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.
Counting all is the base that serves as the foundation for the development of the other strategies. Count all introduces students in Kindergarten to the concept of creating a total by counting all the numbers once the two amounts have been represented by a drawing or fingers (Common Core Standards Writing Team, 2011). Simultaneously, the count on strategy draws from the knowledge acquire as the student progress on the count all method. For this approach, students learn to determine the total of the two addends by counting on from any of the addends. Lastly, students can use a recomposing strategy. The recomposing strategy encourages students to discover the sum by creating sets of numbers that equal the original digit, but are easier to manage. For instance, creating doubles or tens out of odd numbers.
The first problem I created was a join add to result unknown. The problem reads, Carlos collected 8 toy cars. His mom gave him 7 more cars. How many toy cars does Carlos have in all? This problem prompts students to joi...
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thinking, pp. 1–21.Used by permission of the Council of Chief State School Officers.
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Fuson, K. C., Clements, D. H., & Beckmann, S. (2011). Focus in grade 2: teaching with
curriculum focal points. Reston, VA: The National Council of Teachers of Mathematics,
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Van de Walle, J.A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Publication
The lesson is about knowing the concept of place value, and to familiarize first grade students with double digits. The students have a daily routine where they place a straw for each day of school in the one’s bin. After collecting ten straws, they bundle them up and move them to the tens bin. The teacher gives a lecture on place value modeling the daily routine. First, she asks a student her age (6), and adds it to another student’s age (7). Next, she asks a different student how they are going to add them. The students respond that they have to put them on the ten’s side. After, they move a bundle and place them on the ten’s side. When the teacher is done with the lesson, she has the students engage in four different centers, where they get to work in pairs. When the students done at least three of the independent centers, she has a class review. During the review she calls on different students and ask them about their findings, thus determining if the students were able to learn about place value.
Kathleen Shine Cain et al. at. The. Boston: Pearson Education Company, 2011. 52.
13th Ed. -. Jo Ray McCuen-Metherell and Anthony C. Winkler. Mason, OH: Cengage Learning, 2011. 428.
, 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.
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.
Guthrie , J. W., Heyneman, S. P., & Braxton , J. M. (2002).Encyclopedia of education . (2nd ed., pp. 283-289). Farmington Hill, Michigan: Cengage Gale.
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
The ASCA National Model. (n.d.). Newport News Public Schools. Retrieved June 5, 2014, from http://sbo.nn.k12.va.us/guidance/document
Reys, R., Lindquist, M., Lambdin, D., Smith, N., & Suydam, M. (2001). Helping children learn mathematics. New York, NY: John Wiley & Sons, Inc.
Math vs. Zombies- Grade Level: Third. Standard: The specific content area and Standard: CCSS.MATH.CONTENT.3.OA.C.7. Description: Math vs. Zombies can be set for students to practice with addition, subtraction, multiplication, division, and comparison. Within the game, students must solve the simple math problem correctly and quickly enough to be able to have time to zap the zombies. The app also offers games and practice problems for students in grades kindergarten-4th grade. Having such a wide variety of content allows for the independent work in the classroom to differentiated for each student. While the majority of the class might be working on multiplication, some students might still need to be working with addition or there could be high fliers working on more complicated concepts, such as division. This app is a great resource because it grows with the children and has something for them at nearly each stage in the early math education.Bloom's Taxonomy: Bloom's Taxonomy: 3.1 Executing- Students solve multiplication equations using the process that they have previously learned and can apply it to problems that are new to them.
The benefit of this method would be to understand the relationship between the addition and subtraction, however it does not allow the student to build upon that idea naturally and it seems that this was the case for other mathematical concepts: it was unnatural. I had the opportunity to interview a middle school student this semester and he was saying that although math wasn't his best subject, the assignments weren't fair. He elaborated on this idea by saying how his answers would be correct but because he used the method that he felt most comfortable with, he had points deducted. With Common Core in math, students are expected to learn a variety of different solving methods and solve problems using the particular method. I remember when I learned how to factor binomials, I had my own way of solving those types of problems because I didn't understand the conventional solution methods that were taught in my school.
During elementary school, children are not only developing their physical bodies, but there minds as well. They a...
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
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.
Hendron, J. (2003). Goochland County Public Schools. Retrieved from Goochland County Public Schools Web site: http://www.glnd.k12.va.us/resources/graphicalorganizers/