Vaughn Ch.15

 What are some of the  reasons students with learning problems have difficulty with traditional mathematics curricula?

Students with learning problems may need more time and practice to learn math facts and math computations because they often lack the "automatization" to perform math computation effectively and efficiently. Some of their difficulties may relate to understanding the problem, they may lack the computation skills to solve the problem. Some may have difficulties with motivation. Students have difficulty reading the information provided because the vocabulary is too difficult and the reading level is too high. All information in the book must be directly taught to them and the math concepts are often presented poorly. Information may be scattered and multiple concepts are introduced at one time. There are insufficient problems covering any one concept or operation and too few opportunities for application of knowledge learned. The problems are not presented in enough different situations for students to learn and transfer what they know to real life settings. Also, students already do have difficulty transferring knowledge to real problems. Students often do not have the necessary prerequisite skills mastered to move on to the next unit. In addition, students with learning problems may have trouble with traditional curricula because the organization of the text varies considerably and makes learning from the book difficult.

Reys Ch. 10

What are some myths and facts about using calculators?

Some myths about using calculators are that they do not require thinking from students, they lower math achievement, that using a calculator always makes computations faster, and they are only useful for computations. Calculators do require that a person think of what numbers they need to compute to problem solve. For example, helping the student use process of eliminator to find common factors between numbers to further solve the problem. Calculators can also raise a student's achievement and are also useful for instructional tools. Calculators can be used as an instructional tool to facilitate search for patterns, support concept development, promote number sense, and encourage creativity and exploration. Today's calculators are able to efficiently plot graphs among other things. Also, it is not always faster to use a calculator because computations that one has memorized or that are simple enough to compute mentally will be much faster to retrieve than punching it in to a calculator. Allowing students to use calculators in the classroom can facilitate problem solving, ease the burden of long tedious computations, focus the attention on meaning, remove anxiety and provide motivation and confidence.

Reys Ch. 4

I feel like chapter four was a lot of information that I will not have a complete understanding of until I am able to experience doing it for myself. There were many ideas and prompts that made me think about how I can incorporate different strategies in my teaching. The chapter was very informative of all the various ways of assessment. I have heard of many of the assessment forms in my previous classes. I really think portfolios are a great idea. It is amazing for the students to see their progress and to be involved in picking what will be put in it. As a teacher I would like to incorporate portfolios into my classroom. The chapter also mentioned communication between the students, the parents or guardians, and the school administration. The portfolios are a great way to communicate with parents during conferences, with students and with the school administration about students goals and progress. Also, the chapter mentioned having students take time to reflect on themselves through self assessments. Self assessments is something I would like my students to do, and to include in their portfolio. The section about observation was very informative. I agree that observing students and recording notes on a checklist would be very helpful in monitoring student performance. I want to make it a point to create a checklist of a few important aspects to focus on for at least one student a day to observe and record notes about.

Ch. 3

Planning curriculum is very important and I do strongly agree that it lies at the heart of good teaching. Lesson plans should be carefully organized and developed, and enriched through activities, technology and manipulates. I am intimidated that teachers plan their entire year of curriculum before the school year begins. It is then narrowed down into units, and finally into a weekly and daily basis. I do find it comforting that we cannot expect to follow our year plan exactly, but we review the progress of our class and the students as individuals to vary the pace, reteach and revise the lessons. It is important to write out a detailed lesson plan to make predictions and to use as a way to assess your own teaching. Also, if the lesson plans are written out instead of just planned in our minds we are better able to share ideas, and receive feedback from others. I also find it comforting that the state standards and school districts provide a framework of the curriculum to be taught. Having an outline to go off of is going to be very helpful in planning an entire years worth of class activities, tests and homework. I am also hopping that when I become a teacher my colleagues will share fun and effective lesson plans with me, so I am able to use them to help my students have fun and be engaged while learning.

Ch. 2

In creating a positive learning environment, Reyes says "Make sure Students understand that they will not all learn the same things at the same time and that they will not all be equally proficient, but that everyone can indeed become proficient'.  I think this is great advice and I completely agree; I wish I knew this when I was learning math. When I was learning math in elementary and middle school I always a little behind, until eventually I did fall behind and couldn't catch up to the majority. I ended up needing one on one tutoring at a learning center. Lessons not only need to be modified for students with learning disabilities or special needs, but for each students' proficiency level. This is a lot of work a teacher needs to do with a class size of 25 to 30 students, but it is very important for children to learn at their own pace and be comfortable with that. It is very important that the students feel safe and comfortable with their own progress. Part of learning and making progress comes from trial and error. Students need to feel comfortable enough to make errors. That they may not fully understand how to solve particular problems right away but it's ok. Student's need to understand that this is a natural thing, that it is different for everyone and that it is ok to make mistakes and progress at their own speed.

Ch. 1

I do agree that math is used in everyday life and that society needs all of it's members to be able to problem solve in everyday life. I do think that the basic needs of society is a starting point of knowing how advanced to educate citizens.  However, we live in a fast changing world that is rapidly advancing in technology. We do not know what jobs will be available in five, ten or twenty years from now. It is important for everyone to have as much knowledge and technological experience as possible in today's age. The needs of society seem to be changing and updating every year. It is interesting to look back in past to see the pattern of what was considered the standard of basics to be taught in school. In the 1970's the minimal competency movement stressed the basics of addition, subtraction, multiplication and division which included whole numbers and fractions. Today, and even in the 1970's, advanced technology had been developed that does these calculations in a matter of seconds. I find it disappointing that only addition, subtraction, multiplication, and division were the basics of what was taught in schools. I am pleased that this has changed and society has not fallen back into the pattern of stressing only the basics, and instead we are expanding.