• 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.
    • 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. Because 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 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.

    Summary
    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.

    The NumberSense Mathematics Programme Curriculum
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  • 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 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, full curriculum coverage is achieved.

    The NumberSense Workbooks offer full curriculum coverage.  The NumberSense Mathematics Programme has been created to support children’s development of a robust sense of number and deep understanding of mathematics. The programme 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 Workbooks 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.

    The NumberSense Mathematics Programme Curriculum
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  • FAQ 3: Which NumberSense Workbook should I use for my child?

    Understanding the NumberSense Mathematics Programme Workbooks:

    The workbooks of the NumberSense Mathematics Programme represent a mathematical journey from the start to the end of primary school. Presented as a journey, the programme provides for differentiated teaching that is responsive to the developmental level of each child. The NumberSense Workbooks provide a coherent mathematics programme that addresses all the elements of the primary school mathematics curriculum in one place.

    There are four Workbooks per year, per grade. The four Workbooks per grade provide full curriculum coverage for that grade, without the need to develop and/or supply additional learning materials.

    Understanding how children learn:

    Children learn best when the learning content (and conceptual demand) match their developmental level. A child’s developmental level may not always be grade appropriate and therefore materials that provide for differentiated teaching which is responsive to the developmental level of each child are crucial.

    Children will benefit most from the NumberSense Mathematics Programme if they start with the workbook that matches their stage of number sense development. In that way they will be able to work confidently and independently through the workbook. The workbooks are developmental in nature. Each workbook builds on the concepts and skills developed in the previous workbook. To gain as much as possible from the workbook series, children should work through the materials in the sequence that they appear in the workbook.

    Please contact for further assistance.

    NumberSense Workbook selection (grade level guide)
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  • 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. 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 understands the philosophy behind the books. The workbooks should not be taught but rather worked through and patterns and strategies discussed. 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.
    • Downloadable print masters of teaching aids and resources.
    • Resources (GeoGenius Construction Kit, GeoGenius Visualisation Kit, Number line, Flard cards, Projection files, NumberSense Activity Kit and resources).
    • Regular teacher and parent workshops in major centers 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.

    Please contact 021 706 3777 or mail info@NumberSense.co.za for further assistance.

    Resources and Support
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  • FAQ 5: Is there a memo or answer key for the NumberSense Workbooks?

    Short answer:

    No, there is no solution set for the NumberSense Workbooks. Moreover, it is unlikely that we will develop one.

    Extended answer and rationale:

    The NumberSense Mathematics Programme has been developed based on our understanding of how children learn. Learning involves the construction of knowledge based on experiences and prior knowledge.

    Children are actively involved in the construction of their knowledge through interacting with situations, and then reflecting on what they did and noticed when they have completed the task(s).

    Simply knowing that a response is correct or incorrect does not encourage children to reflect on the tasks that they completed and on how they completed them. Focusing on whether responses are correct or incorrect alone does not support learning. Instead, it encourages the development of procedures that children do not understand and which they cannot apply in unfamiliar situations.

    Our concern with providing a solution set is that it will reduce teaching to a focus on correct and incorrect answers; a focus on performing procedures over developing understanding. Success in mathematics is much more than ‘getting the right answer’ – it involves understanding what you are doing.

    It is against this background that we do not provide a solution set. We want teachers to prepare for lessons by doing the pages themselves so that they are ready to support children in a reflection of what they did and what they noticed. Such reflection supports children in constructing their knowledge with understanding.

    The NumberSense Mathematics programme has been thoughtfully developed to support children in developing knowledge with understanding. The role of the teacher is not only to check whether answers are correct or incorrect; it is to support children in reflecting on what they did. This involves teachers asking 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?

     

    A key responsibility of teachers is to prepare for their lessons.

    The pages of the NumberSense workbooks are the lesson, and, with time and practice, children should be able to complete these pages without much direct instruction.

    Teachers using the NumberSense Workbooks do not have to develop the content of the lesson. Rather, lesson preparation for them involves thinking about the questions they will ask children on the completion of the task to help the children reflect on what they did, to notice patterns and structure, and to develop their understanding.

    In the absence of a solution set, lesson preparation involves teachers completing the page of the lesson themselves. We maintain that it is in doing the page themselves that teachers become aware of what it is that we want children to notice and reflect on when they complete the page. By completing the page of the lesson themselves, teachers are better prepared to lead the reflection that is needed. By completing the page of the lesson themselves, teachers are also better prepared to support learners when they get stuck.

    We are confident that teachers should be able to complete the page of the workbook that their class will be working on. After all, a teacher should not be teaching Grade 2 mathematics, if they are not – at a minimum – able to do Grade 2 mathematics.

    In summary, because we know that learning involves so much more than knowing if your answer is correct or incorrect, we have not provided a solution set. This forces teachers to develop their own solution set, which, in turn strengthens the teacher’s ability to support their learners.

    Teachers are always welcome to contact the NumberSense Team (info@NumberSense.co.za) if they get stuck or need help with a particular task.

  • 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 256 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.

    Please contact info@NumberSense.co.za for further assistance.

    NumberSense Workbook 1 Supplementary Worksheets
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  • 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.

    Please contact orders@NumberSense.co.za for further order-related assistance.

  • 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 no 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.

    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 download is sufficient for an entire school as the information may be shared within a school computer network.

    NumberSense Workbook Projection Files
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  • 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.za

    NumberSense Mobile App
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  • FAQ 11: What other products does NumberSense offer?

    The NumberSense Mathematics Programme offers the following products:

    • NumberSense Workbooks 00 & 0 (Grade R)
    • NumberSense Workbooks 1-28 (Grade 1-7)
    • Activity Kits
    • Activity Cards and resources
    • NumberSense Projection Files which have all the NumberSense Workbooks in English and Afrikaans
    • Flard Cards
    • GeoGenius Construction Kit
    • GeoGenius Visualisation Kit
    • Number line
    • Device Stamp Set
    • MathsSense (Grade 8 & 9)

    Please call the office 021 706 3777 or email info@NumberSense.co.za to find out more.

    NumberSense Product Range
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  • 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; can 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) using 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.

    From Workbook 3 an extra question that has been added to many counting activities to make the multiplicative reasoning that the counting activity is meant to reveal more visible. For example, a counting activity on the page will ask to count not only the number of hands and the total number of fingers, but also to think about the number of fingers on a hand. This draws attention to the relationship between hands and fingers, namely that three hands with five fingers per hand have (3 × 5) 15 fingers altogether.

    The multiplication symbol is introduced in Workbook 6 (second term of Grade 2).