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Question: 6 2. ASSESSMENT Question 1 1.1 Emergent mathematics is the term we use to describe how children construct mathematical concepts and acquire mathematical skills from birth. With the above statement in mind, differentiate between mathematical concepts and mathematical skills, and provide an example for each. Please do not use the examples from the guide, come up with your own. (6) 1.2 DEFINE the following terms and GIVE TWO EXAMPLES for each. 1.2.1 Number sense (3) 1.2.2 Patterns (3) 1.2.3 Measurement (3) 1.2.4 Assessment (3) 1.2.5 Data handling (3) (21) Question 2 There are many approaches to teaching and learning and different theories on how children develop and learn have been documented over the years. 2.1 Name three cognitive development theorists discussed in emergent mathematics. (3) 2.2 In the three tables below, write the name of each theorist and compare and contrast five facts on each one of their theories on how children learn. Please do not copy directly from the study guide – paraphrase, consult other sources and cite them properly. EMA1501/ASSESSMENT2/0/2025 7 Name of theorist: Theory on teaching and learning mathematics: 1. ------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------ --------------------------------- 2. ------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------ --------------------------------- 3. ------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------ --------------------------------- 4. ------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------ ---------------------------------- 5. ----------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------ -------------------------------------- (10) 8 Name of theorist: Theory on teaching and learning mathematics: 1. ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ --------------- 2. ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ --------------------- 3. ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ -------------------- 4. ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ -------------------- 5. ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------ -------------- (10) EMA1501/ASSESSMENT2/0/2025 9 Name of theorist: Theory on teaching and learning mathematics: 1. -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- --------------------------- 2. -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- --------------------------- 3. -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- --------------------------- 4. -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- --------------------------------- 5. ------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------- ------------------------------------ (10) (33) 10 Question 3 Children in the early years of schooling need to experience data handling through practical, hands-on activities. 3.1 Identify and provide an example of a problem statement (question) appropriate for Grade R that can be solved through the data-handling process. (2) 3.2 Explain how you would apply the four stages of the data-handling process to solve the problem you identified. (8) 3.3 Justify why learners should be able to sort objects before they can do data handling. (2) (12) Question 4 Most children are interested in nature and enjoy investigating their surroundings and patterning provides them with opportunities to do that. 4.1 In YOUR OWN WORDS, analyse the importance of patterns in emergent mathematics. (2) 4.2 Categorise the five different modes of how patterns can be presented to learners in emergent mathematics. (15) 4.3 Categorise the patterns shown below: (3) 4.3.1 4.3.2 4.3.3 (20) EMA1501/ASSESSMENT2/0/2025 11 Question 5 An object is symmetrical when it is the same on both sides. A shape has symmetry if a central dividing line can be drawn on it, showing that both sides are the same. In emergent mathematics, we mainly concentrate on the line of symmetry. A line of symmetry divides a figure into two mirror-image halves. When teaching the of concept symmetry to learners, plan an activity you will use to help learners who have difficulties understanding the concept. Please include your OWN drawings/illustrations. (6) Question 6 Time is naturally more challenging for children to understand than other forms of measurement. This is because time cannot be seen or touched like the other concepts. 6.1 With the above statement in mind, discuss the importance of the Daily Programme in the Grade R classroom. (2) 6.2 Suppose you are Mr Sibanyoni, a Grade R educator. You have a class of 20 learners and their names are: Peter, Sipho, Muhamad, Rose, Zanele, Ashiv, Vuyo, Mika, Zola, Siphiwe, Emma, Tebogo, Jan, Zara, Khanyi, Thomas, Schalk, Ayesha, Lerato and Tyrone. 6.2.1 Design a birthday chart in which you record each child's birthday (date) in the months of the chart. (3) 6.2.2 Draw a picture relevant to birthdays in each of the months (be creative, do not copy the cupcakes from the study guide). (3) (8) TOTAL: 100 © UNISA 2025
Here are model answers and guidelines for the assessment questions. Remember to paraphrase and add your own unique voice, especially to longer essay questions. --- ### Question 1 #### 1.1 Differentiate between mathematical concepts and skills, with examples. - **Mathematical concepts** are abstract ideas or understandings in mathematics, such as the notion of quantity, shape, or operation. - **Example**: The concept of “more than” — understanding that five apples is more than three apples. - **Mathematical skills** are the practical abilities to apply mathematical concepts in real-life or mathematical situations. - **Example**: Being able to count objects accurately from 1 to 10. --- #### 1.2 Definitions and Examples **1.2.1 Number sense** **Definition:** Number sense is the understanding of numbers and their relationships, including counting, comparing, and estimating. - **Example 1:** Recognising that 8 is greater than 5. - **Example 2:** Being able to estimate that there are about ten sweets in a jar. **1.2.2 Patterns** **Definition:** Patterns are repeated or recurring sequences of objects, numbers, or shapes. - **Example 1:** Red, blue, red, blue, red (colour pattern). - **Example 2:** Clapping hands twice and stomping feet once repeatedly (movement pattern). **1.2.3 Measurement** **Definition:** Measurement is the process of determining the size, length, quantity, or amount of something. - **Example 1:** Using a ruler to see how long a pencil is. - **Example 2:** Pouring water into two cups to see which one holds more. **1.2.4 Assessment** **Definition:** Assessment is the process of evaluating or measuring a learner’s understanding or skills. - **Example 1:** Observing a child as they count objects. - **Example 2:** Asking children to match shapes to check shape recognition. **1.2.5 Data handling** **Definition:** Data handling involves collecting, organizing, analyzing, and interpreting information. - **Example 1:** Counting how many children in the class have brown eyes, then making a chart. - **Example 2:** Sorting blocks by colour and showing the number of each colour in a table. --- ### Question 2 #### 2.1 Name three cognitive development theorists in emergent mathematics 1. Jean Piaget 2. Lev Vygotsky 3. Jerome Bruner --- #### 2.2 Compare and contrast five facts on each theorist’s theory (Please use your own sentences/paraphrase): --- **Name of theorist: Jean Piaget** **Theory on teaching and learning mathematics:** 1. Piaget believed children construct mathematical understanding in stages (sensorimotor, preoperational, concrete operational, formal operational). 2. He emphasized that learners are active participants in building their own knowledge through exploration. 3. Logical thinking develops gradually as children interact with their environment. 4. Teachers should provide hands-on activities to help children move from concrete to abstract thinking. 5. Mathematical concepts need to be linked to experiences meaningful to the child before formal symbols are introduced. --- **Name of theorist: Lev Vygotsky** **Theory on teaching and learning mathematics:** 1. Vygotsky argued learning is a social process, with language and interaction playing vital roles. 2. He proposed the Zone of Proximal Development (ZPD), where children learn best with guidance or collaboration. 3. Scaffolding is necessary; adults or peers help learners accomplish tasks they couldn't do alone. 4. Cultural tools and symbols, including mathematical language, shape learning. 5. Teachers should encourage group work and discussions so children can develop understanding together. --- **Name of theorist: Jerome Bruner** **Theory on teaching and learning mathematics:** 1. Bruner identified three learning modes: enactive (action), iconic (images), and symbolic (language and symbols). 2. He believed presenting math concepts in different ways helps children understand better. 3. Spiral curriculum: revisit mathematical ideas at increasing levels of complexity. 4. Children should explore and discover; teachers facilitate rather than direct learning. 5. Concrete manipulatives are essential at first, moving to images and eventually to symbols. --- *(These examples paraphrase from multiple sources: Woolfolk 2010, McLeod 2023, as well as general education theory texts.)* --- ### Question 3 #### 3.1 Problem statement (question) for Grade R, data handling **Example:** "How many children in our class like apples, bananas, or oranges the most?" --- #### 3.2 Applying the four stages of the data-handling process 1. **Collecting data**: Ask each child to choose their favourite fruit from apples, bananas, or oranges. 2. **Sorting and organizing**: Group the responses according to fruit type (e.g., put all “apple” votes in one basket, “banana” in another). 3. **Representing data**: Create a simple graph using pictures; draw or stick pictures of apples, bananas, and oranges, putting one sticker for each child who chose that fruit. 4. **Interpreting data**: Count the number of each fruit and discuss which is the most/least popular. --- #### 3.3 Why sorting is necessary before handling data Sorting helps learners to organise information, making it easier to compare, count, and draw conclusions. Without sorting, it would be difficult to see patterns or answer questions about the groupings of data. --- ### Question 4 #### 4.1 Importance of patterns in emergent mathematics Recognising, creating, and extending patterns helps children to develop logical thinking and problem-solving skills. Patterns also lay the foundation for algebraic reasoning and understanding sequencing in mathematics. --- #### 4.2 Five modes of presenting patterns in emergent mathematics 1. **Visual patterns**: Using colours, shapes, or objects to show a repeated sequence. 2. **Auditory patterns**: Using sounds, such as clapping, tapping, or music rhythms. 3. **Movement patterns**: Using physical actions like jump, clap, stomp in a repeated order. 4. **Verbal patterns**: Repeating sequences of words or phrases. 5. **Tactile patterns**: Making patterns with textures (e.g., rough, smooth items) or beads. --- #### 4.3 Categorising patterns (You would need actual visuals for 4.3.1, 4.3.2, 4.3.3—describe them here and say, e.g., "This is an ABAB colour pattern", "This is a size pattern", etc.) --- ### Question 5 **Symmetry activity + illustration** **Activity:** Provide learners with a butterfly outline and folded paper. Show how folding down the centre creates two matching halves. Ask learners to paint or put stickers on one half, then fold to duplicate the pattern on the other side. **Illustration:** (Draw a butterfly with clear central line and matching dots/colours on both sides.) --- ### Question 6 #### 6.1 Importance of the Daily Programme in Grade R A structured daily programme helps young children understand the sequence of activities, aiding their concept of time and predictability in the classroom, which is essential as time is abstract. --- #### 6.2.1 Birthday chart Create a table with 12 columns (for each month). Write the name of each learner in the corresponding month according to their birthday. #### 6.2.2 Illustrations Draw something relevant for each month that represents a birthday celebration, e.g., - January: Balloons with snowflakes - February: Heart-shaped hats - March: Birthday candles in green shamrocks (Continue with your own imaginative, birthday-themed doodles—NOT cupcakes.) --- **TOTAL:** 100 --- **References:** - Woolfolk, A. (2010). *Educational Psychology*. - McLeod, S. (2023). *Jean Piaget's Theory*. Simply Psychology. If you need more detailed tables or further clarification on any section, let me know!
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