Introduction Generalized instructional sequence, also referred to as concrete- representational-abstract (or CRA), is a strategy for teaching that benefits struggling students in many ways. Mathematics is a daunting subject to many secondary learners and it is common for students to struggle in math classes. Moreover, this subject may come especially difficult for students who have a learning disability. For this reason, teachers need to be able to adapt their teaching to reach all students and must have knowledge of many different and effective teaching strategies. General instructional sequence is just one method that can help secondary students reach their full potential in their mathematics class. Through this strategy, teachers deliver concrete instruction, representational instruction, and abstract instruction. (Sabornie, E. & DeBettencourt, L., 2009) Research has shown this method to be useful thus it is important for teachers to be aware of it and use it in their classroom. Description of Strategy Graduated instructional sequence is useful for teachers of secondary mathematics learners. Especially helpful for those having difficulty in algebra, this strategy is potentially more effective on those who struggle with conceptual understanding of numbers, symbols, and the relationship between them. However, it is useful for teaching fractions, percentages, geometry, and many other concepts as well. (Leone, P., Wilson, M. & Mulcahy, C., 2010) Additionally, certain
Students will also verbally share with the class the different comparison problems they created which will allow students to use the vocabulary terms. The last learning experience, 4, will allow students to continue to build from experience 3 in practicing the vocabulary terms and math symbols. Students will say true math statements as well as create their own. There are several ways students will implement their vocabulary terms in meaningful ways.]
Dacey, L., & Gartland, K. (2009). Math for All: Differentiating instruction, grades 6-8. (J. Cross, Ed.) Sausalito, California, USA: Math Solutions.
The math concepts taught in this lesson are teaching the students how to use certain math formulas, and practice addition and multiplication. It is beneficial for students to know what tools to use for capturing and displaying information that is important to them (Davis, 2011). The science concepts taught in this
What preparations have you made to anticipate students’ prior mathematics knowledge, students’ differentiated responses and knowledge, and their evolving mathematical thinking throughout the lessons?
The research in this paper is to discuss strategies used to teach students with severe disabilities in mathematics. “According to the American Association on Intellectual and Developmental Disabilities, (AAIDD) Intellectual disability is characterized by significant limitations both in intellectual functioning and in adaptive behavior as expressed in conceptual, social, and practical adaptive skills. The diagnoses of the disability should come before the age of 18 (Westling, Fox, & Carter, 2015).” Mathematics is a core subject area that can pose a challenge for a large amount of students in America, and especially those with severe disabilities. “According to a study, only a quarter of students with disabilities that
This is one unit in a yearlong 6th grade math course. In this unit, the students will learn about expressions and equations. Students will learn how letters stand for numbers, and be able to read, write, and evaluate expressions in which these letters take the place of numbers. In this unit, students will learn how to identify parts of an expression using various new terms. They will learn to solve both one- and two-step equations. Students will be able to distinguish between dependent and independent variables. They will be able to identify the dependent and independent variables of equations and in turn, be able to graph them. Various activities to be completed inside and outside of the classroom will be used to show
The author explains how many students, especially those in the focused-upon second grade class, have difficulty explaining their “mathematical thinking process”. While they may provide correct answers using memorized calculations, they are unable to demonstrate their conceptual understandings or explain how they achieved the right results. As stated by the researcher, “it is important for students to be able to demonstrate their mathematical thinking as well as their method of solving a problem” (Kostos & Shin, 2010, p.223).
Upon observing your class, we have learned a lot about the methods you utilize in order to help the students with mathematics and about how the students learn. Observing your class was both an honor and a learning opportunity for us, as you are an important, and well-respected faculty member in the school system. However, while we appreciate your goals and tactics to make learning mathematics easier for the students, we have discovered some flaws in the use of mnemonics, rules, and tricks for helping students understand the subject material.
Another idea to improve mathematics performance in elementary level is to encourage the student to link the existing knowledge and the new knowledge effectively while working math problems/examples. A worked example is “a step-by-step demonstration of how to perform a problem” (Clark, Nguyen, & Sweller, 2006, p. 190). This will prepare the students for similar problems in the future as they bridge the connection between the problems and the examples. In many cases, students are encouraged to link the informal ideas with the formal mathematics ideas that are presented by the teacher to be able to solve problems. When students examine their own ideas, they are encouraged to build functional understanding through interaction in the classroom. When students share among themselves on differences and similarities in arithmetic procedures, they construct the relationship between themselves hence making it the foundation for achieving better grades in mathematics. Teachers can also encourage students to learn concepts and skills by solving problems (Mitchell et al 2000). Students do perform successfully after they acquire good conceptual understanding because they develop skills and procedures, which are necessary for their better performance. However, slow learning students should engage in more practice
This artifact addresses the standards of content/subject matter, diverse learners, instructional strategies, and methods of teaching in several different ways. The artifact deals with the content of 8th grade math, in this particular artifact it deals with slope, proportionality, and slope intercept form. With using these concepts, I used a variety of strategies including creative thinking and problem solving to make questions. I was also able to create opportunities for diverse learners in this lesson with the strategies and methods of the 8th grade math content. When creating this lesson it was not my goal to interconnect these four standards, it was after reflecting on the lesson that I observed I connected these four standards in my lesson
To be an adequate teacher to students all teachers need to understand the basics of literacy and numeracy to enable them to convey the curriculum sufficiently and accurately. “In an increasingly complex world, being able to read, write, add, subtract, divide and multiply is crucial” (Rankine, 2013, p.3).
Their 2000 publication, the Principles and Standards for School Mathematics, is still prevalent. This document, setting forth ten guidelines for improving math education, refined, extended, and replaced NCTM’s earlier recommendations. Not only does the Principles and Standards for School Mathematics address five important content areas, it also establishes five important mathematical processes deemed necessary in quality education, like problem solving, reasoning and proof, communication, representation, and connections. When it comes to making connections, NCTM further asserts that instructional programs from prekindergarten through grade 12 should enable all students
The purpose of this study is to evaluate the effectiveness of the Comprehensive Instructional Sequence when decoding complex text on students’ reading comprehension. Two groups of students were selected: one group used Comprehensive Instructional Sequence to decode and scaffold text; the other group used the previous classroom methods in which there was no continuity. Students were measured using State of Florida progress monitoring tests in which reading comprehension and Lexile were measured. Students in the experimental group were taught using the Comprehensive Instructional Sequence for four weeks. Analysis has yet to be determined. Therefore, the findings are unable to be reported. The abstract will be updated when the study period
For the professional development intervention the researchers have developed nine content-based mathematical courses for a 5-year National Science Foundation-funded Maths and Science Partnership - the Rocky Mountain Middle School Math and Science Partnership (RM-MSMSP). The courses contained approximately 80% content knowledge and 20% pedagogical content knowledge and were taught in 2 to 3 weeks during summer. In addition, a structured follow-up (SFU) units associated with each content course were also taught for 4 Saturdays during one academic semester. These units were focused 80% on pedagogical content knowledge and a review of the content from summer course and 20% on general pedagogy.
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.