Wait a second!
More handpicked essays just for you.
More handpicked essays just for you.
Mathematics practice standards compared with elementary grades' mathematical understanding
Don’t take our word for it - see why 10 million students trust us with their essay needs.
Recommended: Mathematics practice standards compared with elementary grades' mathematical understanding
The biggest difference between eight mathematical practice standards and mathematical content standards is the mathematical content are the math concepts are the same for each grade level and the eight mathematical practice is where the children would apply the math concepts through reasoning, modeling, using tools, etc. When a child is first learning to add, they must understand the basic math concepts. The child would either draw pictures to help understand the concept, for example, when I learning fen I would draw out the pieces. The child would ask themselves questions or ask the teacher for help. Learning to add and subtract requires thinking and reasoning which does not allow for an easy solution, for example, what step is next? It
also requires communication for their peers to see what they are doing wrong. From my understanding contextualize is pausing and thinking during a problem to check your work and decontextualize is to understand the problem and change the symbols in the problem.
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.
, the value of teaching subitizing skills in the classroom is clear. This ability provides a visual tool to young students as they develop a basic understanding of numbers and one to one correspondence, and it establishes a firm foundation for the future skills of addition and subtraction facts. Possessing the knowledge of how and when students develop the cognitive understanding of this concept can drive a teachers instruction so that the students find greater success in the lesson. Knowing that comprehension of number conservation does not occur until age 5 or 6 will definitely have an effect upon early teaching of number sense.
Since 2010, there were 45 states that have adopted the same educational standards called Common Core State Standards (CCSS). The initiative is sponsored by the National Governors Association and the Council of Chief State School Officers and seeks to establish consistent education standards across the states. The Common Core Standards is initiative state-led effort that established a single set of clear educational standards for kindergarten through 12th grade in English and Mathematical standards. These standards help to educate all of the students equally, they help children who move from state to state, as well as they help to prepare students for college and workplace. The common core standard helps to provide a clear understanding for teachers and parents of what is expected of the students to learn. It is designed to help educate our children for the future; it gives them the knowledge and skill they need to be prepared for post secondary education and employment. "The standards are designed to be robust and relevant to the real world." (National Governors Association Center for Best Practices, Council of Chief State School Officers)
Mathematics has become a very large part of society today. From the moment children learn the basic principles of math to the day those children become working members of society, everyone has used mathematics at one point in their life. The crucial time for learning mathematics is during the childhood years when the concepts and principles of mathematics can be processed more easily. However, this time in life is also when the point in a person’s life where information has to be broken down to the very basics, as children don’t have an advanced capacity to understand as adults do. Mathematics, an essential subject, must be taught in such a way that children can understand and remember.
Improving the mathematical skills is one of the most important educational aims of Monopoly and Uno game. These types of games depend mainly on numerical skills, such as subtraction and addition which Strengthens and improve these Arithmetic operations for children and in an easy and entertaining way.
Display the Unifix cubes on the table; first, explain to the child what we call a subtraction. Next, write down for the child the
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.
These new standards seem to be focusing more on both accountability and back to basics. As a math teacher I can be delighted by this focus. However, as a potential administrator, I realize this is too myopic a view. Indeed these standards have created a dilemma -- a conundrum -- a paradox.
In contrast, students with dyscalculia often use a count all method when working with math problems. As stated in Socioeconomic Variation, Number Competence, and Mathematics Learning Difficulties in Young Children “Young children who develop mathematical learning difficulties rely on the more basic “count all” finger strategies for extended periods…thus make frequent counting errors while adding and subtracting” (Jordan & Levine 2009, pp.63). Students with dyscalculia approach problems in a similar fashion and do not use effective strategies when working with numbers. As a result, they tend to take long periods of time to figure a problem and make mistakes when counting. On the other hand, students who use effective strategies, such as grouping when doing addition or subtraction are more likely to arrive at the correct
Mathematical dialogue within the classroom has been argued to be effective and a ‘necessary’ tool for children’s development in terms of errors and misconceptions. It has been mentioned how dialogue can broaden the children’s perception of the topic, provides useful opportunities to develop meaningful understandings and proves a good assessment tool. The NNS (1999) states that better numeracy standards occur when children are expected to use correct mathematical vocabulary and explain mathematical ideas. In addition to this, teachers are expected
Depending on one’s perspective, the use of calculators at the elementary school level is seen as either the solution to or cause of many of the problems affecting math education in this country. It has been known for a long time that early experience is able to shape the brain and behavior. In the stages of learning at a young age, to fully grasp a concept, a child must understand the principles how and why in order to apply any significance or relation to anything. This particularly applies to such a subject as that of math. Diane Hunsaker expresses her view as well in the following quote: “Math is as much about knowing why the rules work as knowing what the rules are” (668). It seems that Hunsaker is saying that before rules can be applied, there must be a foundation for them. This concept for math, and in general, trains the mind by exercising thinking skills. It is apparent that she agrees by examining her direct statement, “Math trains the mind.”
I believe that learning mathematics in the early childhood environment encourages and promotes yet another perspective for children to establish and build upon their developing views and ideals about the world. Despite this belief, prior to undertaking this topic, I had very little understanding of how to recognise and encourage mathematical activities to children less than four years, aside from ‘basic’ number sense (such as counting) and spatial sense (like displaying knowledge of 2-D shapes) (MacMillan 2002). Despite enjoying mathematical activities during my early years at a Montessori primary school, like the participants within Holm & Kajander’s (2012) study, I have since developed a rather apprehensive attitude towards mathematics, and consequently, feel concerned about encouraging and implementing adequate mathematical learning experiences to children within the early childhood environment.
Finger counting has been commonly practiced to facilitate children’s numerical development across cultures and times (Butterworth, 1999; Domas, Moeller, Huber, Willmes, & Nuerk, 2010). During early stages of development, fingers and external objects are often used to help children understand basic numerical concepts such as numerical quantity, the counting system and the symbolic representations using Arabic digits. The external numerical representation using fingers help children understand the one-to-one correspondence principle in meaningfully forming their fundamental knowledge in numeracy. Finger counting is considered a readily available and concrete scaffolding tool which aids calculation before children can master more advanced and adaptive cognitive strategies such as
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
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.