Boat Landing Problem – Classroom/Home Simulator and Build your own Simulator by LFS ** **

http://geogebrawiki.wikispaces.com/Boat-Landing-Problem

I used this design for boat problem. I am still getting aquainted with GeoGebra.

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**Summative Assessments** are given periodically to determine at a particular point in time what students know and do not know. State administered summative assessments could be very bias because all students do not learn in the same way or at the same rate. There are several types of summative assessments such as; state, district, interim, end-of-chapter, or end-of-term, but the one that carries the biggest accountability is PSSA assessments. However, I believe that the PSSA’s to not reflect the true ability of a child.

http://www.nmsa.org/portals/0/pdf/publications/Web_Exclusive/Formative_Summative_Assessment.pdf

Assessment (either summative or formative) is often categorized as either objective or subjective. **Objective assessment** (usually multiple choice, true false, short answer) is a form of questioning which has a single correct answer. These are good for testing recall of facts and can be automated. Objective tests assume that there are true answers and assume that all students should learn the same things.

**Subjective assessment** is a form of questioning which may have more than one correct answer (or more than one way of expressing the correct answer). In subjective assessments the teacher’s judgment determines the grade. These include essay tests. Essay tests take longer to answer and they take longer to grade than objective questions and therefore only include a small number of questions, focusing on complex concepts.

http://vudat.msu.edu/objective_assess/

**Peer Assessment** and self-assessment is much more than children marking their own or each other’s work. To improve learning, it must be an activity that engages children with the quality of their work and helps them reflect on how to improve it. Peer assessment enables children to give each other valuable feedback so they learn from and support each other. One of the ways in which students internalize the characteristics of quality work is by evaluating the work of their peers. However, if they are to offer helpful feedback, students must have a clear understanding of what they are to look for in their peers’ work. Students can also benefit from using rubrics or checklists to guide their assessments. The instructor must explain expectations clearly to them before they begin. For peer evaluation to work effectively, the learning environment in the classroom must be supportive.

**Self Assessment** -Students can become better language learners when they engage in deliberate thought about what they are learning and how they are learning it. In this kind of reflection, students step back from the learning process to think about their language learning strategies and their progress as language learners. Such self assessment encourages students to become independent learners and can increase their motivation.

The successful use of student self assessment depends on three key elements:

- Goal setting
- Guided practice with assessment tools
- Portfolios

http://www.nclrc.org/essentials/assessing/peereval.htm

http://nationalstrategies.standards.dcsf.gov.uk/node/18700

Although **constructed response assessments** can more easily demand higher levels of thinking, they are more difficult to score.

**Selected response assessment** items (also referred to as objective assessments) include options such as multiple choice, matching, and true/false questions. These question types can be very effective and efficient methods for measuring students’ knowledge and reasoning. Because many of the standardized tests are based heavily on multiple choice questions, teachers should be skilled at developing effective objective assessment items. In addition, teachers should be able to construct quizzes that target higher level thinking skills (consistent with the application, analysis, and synthesis levels of Bloom’s taxonomy), and they should evaluate their instruments by conducting item analyses.

http://fcit.usf.edu/assessment/selected/response.html

Pearson **ability assessments** help you more accurately assess the dimensions of ability, including cognition, reasoning, intelligence, problem solving, and learning potential. These assessments yield detailed information to understand the learning process, predict rate and depth of learning, and pinpoint reasons of performance.

* Performance assessment*, also known as alternative or authentic assessment, is a way to measure

http://www.etni.org.il/etnirag/issue4/irit_ferman.htm

http://psychcorp.pearsonassessments.com/pai/ca/productlisting.htm?Community=CA_Ed_AI_Ability

Assessment is **authentic **when we directly examine student performance on worthy intellectual tasks. Traditional assessment, by contract, relies on indirect or proxy ‘items’–efficient, simplistic substitutes from which we think valid inferences can be made about the student’s performance at those valued challenges. Authentic assessments require students to be effective performers with acquired knowledge. Traditional tests tend to reveal only whether the student can recognize, recall or “plug in” what was learned out of context.

http://pareonline.net/getvn.asp?v=2&n=2

Assessment is authentic when we directly examine student performance on worthy intellectual tasks. Traditional assessment, by contract, relies on indirect or proxy ‘items’–efficient, simplistic substitutes from which we think valid inferences can be made about the student’s performance at those valued challenges.

Authentic assessments require students to be effective performers with acquired knowledge. Traditional tests tend to reveal only whether the student can recognize, recall or “plug in” what was learned out of context.

Authentic assessments present the student with the full array of tasks that mirror the priorities and challenges found in the best instructional activities: conducting research; writing, revising and discussing papers.

http://pareonline.net/getvn.asp?v=2&n=2

A **standardized test** is a test that is administered and scored in a consistent, or “standard”, manner. Standardized tests are designed in such a way that the questions, conditions for administering, scoring procedures, and interpretations are consistent and are administered and scored in a predetermined, standard manner. Any test in which the same test is given in the same manner to all test takers is a standardized test.

http://en.wikipedia.org/wiki/Standardized_test

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1) Student will use create and solve a quadratic equation about something that is meaningful.

2) Graph the quadratic equation in GeoGebra

3) Using your musical ability put together a rap or song that describe the problem and solution.

Rubrics would be used to assess the creativity of these mathematical entities. I will assess the first two and peers would assess the third entity. Students would be given the rubic at the time of the project, so they would be fully aware of the criteria.

http://school.discoveryeducation.com/schrockguide/assess.html

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Lament listed the problem very eloquently, however there were no solutions. I am in agreement that the Mathematics curriculum needs drastic change, however change cannot come overnight. My method of teaching was pretty much the same as everyone else – formulas, exercises and testing. I have since learned differently. I hold myself responsible if I should return to the same mundane way of teaching. Technology is such that our children can be engaged in creativity, problem solving and logical reasoning.

I beg to differ about the qualification of teachers. Teachers are only teaching what they were taught. It has been a trickledown effect and those who know better are doing better. Lament should reach out to teachers and share the excitement of teaching math, so that the beauty of art in mathematics can be fully expressed in the classroom.

http://www.maa.org/devlin/devlin_03_08.html

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First of all I was not expecting to be in a classroom talking with classmates. I was. It was a virtual classroom and it was wonderful. I had more fun than I have had in actual classrooms. I learned so much from my classmates. Everything we did was available to everyone. We were able to comment on each other’s work and give constructive feedback. But our learning experience did not stop there.

We made a Wikipedia page on multiple representations. Was that possible? Yes, we really did. We attended several webinars each week where we listened to experts talk about changing the face of Mathematics. We were expected to ask question or comment- Intimidating, yet exhilarating. We were expected to critique several articles online. I was scared but had to gain the confidence to do this in order to move forward.

The question is asked to reflect on the course and give my highlights and low points. Well my low point is that the class is over and I haven’t had the opportunity to really let everything that took place sink in. I have been to so many places in cyber world, places I never knew existed. Places that would only enhance the teaching of mathematics in any classroom. Places that was exciting, fun and engaging. I have learned to use technology that I did not think was possible

Thank You Maria Droujkova. I just hope I can go and do likewise.

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He showed a simplistic approach that just required some thought could change an entire lesson-such as still waters and rafting down a hill with gushing waters. His question was what would make a more exciting and interesting problem. One of his concerns was that students may become engrossed in the event and not the problem.

The bigger picture here is to create more interesting lesson by having a great hook. Students love challenges and teachers need to raise the bar in preparing the students for the future. Maybe the students can sometimes come prepared to share (my thought borrowed from BYU). This way they are kept engaged.

Dan believes that teachers should dare to be different. They need to be confident and comfortable in their classroom. I agree with this philosophy. It is just getting the school system to buy in, especially with the rigorous format and testing. However change is needed.

http://mathfuture.wikispaces.com/WCYDWT+-+A+New+Vision+for+Math+Curriculum+Development

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The BYU -Idaho Learning Model has three processing steps.

1) Come to class prepared

2) Teach one another

3) Ponder and prove

The students are required to come prepared to teach. They do must do research on the subject matter before coming to class. Then they share with each other under the guidance of the instructor. After which the students analyze the solutions to see if it was the best solutions based on everyone’s input. Based on the principles and process of learning BYU said they have experienced much success.

Students come prepared because they are bring things to their liking or their style. Because of this they are engaged and are able to contribute intelligently, as opposed to the teacher doing the entire lecture.

http://www.stevehargadon.com/2010/08/wednesday-live-in-elluminate-byu-idaho.html

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Anxiety is relaxed or turned off when students are made to feel comfortable. When students feel that their interest is met and they are challenged. When they realize that the teacher is also human. An educator one asked the students on the first day of class “Are you nervous?” The response was “Yes”. He replied, “So am I”. Everyone had a good laugh and the tension was broken. Once students know that you feel as they feel and that you have their best interest, there will be flow.

Knowing our students and subject matter are key to anxiety reduction. We must be able to see the blank or confused looks and adjust our lesson to meet the students need. When we are prepared and are familiar with our subject we can begin to differentiate at that time to alleviate anxiety for those who seem to be lost or bored. Anxiety is reduced when both students and teachers know what is to be expected. Student also knows that part of this process is testing. How we plan, teach and execute our assessment would also ease the tension of the students.

Most people would not be against a surprise birthday party. However, a surprise test is entirely a different issue. Students not only want to know that a test is coming, but what is on the test, what is the format of the test and how it will be graded. If the teacher has laid a good foundation by engaging the students, giving positive feedback and having some fun, then the anxiety level towards assessments becomes next to nil.

Most of us wrote our required lesson plans for the course and they were wonderful, excellent and I’m sure stimulating. The practicality of the matter is that some students may not care, some students may not know how to start the assignment, some students may be low readers and just don’t understand. Our responsible is to encourage by building up their self-esteem and confidence. When a student knows that a teacher has confidence in them, the students go the extra mile to show that they are worthy of that praise. Anxiety – what’s that?

http://www.ericdigests.org/2005-2/anxiety.html

http://www.mathgoodies.com/articles/math_anxiety_model.html

*Look up, out, and beyond. Math helps answer big questions, not just mundane ones. *

*Let the spirit of inquiry be a comfortable and joyous one – not a chore! *

*It’s okay to let them struggle to find their own answers, their own way, in their own time. It’s important for children to feel comfortable with hard questions, and not to feel the need for fast answers. *

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Hastings gave the three rules that must be followed in doing various calculations. He also demonstrated the way a function could be manipulated to allow for ‘what if ‘ scenarios. Not only does the system give solution to problems, but it also explains the concept, if needed. What was shown and explained is only the top of the iceberg. There are several topics that are covered by Mathematica, including information on other subject. The attached link would be able to get you started

http://www.wolfram.com/broadcast/seminars/s01/

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The following is what Chapter III looks like. It deals with Congruent Triangles and it is focused on skills.

A student has to go through all those pages of agony in order to understand congruent triangles. It looks like so many words to read. Is it necessary? Devlin stated in his article ‘In *Math you have to Remember*….’ That mathematics is a way of thinking about problems and issues in the world. Get the thinking right and the skills come largely for free.’ In this text you have to get the skills first-memorize. Where do I start to decode to make this chapter user-friendly and not have students zone out on me.

This text fits into Bloom’s lower level task with knowledge (remember and memorize). It also covers application, in using the formulas to apply to the exercises at the end of the chapter. However, there is no stimulation, creativity and higher-order critical thinking. The text did it all for the student. Other sources would have to be utilized in order to bring this lesson to life.

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