INTRODUCTION
Place value and the base ten number system are two extremely important areas in mathematics. Without an in-depth understanding of these areas students may struggle in later mathematics. Using an effective diagnostic assessment, such as the place value assessment interview, teachers are able to highlight students understanding and misconceptions. By highlighting these areas teachers can form a plan using the many effective tasks and resources available to build a more robust understanding. A one-on-one session with Joe, a Year 5 student, was conducted with the place value assessment interview. From the outlined areas of understanding and misconception a serious of six tutorial lessons were planned. The lessons were designed using
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Joe’s diagnostic assessment started out strong completing the two digit numbers with confidence. Moving on to the three digit numbers cracks in Joe’s understanding started to appear. Joe showed a good understanding of reading, writing and ordering two and three digit numbers. The knowledge of some more, some less and the ability of partitioning two digit numbers were also clear. Joe acknowledged that 36 less 10 is 26 because, “if you take away one bundle you are left with two bundles and six single ones.” The partitioning of the number 36 was achieved by splitting it into 26 and 10. Up until the point of some more, some less in the three digit numbers section Joe was displaying a strong understanding of place …show more content…
Though when asked what number is ten less than 408 Joe answered “three hundred and ninety two”. Joe being unable to give the number that is ten less of 408 displays a misconception of the base ten number system and the role the tens play, Burns (2010). Joe did not display the understanding that 408 is 40 tens and 8 ones and when one ten is removed he is left with 39 tens and 8 ones giving him the answer of 398. This misconception was displayed again when Joe declared he was unable to partition 592. Joe could not see 592 as 4 hundreds, 19 tens and 2 ones or 5 hundreds, 8 tens and 12 ones. In addition to the misconception of the base ten number system and the role the tens play Joe displayed a misunderstanding of early multiplicative thinking. Joe was asked how many times bigger is 300 than 3 and how many times bigger is 300 than 30. Joe answered the multiplicative questions using subtraction giving the answers 297 and 270, respectively. The use of subtraction implies that Joe sees multiplication as addition and does not relate multiplication with division, Booker et al. (2014). Joe did not make the connection that 3 goes into 300 one hundred times therefore 300 is one hundred times bigger than 3. The same connection was not made for the second question, 30 goes into 300 ten times therefore 300 is ten times bigger than 30. At this point in the interview it was clear what areas of
In the Case study of Reclaiming Rose Place there are several issues to think about. The first is the community in which the issues are occurring. This community has an extended history of racial discrimination and hate. There are several white supremacist leaders who lived in the area and have left family living in the area. This hate has been ingrained in the family members who still live in the community. The second issue is the district forcing integration on this community’s school which is causing multiple problems. The new principal being part of the minority that has been hated for so long is immediately met with distrust and disregard. The community does not want a minority in control of their school. The school currently employs only
For most people who have ridden the roller coaster of primary education, subtracting twenty-three from seventy is a piece of cake. In fact, we probably work it out so quickly in our heads that we don’t consciously recognize the procedures that we are using to solve the problem. For us, subtraction seems like something that has been ingrained in our thinking since the first day of elementary school. Not surprisingly, numbers and subtraction and “carry over” were new to us at some point, just like everything else that we know today. For Gretchen, a first-grader trying to solve 70-23, subtraction doesn’t seem like a piece of cake as she verbalizes her confusion, getting different answers using different methods. After watching Gretchen pry for a final solution and coming up uncertain, we can gain a much deeper understanding for how the concept of subtraction first develops and the discrepancies that can arise as a child searches for what is correct way and what is not.
During this lesson, I pushed my students to be able to justify their answers using their knowledge of tens and ones. While not explicitly taught during any of the curriculum lessons, it is a skill required on a number of questions on the test. I predict that some students will struggle with this portion of the test due to their lack of practice using academic language to rationalize their answers. My students “know” what numbers are greater or less, but during this lesson I still heard “I just knew” instead of them going back to their models every time to cite evidence to support their answer. As I finish out this year, and as I think about my teaching practice next year, this is definitely an area of growth that I want to focus
John has a strong performance among the Digit Span and Arithmetic subtests. The digit span subtests required John to recall and repeat auditory information in the proper sequences, both forward and backwards. A more complex sequence is required with the Digit Span Sequencing as it not only requires recall of digits, but manipulation and rearrangement of information in the correct sequence (Digit Span scaled score = 13). John scored higher in his Digits Backwards than on his Digits Forwards that suggests excellent numerical abilities. This is a rare event and only occur in 0.9% of Adult WAIS-III profiles (Digit Forwards scaled score = 10 and Digit Backwards scaled score=14). The Arithmetic subtest measures John’s computational skills, auditory short-term memory, numerical reasoning and speed, concentration, distractibility, acquired knowledge and logical reasoning. This subtests is a good indicator of John’s alertness, capacity for concentration, freedom from distractibility, auditory short-term memory and suggested John possesses the ability to focus on facts during emo...
Forest Woodward is well known as one of the adventures photographer and the filmmaker. As a young shooter, Woodward, shows unique techniques to direct few documentaries features films. Although, his contribution towards the photographer let him to a successful filmmaker and he able to manages good relationship between a photographer and a film director. Later on his life, filmmaker Woodward was able to discovers that he was a great influence by this dad, Doug Woodward, who walked into the wild and discovers the important place when he was a young man. The Important Places is one of my favorite documentary film directed by Woodward in 2013 from his dad landscapes’ memories when his father was a young man down the Colorado River, which ultimately
The front porch of my house was dirty, covered with red mud and the pain was chipping off the floor. So I decided to give it a face lift. This process involved washing and removing the furniture. Scrubbing the chipped paint of the floor. Giving the front porch floor a coat of paint.
This numbness is natural, stemming from the fact that humans simply do not deal with such numbers very often, and even when they are dealt with, they are seen as words, not rational concepts. The fact that absolutely everyone suffers from this difficulty could prove to be harmful in the future, as population grows at the seemingly infinitesimal rate of 2% per year, an amount that is actually quite large when the current number of people on Earth i...
Children can enhance their understanding of difficult addition and subtraction problems, when they learn to recognize how the combination of two or more numbers demonstrate a total (Fuson, Clements, & Beckmann, 2011). As students advance from Kindergarten through second grade they learn various strategies to solve addition and subtraction problems. The methods can be summarize into three distinctive categories called count all, count on, and recompose (Fuson, Clements, & Beckmann, 2011). The strategies vary faintly in simplicity and application. I will demonstrate how students can apply the count all, count on, and recompose strategies to solve addition and subtraction problems involving many levels of difficulty.
From the beginning of time there have been many anomalies in humanity. With the advancement of techniques, tools, and knowledge, our understanding of the world aspires to clarify our curiosities. The most beneficial to factors throughout our history would include our knowledge of numbers. Numbers hold great possibilities and bring forth answers to the most complex systems of life. Our mathematics is incorporated into basic aspects of our daily lives, allowing us to unlock our potentials and give keys to uncover the hidden secrets in the universe.
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
Sherley, B., Clark, M. & Higgins, J. (2008) School readiness: what do teachers expect of children in mathematics on school entry?, in Goos, M., Brown, R. & Makar, K. (eds.) Mathematics education research: navigating: proceedings of the 31st annual conference of the Mathematics Education Research Group of Australia, Brisbane, Qld: MERGA INC., pp.461-465.
This representation is called preverbal number knowledge, which occurs during infancy. Preverbal number knowledge occurs when children begin representing numbers without instruction. For instance, children may be familiar with one or two object groupings, but as they learn strategies, such as counting they can work with even larger numbers. As stated in Socioeconomic Variation, Number Competence, and Mathematics Learning Difficulties in Young Children “Thus only when children learn the count list and the cardinal meanings of the count words, are they able to represent numbers larger than four” (Jordan & Levine 2009, pp.61). Typical development occurs along a continuum where children develop numerical sense, represent numbers and then begin to understand the value of the numbers. These components are required when differentiating numbers and
The early acquisition of mathematical concepts in children is essential for their overall cognitive development. It is imperative that educators focus on theoretical views to guide and plan the development of mathematical concepts in the early years. Early math concepts involve learning skills such as matching, ordering, sorting, classifying, sequencing and patterning. The early environment offers the foundation for children to develop an interest in numbers and their concepts. Children develop and construct their own meaning of numbers through active learning rather than teacher directed instruction.
As a secondary subject, society often views mathematics a critical subject for students to learn in order to be successful. Often times, mathematics serves as a gatekeeper for higher learning and certain specific careers. Since the times of Plato, “mathematics was virtually the first thing everyone has to learn…common to all arts, science, and forms of thought” (Stinson, 2004). Plato argued that all students should learn arithmetic; the advanced mathematics was reserved for those that would serve as the “philosopher guardians” of the city (Stinson, 2004). By the 1900s in the United States, mathematics found itself as a cornerstone of curriculum for students. National reports throughout the 20th Century solidified the importance of mathematics in the success of our nation and its students (Stinson, 2004). As a mathematics teacher, my role to educate all students in mathematics is an important one. My personal philosophy of mathematics education – including the optimal learning environment and best practices teaching strategies – motivates my teaching strategies in my personal classroom.