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Wiki for Maths Interviews hello girls :) just started the intro please add in more or change round if you want :) also please place your part of the report here and we'll read and put together the full report together, so feel free to swap and cange things around!!! and don't be offended if your bit gets changed hahaha I know you'll prob want to change some of mine!!! hahaha love Allison... See you all Friday :)

Looks good Allison :) I added mine everyone and put in something for the intro...I hope it makes sense??? xxx

Intro
Throughout the semester a number of mathematical interviews were conducted to discover a child's number concept. Students were selected from different classrooms and year levels, which include, two grade preps, two grade ones, two grade twos and two grade threes. Throughout the interviews their development of number concepts were investigated and they were placed on the Victorian Essential Learning Standards levels based on their capabilities of answering all questions throughout the interview. Teacher implications were also analysed, which will be discussed further in this report.

The number concepts explored were conservation, group recognition, comparisons and one-to-one correspondence, all of which are important stages of early number development. The interviews also looked at counting; the 'intricate process by which children call numbers values by name' (Reys et al. 2009, p.143) and how each child used different counting strategies to problem solve and identify various numbers. In particular the data collected recorded each child's capability to count on, count back, skip count. In addition to this, the four important principals on which the counting process rests were investigated further. These are; 1) one-to-one correspondence, 2) stable-order rule, 3) order-irrelevance rule and 4) the cardinality rule. Through the information gathered, interviewers were able to determine the students interviewed familiarity with numbers. Students familiarity with numbers are built on their prior experiences where they have seen numbers at home, down the street and at school just to name a few places. The knowledge that children gain about numbers are termed prenumber experiences. Prenumber experiences are important for children as they are the building blocks for childrens number concepts which helps to create number sense in children.

vels part...
Throughout the interviews the students were ranked in accordance to the Victorian Essential Learning Standards (VELS). The Victorian essential learning standards for mathematics are outlined further in this report. According to the VELS website (2005) the following levels apply. Level 1- Students model addition by using objects and count them together. They use ordinal numbers to describe the position of elements. They use materials to model addition and subtraction. Students use simple conjectures such as, ‘nine is four more than five’. Level 2-Students usemathematical symbols and language, such as ‘plus and minus’. They are able to order and model the counting numbers up to 1000. Students are able to skip count by 2, 4, 5’s starting from any natural number, and recognise patterns. Students perform simple addition and subtraction up to 100. They add and subtract one and two digit numbers by counting on and back. Level 3- Students are able to confidently skip count and create number patterns. They develop concepts of equivalent fractions and compare fraction sizes. Students are able to round numbers up and down. They extend addition and subtraction computations to three digit numbers. Students are able to skip count forward and backwards using multiples of 2, 3, 4, 5, 10 and 100. Once the interviews were complete and the data was recorded the results are shown as follows. Throughout the prep interviews both children were reported as level 1 as child one used blocks to model addition and subtraction. Although was unable to confidently skip count .Child 2 also used blocks to model addition and subtraction and was unable to confidently skip count. Results from Grade one, showed that there was a significant difference between child one and child two. Child one was found to be at Level 2; as they can skip count up to 100. Whilst also using appropriate mathematical language, such as plus, minus, and so on. The student also relates mathematical symbols to everyday life. Whereas child two was portrayed at a level one standard as they used visual cues such as diagrams to help with subtraction and addition. Throughout the Grade two interviews there was also a significant difference in the students’ standards. Child one was placed at a level two standard as they were able to skip count up to 100, and use mathematical language, such as plus, minus, and so on. Also relates mathematical symbols to everyday life. Whereas child two was placed at a Level one standard as they were unable to skip count and were not confident to attempt any questions about skip counting. Finally the Grade 3 results proved to be (both) seated at a level 2, progressing to level 3. As they are able to skip count and use place value, although unable to compare simple fractions, they were able to identify some fractions on the flashcards. As they were not tested on three digit numbers, it is unable to test whether they can be classified as level 3.

Implications in teaching: Jen

There are many implications for teaching mathematics, especially when students ‘have different background experiences, interests, levels of motivation and styles of learning’ (Reys et al. 2009, p. 15). This was particularly evident in the recent interviews conducted, as each of the eight students showed signs of different background knowledge relating to numbers.

In the prep age group it was obvious that both students had only seen numbers at home and at school. In comparison, in the grade one aged group one of the students had also seen numbers at home, but the other had a very strong understanding of numbers because he loved to watch football. His knowledge of players numbers, stats and goal scores would have greatly helped him with his number recognition skills. In addition to this, looking at the grade two and grade three aged groups, again the students showed they had background knowledge of numbers from their home environments. This sort of information is very important for developing teaching approaches, as the students prior knowledge of numbers can help with help them to improve their abilities and retain mathematical knowledge and skills. A good approach that incorporates this prior knowledge would be to make connections, which ‘help children see how mathematical ideas are related to each other and to the real world’ (Reys et al. 2009, p. 19).

Relating maths concepts to the real world is not always an easy task for teachers. For example, from the studies conducted seven out of the eight students related most of their knowledge of numbers to their home environments and only one related it to the sport of football. In a classroom setting, the teacher would have to evaluate how he or she would engage all eight students in a topic that covered both the sporting and home interests. The teacher might view the planning of the learning in two different ways; 1) The Constructivism Approach, or 2) The Behaviourism Approach.

Constructivism ‘suggests that rather than simply accepting new information, students interpret what they see, hear or do in relation to what they already know’ (Reys et al. 2009, p.21), whereas Behaviourism ‘focuses on observable behaviours and is based on the idea that learning means producing a particular response (behaviour) to a particular stimulus, (something in the external world), (Reys et al. 2009, p.21). Both views could help students learn and both also have their own implications for teaching, however the constructivist view would be better suited to assist students in make connections from maths into the real world. This is because by building on what knowledge the students already have, their knowledge is extended and they are more likely to retain the information taught at a later date. For example, a group of students might all be at the same level of understanding but if their prior knowledge is different how they construct new ideas will be different. In a classroom setting there might be twenty students all excellent at skip counting by fives, however ten students love watching football and know that every goal is six points. Therefore, when the skill of learning how to count by sixes is introduced, their new knowledge will develop faster than the students would are not familiar with watching football scores.

Another implication in teaching mathematics is how communication is used in conjunction with various teaching approaches. The studies conducted focused mainly on obtaining verbal answers, instead of using written communication to convey thinking. This worked for most of the children, however for Susie’s first child in grade two, writing out the problem for section 8.9 helped her to reach the correct answer. This was also evident in Allison interview with her first child, as she too had to write out the problems to solve for section five. The results from the interviews may have been different if the children were given more questions that required written answers because studies have shown that ‘putting our thoughts in writing forces us to think more deeply or helps us clarify our thoughts’ (Reys et al. 2009, p. 30). In conclusion, the approach of discussing mathematics is still a great way of communicating answers however, when assessing all students both written and verbal communication should be incorporated in the learning process.