Week 4 lesson 4

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

Problem setting: A man with a boat at point S at sea wants to get to point Q inland. Point S is distance d1 from the closest point P on the shore, point Q is distance d2 from the closest point T on the shore. The points P and T are at a distance of d from each other.Question: A man rows with a speed of vr and walks with a speed of vw . At what point R should he beach the boat in order to get from point S to point Q in the least possible time?

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

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Types of Assessments

Formative Assessment is part of the instructional process. When incorporated into classroom practice, it provides the information needed to adjust teaching and learning while they are happening. In this sense, formative assessment informs both teachers and students about student understanding at a point when timely adjustments can be made. These adjustments help to ensure students achieve, targeted standards-based learning goals within a set time frame. Although formative assessment strategies appear in a variety of formats, there are some distinct ways to distinguish them from summative assessments.One distinction is to think of formative assessment as “practice.” We do not hold students accountable in “grade book fashion” for skills and concepts they have just been introduced to or are learning. We must allow for practice. 

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. 

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. 

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 

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. 

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 what students can do with what they know, rather than how much they know. It is a form of assessment that requires students to perform a task rather than select an answer from a ready-made list (Sweet, 1993). It is not just a testing strategy but an assessment method that involves both process and product. It integrates teaching, learning and assessment. Performance assessment is a dynamic process calling for students to be active participants, who are learning even while they are being assessed. No longer is assessment perceived as a single event (Wangsatorntanakhun, 1997). “The purpose of assessment is to find out what each student is able to do, with knowledge, in context,” (Wiggins, 1997, page 20). 

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.

 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.

 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.

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Assessments on Creativity

Assignment 6-2

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.

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Mathematician’s Lament

The article A Mathematician’s Lament written by Paul Lockhart was very passionate as he articulated his views on the death of mathematics. Lockhart stated that mathematics is an art that is taught by teachers who are not qualified to do this subject justice. As a result of unqualified teachers, educators and the system, children suffer the agony of receiving misinformation, have to learn formulas that are not important and are tested just to add anxiety to their lives. He claims it is a nightmare and the child’s natural curiosity and love for pattern-making is being destroyed. He also stated that everyone knows what’s best for the students, but no one has asked the students what is best for them.

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.

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Course Highlights

What are Jing, blog, GeoGebra, webinar, screencasts, diigo, and wordpress? No silly. I didn’t go to a dance class. It was a Math class. I attended Learning and Assessment in Secondary Math. I started this course expecting to do just what was required as any other online course. I thought I came prepared – SURPRISE. I was wrong, wrong, wrong. It was nothing like I expected.

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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New Vision for Math

 Dan Meyers has a vision to take the teachers into the 21st Century and beyond so that we don’t kill the students with boredom. His Presentation on a New Vision for Math was very enlightening. He pointed out that students are impatient in their problem solving and that they are not engaged by Math applications.

 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.

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Future of Education

Today I attended the Future in Education seminar, The BYU -Idaho Learning Model moderated by Steve Hargadon with special guest Kelly Bugener and Dr. Fenton L. Broadhead. This is a University that has its base in the Mormon Church. The University is open to everyone. They operate on five principles which all faith-base. They believe in Christ as the foundation which enhances learning. 

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.

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