Describe at least four significant ways in which differentiated instruction differs from traditional classroom instruction.
When the denominator is the same he is able to partition and see what fraction is needed to make the whole. When comparing fraction pairs, Adam is using gap thinking of the fractions 5/6 and 7/8 “both need 1 of their fraction to make a whole” understanding that each numerator needs one more part to make it a whole. In saying that, when comparing ¾ to 7/9 that have more than 1 to the whole, Adam said ¾ is larger, “1 more ¼ to make 1. 2 more 9ths to make a whole” He tried to apply gap thinking, incorrectly not understanding the unit of fractions. Adam has limitations surrounding improper fractions, not recognizing that 4/2 is larger than 1 whole and is equal to 2. He has misconceptions when comparing fractions with proportional reasoning is limited. When asked to draw a fraction he automatically swaps the numerator and denominator (6/3 to 3/6) when the numerator is larger than the denominator, when considering improper fractions, rather than converting to a mixed number fraction or whole number.. This displays Adams misconceptions of the understanding of the
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
I want to know my students. This way I can tailor my teaching methods to the specific needs of my students and class. This is also helpful in resolving discipline problems, which I anticipate to be few and far between. I will do everything in my power to resolve problems within my classroom, using the principal’s office and the administration as a last resort. Students respect a teacher who respects them in return. This approach allows a teacher to get to the heart of a student’s problems without involving outside forces that may alienate the child.
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).
The Case of Randy Harris describes the lesson of a middle school mathematics teacher, and how he uses diagrams, questions, and other methods to guide his students to a better understanding. Throughout his case study, Harris’ methods could be easily compared to that of the Effective Mathematics Teaching Practices. There are eight mathematical teaching practices that support student learning, most of which are performed throughout Randy Harris’ lesson. Harris didn’t perform each teaching practice perfectly, despite doing the majority of them throughout his lessons. The following are examples of how Randy Harris implemented the eight mathematical teaching practices into his lesson, and how the ones that were neglected should have been
Marilyn Burns attest to the fact that more learners are unsuccessful in math than any other core subject, Dylan William’s believes with application of principles effective lessons can be constructed to take shape where learners can progress to the top 5 in intercontinental standings in math. Robert Marzano, on the othehand, ascribe to vivid learning objectives with employing the chunking procedure to increase learning along with continuous check points for
The magnet board and dots allow the students to interpret problems as the total number of objects in different groups; for example, 5x7 is interpreted as 5 groups of 7 objects each. The math fact table, supplied to Peter, will help build connection between prior learning that is essential for the lesson; furthermore, repetition of concepts over the course of the day will be supplied to the student. For example, the skills practiced will be extended into the other courses throughout the day (i.e. english, science, etc.) ]
Peshek (2012) cites the benefits of differentiation in the math classroom as “greater student engagement, achievement, and equity.” She emphasizes the importance of developing objectives in lessons before thinking about how to differentiate the content. After stating the objectives the teacher must find a way to pre-assess their students in order to figure their readiness for the lesson. My favorite idea that she gives for pre-assessment is a discussion on “precisely what meanings students associate with the concept.” Throughout the article she gives examples dealing with fractions, but this would work well with the beginning of all math concepts. Even if the students have no experience with the topic, then the teacher will know exactly where he or she needs to start.
In my classroom, I will differentiate learning by offering a variety of methods of instruction such as hands on models, cooperative learning, technology, lectures, group activities, independent learning assignments. I will also adjust delivery based on understanding of concepts. I
Within a scheme of work differentiation must also be used as this is an approach to teaching that attempts to ensure that all the learners learn well despite their many differences. Having the ability to differentiate within teaching is a great attribute as “A teacher who understands what helps a learner learn will be a better teacher because they recognize differences and are prepared to alter
This example gives students an idea of how the concepts that they are learning in the course can be applied to real world situations. The problem does not provide the students with the needed mathematical model, but gives them all the needed information to create a model that will help them solve the problems. Students have to recognize that this is an optimization question dealing with maximizing an area.
It is important to teach or at least try to teach students problem solving related to math. Problem solving plays a big part in the math process. Teaching problem solving is beneficial to students because helps the students find solutions when struggling. It helps math to be more interesting and less stressful. Students see math with less negative reaction and more hope. Problem solving helps and improves student’s ability to think, solve, and find solutions. It is important for students to have the ability to have problem solving skills and this is what it teaches the students. Ultimately, problem solving helps students focus increase and learn what works best for them.