What Is An Instructional Problem

In order to improve my instructional practices, I analyzed instructional data from district math diagnostic and proficiency assessments. The most recent assessment assessed student’s abilities to count, add and subtract, and their understanding of place value. My students scored below not only the other first grade students at the school, but also all first grade students in the district. 81.6% of my students could count, read, and write numbers to 120. This was an improvement from their diagnostic assessment. However, only 66.7% could relate counting to addition and subtraction, and only 45% demonstrated understanding of place value in two digit numbers.

Algebra is a critical aspect of mathematics which provides the means to calculate unknown values. According to Bednarz, Kieran and Lee (as cited in Chick & Harris, 2007), there are three basic concepts of simple algebra: the generalisation of patterns, the understanding of numerical laws and functional situations. The understanding of these concepts by children will have an enormous bearing on their future mathematical capacity. However, conveying these algebraic concepts to children can be difficult due to the abstract symbolic nature of the math that will initially be foreign to the children. Furthermore, each child’s ability to recall learned numerical laws is vital to their proficiency in problem solving and mathematical confidence. It is obvious that teaching algebra is not a simple task. Therefore, the importance of quality early exposure to fundamental algebraic concepts is of significant importance to allow all

First, Standardized tests help show teachers what they need to teach students. Throughout the years' standardized test that students take to follow the when they go to the next grade. By the test tracking students, it shows the teacher what they need the students to learn to get to the next level or get better. According to source B,"Standardized test also help show the students progress, growth, and what the students have learned. By showing the students progress and growth it helps determine if the student should go on to the next grade or stay behind. Theses things provide an accurate comparison between groups." This tells is that without these types of tests, it would be difficult to measure student achievement in different subjects.

Based on data from student work samples, benchmark assessments, classroom tests and quizzes, John is able to solve basic multiplication facts with 100% accuracy. He can solve basic division facts with 92% accuracy. John can subtract numbers to the hundred thousands place with regrouping and across zeros with 90% accuracy. He can solve 2 digit by 1 digit multiplication problems with 85% accuracy, 3 digit by 1 digit multiplication problems with 95% accuracy and 4 digit by 1 digit multiplication problems with 90% accuracy. He can solve 2 digit by 2 digit multiplication problems with 85% accuracy. He can solve 3 digit by 1-digit division problems with 83% accuracy. He can identify the correct operation used to solve a word problem with 82% accuracy.

The evaluation of the program set by educators is a key purpose of standardized testing. Educators develop a guideline for the amount of work that should be covered in each area of a curriculum. The standardized test scores, in return, allow the educators to establish where a school fits and where it stands in reference to other schools.

[As a result of the step by step direction in the reengagement lesson, I want students to be able fully grasp the concept of addition; and how the knowledge of addition can be used to provide answers to expressions that require the decomposition of numbers totaling 8, 9, 10. The state standard that I am addressing in this reengagement lesson is 1.OA.1 Common Core State standards; use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together,

(Popham 8) Standardized test provide a misrepresentation of how effective a teacher is. (Popham 8) Standardized tests were established to help determine what level a student is on, so they can focus on his or her difficulties and help them become better students. (Popham 9) The way they accomplish this is by comparing each student's grade to the national sample of students of the same age and grade level. (Popham 9) These tests are most useful in determining a student's strengths and weaknesses, but should not be used to judge the teacher on their effectiveness. (Popham 10)

“No issue in the U.S. Education is more controversial than (standardized) testing. Some people view it as the linchpin of serious reform and improvement, others as a menace to quality teaching and learning” (Phelps). A tool that educators use to learn about students and their learning capabilities is the standardized test. Standardized tests are designed to give a common measure of a student’s performance. Popular tests include the SAT, IQ tests, Regents Exams, and the ACT. “Three kinds of standardized tests are used frequently in schools: achievement, diagnostic, and aptitude” (Woolfolk 550). Achievement tests can be used to help a teacher assess a student’s strengths and weaknesses in a

The process of getting the data consisted of many steps. First we got the interview questions from our teacher Ms. Roberts. Then we interviewed students from PLHS, first one inside of class, then one outside of class. After that we put the data into a google form that automatically put the data into a sorted spreadsheet. Then Ms. Roberts put the data into graphs and charts that we looked at to see the trends and patterns in the data. After that we sorted the data in the spreadsheet into separate categories in order to see the patterns and trends that occur in different ethnic groups, genders, etc.

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.

Maths is ubiquitous in our lives, but depending on the learning received as a child it could inspire or frighten. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Solso (2009) explains that math has the ability to confuse, frighten, and frustrate learners of all ages; Math also has the ability to inspire, encourage and achieve. Almost all daily activities include some form of mathematical procedure, whether people are aware of it or not. Possessing a solid learning foundation for math is vital to ensure a lifelong understanding of math. This essay will discuss why it is crucial to develop in children the ability to tackle problems with initiative and confidence (Anghileri, 2006, p. 2) and why mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri).

Mathematics, like every creation of man, have evolved without really knowing how far you can get with them: the scope of the computer, physics, chemistry, algebra, all are evidence of this. Every aspect of our culture is based in some way or another in Mathematics: language, music, dance, art, sculpture, architecture, biology, daily life. All these areas of measurements and calculations are accurate. Even in nature, everything follows a precise pattern and a precise order: a flower, a shell, a butterfly, day and night, the seasons. All this makes mathematics essential for human life and they can not be limited only to a matter within the school curriculum; here lies the importance of teaching math in a pleasure, enjoyable and understandable way. Mathematics is an aid to the development of the child and should be seen as an aid to life and not as an obstacle in their lifes.

The lack of adopted curriculum also means that most, if not all, teachers are supplementing both materials and instructional routines. These students need to pass the state-mandated Smarter Balanced Assessment (SBA) which requires completion of a problem-solving performance task. Students need to know which operation(s) to use (addition, subtraction, multiplication, and/or division) and how to apply them appropriately. This problem has

Mathematics is a type of reasoning. Thinking mathematically includes thinking in a rational way, developing and checking conjectures, understanding things, and forming and validating judgments, reasoning, and conclusions. We show mathematical habits when we acknowledge and explain patterns, build physical and theoretical models of sensations, develop sign systems to assist us stand for, control, and review concepts, and create treatments to address issues (Battista, 1999).