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1. Select two digital technologies that you believe would enhance children's conceptual understanding of place value and/or basic operations.

2.  Share the technologies and explain why you selected each, including how it aligns with your pedagogical approach to teaching mathematics. Justify your thinking.

Background on Children's Conceptual Understanding of Place Value and Basic Operations

Children encounter the four basic operations naturally when they work with real life problems (Reys, Lindquist, Lambdin and Smith, 2007). Through the manipulation of objects and use of drawings of models and pictures, young children are able to identify the type of operation required to solve a word problem. However, Haylock and Cockburn (2013) acknowledge that many teachers over emphasise the use of ‘take away’ as the only model for subtraction. This causes problems when children encounter word problems with a variety of language for subtraction.

The most common structure connected with subtraction is ‘partitioning’. This is when a set of objects are identified and then some are taken away (Haylock and Cockburn, 2013). Examples for young children can include:

• There are 3 teddies on the bus, one teddy gets off. How many teddies are left on the bus now?
• There are 10 cakes on a plate, 5 cakes get eaten. How many are left?
• I have 10p. I spend 3p. How much do I have left?

Research suggests that this is the easiest structure of subtraction for children to learn (Haylock and Cockburn, 2013 and Reys et.al, 2007). This is due to the persistent use of the words ‘take away’ which results in children assuming that this is the only subtraction structure.

A second structure for subtraction is known as 'comparison' (Haylock and Cockburn, 2013). This involves the children finding the difference. Essentially nothing is being taken away in this type of problem but a subtraction operation is being performed. Examples of problem can include:

• Bob had 3 sweets and Tom had 5 sweets. How many more sweets does Tom have?
• I have 15p and Susie has 10p. How much more money does Susie have than me?
• 6 people walk to school and 2 people come in the car. How many more people walk to school that use the car?

The third structure that Haylock and Cockburn (2013) identify is the 'complement of a set'. In this type of problem a set of objects are logically separated into two groups (Reys et al., 2007). The reader knows how many objects there are in the whole set and in one part of the set. They must then find out the number in the remaining part of the set. This requires them to perform a subtraction operation. Examples of these problems include:

• There are 12 animals on the farm. 6 of them are sheep. How many are pigs?
• I have 8 lollies in a bag. 3 lollies are red. How many are blue?
• There are 10 children in a class. 7 children are boys. How many are girls?

The forth structure of subtraction that Haylock and Cockbur (2013) identify is known as 'reduction'. Children need to understand the notion of counting back to use this. Examples include:

• A 7 stone person looses 4 stone. What do they weigh now?
• A 15p chocolate bar in the shop is reduced by 5p. How much does it cost now?
• The 10cm plant gets its stem chopped 3cm. how tall is it now?

The final structure is the 'inverse of addition'. This can be a tricky concept for young children to grasp as there is generally some language features that we relate to addition (Haylock and Cockburn, 2013). Examples of this type of problem include:

• What must be added to 7 to make 10?
• I have \$26 and I want to buy a top that costs \$30. How much more do I need?
• Dan is 8, Susie is 3. How much older is Dan?

If teachers are able to use language, which does not just relate to the formal language of ‘take away’, then they will better equip children in the future to solve a verity of problems. Building up the connections in this language, using concrete materials and real life situations will enable children to solve various subtraction problems using all structures (Haylock and Cockburn, 2013).

Drawing on the subject readings (please indicate which ones), respond to the following

• Research and evaluate 2–3 digital technologies that align with your pedagogical approach to teaching mathematics.
• Select two digital technologies that you believe would enhance children's conceptual understanding of place value and/or basic operations.
• Share the technologies and explain why you selected each, including how it aligns with your pedagogical approach to teaching mathematics. Justify your thinking.

Technology can provide a rich learning tool for children to use (British Association for Early Childhood Education, n.d.), which also gives them a sense of control. It has been argued that technology and its uses are just as important as literacy and numeracy in the school curriculum (Siraj-Blatchford and Whitebread, 2003).  If children are to actively participate in the ever-changing world then we need to equip them the best we can (Siraj-Blatchford and Whitebread, 2003). The challenge for educators is being able to use technology as part of their teaching pedagogy and for it not to feel like an add on to the already busy curriculum (Moir, 2014).

Challenges in Teaching Subtraction Structures

On an interactive whiteboard many experiences can be opened up to children. General searching for information and pictures can support children’s interests around the classroom (Moir, 2014). A simple search for types of different animals can then be transferred into bar graphs. The whiteboard allows for a bigger screen for children to see and the opportunity to tap and press buttons and be a physical part of the learning session. You are able to roll dice, flip coins, set a timer and lay out dominoes on the board, which can be used, in a number of mathematical challenges for the children. Subertising cards can flash up and children respond by calling out a number, two dice rolled and children add up the total.

Online media can be displayed on the interactive board. Games such as SPLAT support the learning of place value. The teacher asks the chid to ‘splat’ a number on the 100 chart. They then ‘splat’ the number 10 more/less. The technology makes the game far more exciting and interactive which helps to engage the learners (Moir, 2014).

Video clips can be watched from various Internet sites such as ABC Splash (2014) and YouTube, which can support the children’s understanding of a particular topic, act as an introduction or simply as revision at the end. This type of media is sometimes what children need to be able to visualise a concept. Videos of counting nursery rhymes can show visually how we count up and down the number line. Songs such as ‘5 little speckled frogs’ or 10 green bottles’ can be used. As well as this, sites such as ‘Topmarks, (2014)’ have many games to choose from to add to a mathematical lesson. These can be used in rotations, whole class or for individual use on tablets.

“Teachers of young children need to lay foundations of experience and networks of connections on to which future experiences of number can be built.”

(Haylock and Cockburn, 2017)

Technology is a tool that can be used to make some of these connections.

Coloured objects are those that have distinguishable colours, that is to say that they can be easily be identified by the viewers {the learners} due to their difference in the appearance hence easy judgement.

More examples of digital tools used in math learning includes;

• Academy of math -is intended at children besieged by math in school, it is also a comprehensive tool that aids students to get results.  There are numerous subjects to choose from, and instructors can device the resources on the platform into their own teaching.
• Pattern shapes -it makes the children top understand the possessions of fractions, shapes and generating precise data is relaxed by means of Pattern Shapes. Children can be able to measure angle3ss using protractor, this encourages creativity in them.
• Math playground -in this case, children will always enjoy learning while playing the games that best interests them. This kind of learning is easy for them since there is no pressurising of the math concept on them or rather they learn due to frequent exposure to the math concepts.

Assessment 2: Portfolio Tasks (Module 3)

An important task that can be used to develop a child’s understanding of estimations is by use of an interesting object. There should be a relation to the child’s daily experience with the object. This can be a big deal in visualizing the practical learning of estimation. The child can easily understand estimation when, for instance portion a fruit that he/she usually consume in their premises in the daily diet. The making of the pieces out of the fruit enables the child to easily understand the estimation factor {Sarama & Clements, 2009}.

Moreover, it can be habitual to the child when relating to estimate the pieces each time the similar objects appear and partitioning is done. The action of portioning assists the children to realize the real estimation of a whole object. The whole process enables them to estimate when the object is portioned into half. Then after that the subsequent portioning will enable them to relate to the succeeding estimation of the fragment in relation to the entire object

The student’s capability of understanding the idea of estimation can be enhanced when relating the diverse parts while portioning. When an object that is being portioned by the teacher is one that the students relates with in their daily life, the idea of estimation becomes easy to grasp by the students since they are conversant with it in their daily basis. basis (N***eau & World Bank, 2011).

Nevertheless, the frequency of the exposure of the students in learning how to portion a fruit, which is they normally consume in their daily life; it helps them to internalize the knowledge of estimation.

Therefore, the idea of estimation should be easy for students to learn since it is a practical activity that they normally indulge in their daily life. For instance, assume one the eldest in a family of four children and he has one orange in that each sibling should at least taste something. The eldest has the task of portioning the orange into desired pieces such that each gets a portion of the fruit {Haylock, D., & Cockburn, A. D.,2013}

References

Moir, T. (2014). Getting in touch with technology without losing touch with early childhood pedagogy. Educating Young Children: Learning and Teaching in the Early Childhood Years, 20(1), 34–37.

Haylock, D., & Cockburn, A. D. (2013). Understanding mathematics for young children (4th ed.). London, England: Sage.

Reys, R. E., Lindquist, M., Lambdin, D. V., Smith, N. L., Rogers, A., Falle, J., Frid, S., & Bennett, S. (2012). Helping children learn mathematics (1st Australian ed.). Brisbane, Australia: Wiley.

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