Importance Of Misconceptions In Mathematics

1007 Words3 Pages
bulb-icon

Recommended: Misconceptions in math

Misconceptions are common place in mathematics. A misconception is defined as 'a perception or concept which does not support the original meaning' and within mathematics misconceptions are frequently misapplied concepts or algorithms. A misconception highlights a students' thinking and how they acquire or fail to grasp mathematical concepts (Cockburn & Littler, 2008).

Misconception 1 relates to question 2 of the sample year 3 Naplan assessment - Money and financial mathematics.
Common misconception students have when dealing with money is distinguishing the size of coins from the value of coins. Often students believe the bigger the coin, the higher the value. Another monetary misconception applies to place value and the student not understanding …show more content…

The knowledge exists to take away the values however their approach is incorrect. Confusion is created in the language used to 'take smaller number from larger' which results in students flipping or reversing numbers to get a result. This is referred to as an inversion error. Many students continue to make inversion errors when taking the smaller number from the larger one irrespective of where the numbers sit in arrangement. Not understanding place value and partitioning of Hundreds, Tens and Ones and the representative value of the digits could lead students to incorrectly answer this question and misconceive that a 4 in the tens place represents 4 instead of 4 groups of ten which equals 40. Teachers can model and use manipulatives such as MAB blocks to provide opportunities for students to remedy this misconception (Ojose, …show more content…

Many students conceive that the larger the denominator indicates a larger value (i.e.) 1/5>1/3>1/2>1/1. Students also misconceive that in adding fractions they add the numerators and denominators and the answers result in separate whole numbers (i.e.) 1/2+1/2=1+1=2 and 2+2=4 instead of the correct answer as 1. Students may choose incorrect answers through a lack of understanding of mathematical language relating to 'left' or 'half' as in question 6. Visually students can identify 8 biscuits in the picture and with that knowledge relate the question to halve this amount answering 4 or identifying half the picture blank, assume the answer would be 8. Hands on practice of adding sectors of fractions can assist students to understand the parts of a whole (Drews,

Show More
Related

  • Content Analysis of Student Learning

    1368 Words  | 3 Pages

    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.

    Read More

  • Douglas H. Clements Subitizing

    851 Words  | 2 Pages

    , 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.

    Read More

  • Frayer Model Of Interstruction: Personalized And Differentiated Instruction

    774 Words  | 2 Pages

    Content may be chunked, shared through graphic organizers, addressed through jigsaw groups, or used to provide different techniques for solving equations. For example, in a lesson on fractions, students could: Watch an overview video from Khan Academy. Complete a Frayer Model for academic vocabulary, such as denominator and numerator. Watch and discuss a demonstration of fractions via cutting a cake.

    Read More

  • Nt1310 Unit 2 Assignment

    2201 Words  | 5 Pages

    An appropriate mental method would be to partition both numbers into tens and ones and then adding them together according to their place value. This strategy requires a strong understanding of place value and encourages to split larger numbers into smaller units so they are easier to work with. First of all, I would change the calculation; 28 into ‘20 + 8’ and 13 into ‘10 + 3’. Now, I would add the tens together: ‘20 + 10 = 30’ and then add the ones together: ‘8 + 3 = 11’, which gives a calculation of ‘30 + 11’. The 11 can also be split into tens and ones (11 → 10 + 1). Once this is complete, I can add the tens (30 + 10 = 40) and then add the ones (40 + 1) to give a total of 41. The purpose of using this method is to encourage children to use the ‘jotting’ (informal) process to visualise mental mathematics and to work out larers number in their practise heads before moving onto addition written calculations in

    Read More

  • Place Value Assessment Paper

    1483 Words  | 3 Pages

    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

    Read More

  • Nt1310 Unit 4 Assignment 1

    676 Words  | 2 Pages

    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

    Read More

  • Misunderstandings and Misconceptions in Society

    421 Words  | 1 Pages

    To Kill A Mockingbird by Harper Lee shows a misunderstanding in society by demonstrating to us how society isn’t perfect. From a child’s point of view children incorporate misunderstanding by learning from their personal experience. I wasn’t aware of how bad our Earth was being destroyed. A similar event happened when Napoleon helped France and everyone thought that Napoleon was France’s savior but what France didn’t expect was that Napoleon had other ideas and was ambitious and planned on destroying cities and killing people in order to obtain power. Nowadays racism isn’t seen as much but people still discriminate and judge people by how they act, look or how economically stable people are.

    Read More

  • Interview With My Host Teacher Interview

    1507 Words  | 4 Pages

    ...ts work on the lessons independently or with a preservice teacher by using manipulatives or other mathematical tools it will allow them to fully grasp the concept that is being taught so they can do well in the long run of learning more complex mathematics.

    Read More

  • Procedural Lessons: Children and Mathematics

    1452 Words  | 3 Pages

    All children learn differently and teachers, especially those who teach mathematics, have to accommodate for all children’s different capacities for learning information. When teaching mathematics, a teacher has to be able to use various methods of presenting the information in order to help the students understand the concepts they are being taught.

    Read More

  • Strategies to Solve Addition and Subtraction

    1124 Words  | 3 Pages

    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.

    Read More

  • Errors And Misconceptions In Mathematics

    1723 Words  | 4 Pages

    This assignment will distinguish the relationships between teaching practice, children’s mathematical development and errors and misconceptions. Hansen explains how “children construct their own knowledge and understanding, and we should not see mathematics as something that is taught but rather something that is learnt” (A, Hansen, 2005). Therefore, how does learning relate to errors and misconceptions in the class room, can they be minimised and is it desirable to plan lessons that avoid/hide them? Research within this subject area has highlighted specific related topics of interest such as, the use of dialogue in the classroom, the unique child and various relevant theories which will be discussed in more depth. The purpose of this

    Read More

  • Piaget Constructivism Theory: Knowing The Concept Of Place Value

    724 Words  | 2 Pages

    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.

    Read More

  • Learning Theories for Mathematical Concepts

    1354 Words  | 3 Pages

    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.

    Read More

  • Numeracy Essay

    1596 Words  | 4 Pages

    The prominence of numeracy is extremely evident in daily life and as teachers it is important to provide quality assistance to students with regards to the development of a child's numeracy skills. High-level numeracy ability does not exclusively signify an extensive view of complex mathematics, its meaning refers to using constructive mathematical ideas to “...make sense of the world.” (NSW Government, 2011). A high-level of numeracy is evident in our abilities to effectively draw upon mathematical ideas and critically evaluate it's use in real-life situations, such as finances, time management, building construction and food preparation, just to name a few (NSW Government, 2011). Effective teachings of numeracy in the 21st century has become a major topic of debate in recent years. The debate usually streams from parents desires for their child to succeed in school and not fall behind. Regardless of socio-economic background, parents want success for their children to prepare them for life in society and work (Groundwater-Smith, 2009). A student who only presents an extremely basic understanding of numeracy, such as small number counting and limited spatial and time awareness, is at risk of falling behind in the increasingly competitive and technologically focused job market of the 21st Century (Huetinck & Munshin, 2008). In the last decade, the Australian curriculum has witness an influx of new digital tools to assist mathematical teaching and learning. The common calculator, which is becoming increasing cheap and readily available, and its usage within the primary school curriculum is often put at the forefront of this debate (Groves, 1994). The argument against the usage of the calculator suggests that it makes students lazy ...

    Read More

  • Analysis of Rich Dad, Poor Dad

    947 Words  | 2 Pages

    The second lesson concentrates on the importance of financial literacy. There is one rule to follow so as to understand financial literacy – “Know the difference between an asset and a liability, and buy more assets.” In order to do this, you need to be able to understand and comprehend numbers instead of jus...

    Read More

More about Importance Of Misconceptions In Mathematics

Open Document