my school. There are few training sessions where I take home fresh ideas, practical guidance and critical thinking skills. The NumberSense workshops that I have had the opportunity to attend are one of those. Your programme really makes a huge difference in the special needs of the children in my class.”
“Thank you so much for the wonderful course today. I learnt a great deal and enjoyed connecting with other teachers.”
“Thanks for another great workshop. We can’t wait to get started on the programme.”
Teacher, Selborne Primary
“Our boys have been using the workbooks for 3 years and although they are flying through them, they also challenge the boys who find the CAPS curriculum too easy. We have also recently been told that the Grade 8 mathematics average at Selborne College has improved by nearly 15% and we are in the process of putting all these statistics together along with the Conquesta Olympiad and ANA results; we are confident that we are going to find that we have had a steady increase in overall results. We are very excited about how the boys are challenged by the NumberSense Mathematics Programme because we feel that the CAPS curriculum alone does not do so. The weaker boys are not as advanced but their attitude towards mathematics has changed in the following ways: they complete a page a day, their mental arithmetic has improved and they are not nervous when approaching word problems.
We are planning to hold a parent-child mathematics challenge because we want to show the parents what their children are capable of. This will cover the basic concepts taught in the NumberSense Workbooks and will be in the form of a race with a few family mathematics ideas thrown in. We are really excited about the progress that has been made thanks to the NumberSense Mathematics Programme.”
Mr Gamiet: Principal, A.W. Barnes Primary School
“For many years our school has struggled to improve the quality of the teaching of mathematics and raise the level of mathematics proficiency amongst our teachers and children. The major challenge for our teachers has been the large numbers of children in our classes. The NumberSense Mathematics Programme was introduced to our school earlier this year by Brombacher and Associates, through the mediation of Shikaya. It has been the best intervention implemented at our school for a number of years. Small-group teaching was re-introduced and the benefits were immediately visible. All the children in the class were kept busy: while one group of children were on the mat, the other children carried on with activities in their NumberSense Workbooks. The teachers were all excited about the introduction of the NumberSense Mathematics Programme and a remarkable improvement in mathematical literacy has been achieved. Children in Grade 1 have extended their numeracy capabilities and the children’s ability to solve problems has improved. The Grade 2 and 3 teachers are excited because at the start of each year they can simply proceed with the activities in the NumberSense Workbooks as the children now have the ability to work independently. The improvement in mathematics teaching has led to some of our children receiving awards for mental mathematics, reading and spelling at a recent East London District competition run by the Department of Education. We believe the confidence that the children have acquired in mathematics assists them in the other learning areas too.”
“I just wanted to offer my sincere thanks to the NumberSense Mathematics Programme developers. My daughter is completing her final NumberSense Workbook in the next few weeks of Term 1, Grade 7. The NumberSense Mathematics Programme has given her a wonderful foundation that will support her future mathematics learning.”
Stina, Kempton Park
“I am using your workbooks in a community mathematics clinic that I started at my church. Any child can attend these classes for free on a Wednesday afternoon. The children vary from Gr 1 to Gr 12. There are approximately 30 – 40 children who attend, of which 16 of them are from the local Children’s Home. Your workbooks really help me to handle the ability levels of the wide variety of children.”
- Affiliates: Shikaya
Shikaya is a non-profit, civil society organisation that recognises the crucial role that teachers can play in deepening and strengthening South Africa’s democracy. As such, Shikaya supports the personal and professional development of teachers to create a South Africa in which young people in schools are inspired and supported to become responsible citizens and future leaders in our democracy, valuing diversity, human rights and peace.
Shikaya and the NumberSense Mathematics Programme
Shikaya has partnered with Brombacher and Associates to provide in-class mathematics training to Foundation Phase teachers in schools across South Africa. As part of the project, NumberSense Workbooks are supplied to every Grade 1, 2 and 3 child in each school. Teacher support and training is provided alongside the distribution of the workbooks so that they are used in the best possible way. The mathematics teacher training project started in 2014 with 3 schools in the Central District in Cape Town and has rapidly grown to 12 schools: 8 in Cape Town, 2 in East London and 2 in Port Elizabeth. Key similarities between the project schools are that they are situated in low socio-economic areas and have teachers that are eager to learn. Each Grade 1, 2 and 3 teacher is visited weekly in their classroom by a coach who instructs the teacher in their mathematics teaching.
Brombacher and Associates look forward to a continued positive relationship with Shikaya and trust that their combined efforts will help to improve the standard of mathematics education in the Foundation Phase across South Africa.Shikaya
- Affiliates: JumpStart
JumpStart is an NPO with a background in youth development programmes. Their name, ‘JumpStart’, and credo – ‘Thinking it forward’, encompasses all that they do in order to give those less-privileged a decisive ‘jump-start’ through three essential keys to development: education, qualification and employment. Since 2002, it has run youth education, skills development and social entrepreneurial initiatives to sustainably empower South African youth. With origins in the ICT sector, the programme grew into an industry-accredited learning and employment programme that is known today as the JumpStart Software Labs.
Two key factors have had a dramatic effect on the success of the JumpStart Software Labs:
- The first came from the learners themselves. From early on, a culture of “Think It Forward” began to develop within the JumpStart Labs. Previous learners gave of their own time and new-found expertise to jump-start their peers and new recruits. This fostered a mentorship relationship amongst the learners which continues to this day.
- The second significant factor was the close partnership with private companies. The number of software engineers in South Africa is limited and the opportunity exists to grow this capacity with local resourcing. The JumpStart Engagement Model, a commercial service offering to the local economy, was initiated to fill the gap. Under private company mentorship, the learners took to the market with their new-found careers to deliver on real-world software solutions.
More recently, JumpStart has extended its programme into schools in the South African townships of Diepsloot, Eldorado Park, Soweto and the Underberg region of KZN. The emphasis here is on educational interventions to address the pre-requisite foundations in Numeracy and Computer Science. JumpStart then partnered with Aarnout Brombacher of Brombacher and Associates in using the NumberSense Mathematics Programme to address the area of numeracy.
JumpStart and the NumberSense Mathematics Programme
JumpStart has adopted the NumberSense Mathematics Programme as a vehicle for making a difference in the mathematical experiences of children in schools supported by JumpStart. Schools are supplied with workbooks for the children, appropriate training for the teachers and year-round, in-class and in-school support by a team of appropriately qualified and trained interns. We call these interns the ‘JumpStart Tutors’. The tutor is there to support the teachers in the NumberSense Mathematics Programme and to provide on-the-ground, quality assurance of the programme’s success. The tutors are often unemployed matriculants and JumpStarts aims to help develop their academic and career aspirations while they intern at JumpStart schools. In addition to the workbooks, training and support, the JumpMedia Labs and JumpStart Software Labs have partnered with Brombacher and Associates to develop both video and software support for the programme. This support will enable the programme to scale effectively.
The video materials will consist of short vignettes that deal with topics such as the importance of the development of number sense and the implementation of the NumberSense Mathematics Programme. These videos will offer support on how to use the workbooks effectively and discuss the role of the different features of the workbooks. Software that is currently being developed will assist the project manager to monitor the progress of the children in their workbooks at all schools and in so doing enable the project to deliver workbooks to children as they finish one workbook and need the next. Other software applications include management of annual testing and monitoring of progress suites. As connectivity in rural schools is not always possible, the NumberSense Mathematics Programme applications are made accessible via mobile tablet and iPad, enabling teachers and field workers to capture the information on site with immediate remote access and reporting.JumpStart