ELN 122 Lesson 8 Backward Design

Backwards Design provides a way to see if students are actually learning what you want to teach them by looking at assessment results. Overall what I have learned is that I am more concerned with a student being able to think for themselves and be creative than most math teachers, I want students to apply mathematics to solve real life problems not just only math skills, terms and facts. I have always said that there are no answer books in real life. A student has to be able to reason whether or not their  answer is correct.
Other than teaching to national standards, which is a requirement no matter what course you teach there are four important concepts to think about when designing. I found this excellent article on :What is backward design?
The main four points of the article were that backward design helps a teacher select topics that help them teach for understanding.
First, the topic has to have importance and meaning in the student's life. For example, how are patterns used in everyday life. A specific example is a pin number or and id number. How important in a persons life are codes and numbers. You can't get any more important than a social security number, and also it is such an important number in a person's life that codes are developed to protect it.
Second, the topic is one that is essential to the discipline. For example, the difference between numbers used as counting and numbers used as code. There is a big difference when you use a credit card for example between the price you pay for an item, the UPC code of the item, and your credit card number and pin number.
Third, what topic do most students intuitively struggle with? For example, students struggle with the concept of base. They are all familiar with base ten, but students who use other bases everyday do not grasp the mathematical significance. We count money in base 10, time in base 60, eggs in base 12, computers in base 2, and in the US uses a system of measurement based on 12, 3,5280 (horrible!!!).
Fourth, the topic is one that is engaging. For example, the performance assessments I used in the unit on patterns in everyday life.

http://asbmb.org/uploadedFiles/Backward%20design.pdf

Next I wanted to apply what I have learned through the course to the concept of backward design. I found another web site that lets you test your Teaching Goals applying what is important to your course and assessments. There were no right or wrong answers. It inventoried what I thought was important as opposed to most teachers.

"Teaching Goals Inventory. This tool, originally created by Patricia Cross and Thomas Angelo, contains 53 prompts to help instructors identify their goals for a particular course. This on-line version offers rapid self-scoring and data comparisons across goal areas and disciplines"

http://fm.iowa.uiowa.edu/fmi/xsl/tgi/results.xsl

http://fm.iowa.uiowa.edu/fmi/xsl/tgi/data_entry.xsl?-db=tgi_data&-lay=Layout01&-view

https://cft.vanderbilt.edu/guides-sub-pages/course-design/

 

The results of my Teaching Goals Inventory:

1. I rated Higher Order Thinking Skills as my top concern (100%).
2.  Next in importance came Basic Academic Skills (56%0,
3. Then came Discipline, Specific Knowledge and Skills (38%) pretty much tied with Liberal Arts and Academic Values were next (40%),
4. Last were Personal Development(33%) and Work and Career Prep (25%).

I compared it to the results of the general population of teachers taking the inventory:

1. Higher order thinking skills (43%-45%)

2. Discipline Specific (36%-37%)

3. Personal Development ((25%-28%)

4. Work and Career ((21%-26%)

5. Liberal Arts (18%-21%)

6. Basic Skills (18%-22%)

 

 I identified my primary goal as a teacher as "Helping students develop higher-order thinking skills,"

 

I identified the following as skills needed:

• Apply Principals
• Math Skills
• Terms and Facts
• Wise decisions
• Analytic Skills
• Think for Self
• Creativity
• Writing skills
• Openness to ideas
• Problem Solving

Math and Science Teachers overall identified the top skills as:

• Math skills
• Analytic skills
• Problem solving.
• Apply Principles
• Terms and Facts

It seems as though most Math and Science teachers rate skills, facts, and applications more important than reasoning, making wise decisions and creativity..

 

 

 

 

 

 

ELN 122 Lesson 7 eLearning Performance Assessments

 

Define performance Assessment

 A performance assessment is one in which the teacher observes the behavior of the student, or assesses an actual object that the student produced from that performance assessment.

Describe how it can be used in eLearning.

Some of my performance assessment projects (performance assessments) ranged from figuring out how long the Phoenix Sun’s basketball players height/arm ratio were compared to the class arm/ height ratio (linear algebra) to making a sun dial (polar coordinates) to finding the length of a light pole (trig).

I tried a tessellation performance assessment in my face-to-face class. I got very good results. The students enjoyed the performance assessment. In my classroom, on the Whiteriver Apache Indian Reservation, I tried to bring as much hands on performance assessments that I could into the classroom. I think this performance assessment would also work for an online class and student. The student would have to have the capability to take pictures, or do a screen shot of their work, and upload it as a file.

What makes performance assessments truly worthwhile in eLearning?

From what comments I read on the various websites most of the students liked doing the tessellation project. I think something like this project would be good for students who are visual/special, musical, or artistic. Even students who are creative need something to make of their own in a math class whether it s online or face-to-face.

 

The tessellation performance assessment was part of monthly projects I had the students do as a substantial part of their grade. 1/3 was in class work (I didn’t assign homework because it didn’t happen, it was more productive to get them to work hard in class than at home), 1/3 was formative and summative AIMS like tests (so they had practice taking high stakes tests), and 1/3 was projects (performance assessments). This way students who had test anxiety but knew the subject matter could prove that they knew the concepts by applying mathematics to a real life project.

 

This particular tessellation assessment was a unit project. Students had to make intricate tessellations of their own design. They had a choice of using one or more of the regular polygons that tessellate, or they could make an irregular tessellation of their own design. They could embellish the drawing as they wished. They had to explain their reasoning, their process, and the mathematics behind the choices they made in a written paragraph. They would have to take a screen shot of their drawing and paste it into their word document. A few students as usual waited till the last minute while many others created elaborate amazing drawings. I was astounded at the creativity of my wonderful students whom I greatly miss teaching.

 

What can you foresee as the pitfalls and problems with performance assessment in the eLearning environment?

Before any kind of assessment is written by a teacher in Arizona, or most states for that matter, the assessment  must adhere to state and national math standards. That is always in the back of every teachers mind. I will assume that any teacher that does a performance assessment keeps in mind the confines of standards no matter how interesting a concept might be for the class. A teacher must justify the activity or performance assessment. I ran into this quite often when I took my class outdoors for real life math projects. When I did a trig experiment to see how tall a light pole was, I was questioned about taking the students outside on the parking lot during class time even though we were replicating the classic tree shadow math problem. Heaven forbid if I actually took my students to a park.

 

I  found this website for Common Core Symmetry Math Standards:

http://www.corestandards.org/Math/Content/HSG/introduction/

 This one is for Common Core Visual Standards:

http://www.edutopia.org/blog/ccia-10-visual-literacy-strategies-todd-finley

 

 I always tried to make physical performance assessments as cheap as possible. I had over 225 students in my face-to-face classes so I had to keep the cost of supplies down since I paid for supplies out of my own pocket. That's why in the face to face classroom I used markers, colored pencils, drawing paper and 3x5 cards. Most classrooms also have scissors, rulers, protractors scotch tape and 3x5 cards so this project is not expensive to do for students at home or online.

Some of the problems are software related. Many students don't have the money for expensive software programs, and technology. Although most students do have cell phones. In many online classes the minimal requirements are internet, and Microsoft office suite student version. Most printers are able to scan documents , and are fairly inexpensive (the ink costs more than the printer).

I think journal writing or a Microsoft Word document helps students to explain their problem solving abilities along with the finished product.

One of the pitfalls that is common in an online class as any other class is copying and cheating. It is very difficult for an online student to create an exact duplicate of a tessellation. It would be very obvious if they had copied it because they will not be able to describe in detail how the product was made form scratch in their journal writing. 

For example, I had some students copy someone else's homework from the "tree shadow" performance assessment. Basically the performance assessment goes like this:

Suppose you are a light pole repair person, you need to change the light bulb in the light pole. I want you to figure out using the trigonometry of right triangles and how tall the light pole is in feet. You are given a yardstick on a sunny day. Have fun!. First the student would have to use proportions: pole height/pole shadow = your height/your shadow. I also had students be partners since measuring your height might be a problem. I could tell which students copied by the date of their paper and the time of day. Some of the students had to redo the project because they didn't realize that the length of a shadow changes during the time of day.

I would have the student journal the experiment and draw a sketch as they went along, also the time of day when they measured the pole. I would ask for an average of readings over a few days.

I would expect them to notice the change in shadows and comment on this phenomenon. At least this project could get them out in some sunshine.

 

 

 

 

 

 

 

 

 

ELN 122 Lesson 6 Constructed response vs fixed response balance

Blog Entry 6: Describe the differences between constructed-response and fixed-response written assessments. Describe the benefits of using both in eLearning. Finally, describe the necessity for a balance between teacher-graded and computer-graded assessment items.

In my previous blog lesson 5 I described the differences between constructed response and fixed response assessments

The benefits of using constructed response in eLearning are that the learner can communicate their ideas in writing. The problem comes mainly with how to solve math problems. As a teacher I am more interested in how a student attacks a problem, even if they have minor arithmetic errors. I like to see how their math brain works. I once had someone tell me there is only one right answer. In algebra, calculus and higher mathematics there are multiple solutions to a problem. Sometimes it's hard for as student to grasp this concept especially when there are many correct answers for a function. For example, lets just take f(x) = x+4 . There are any number of numerals that can satisfy this equation.10=6+4, 8=4+4, and so on. When you are grading things like graphing, I suppose an online teacher could ask the student to take a photo of the calculator, or graph the equation, or maybe scan the work and upload it.
I would hate to do an entire math course by fixed response items. It forces the student to think the most important thing in mathematics is a simple answer, when sometimes difficult problems have no answers for hundreds of years. Take for example Fermat's last theorem, there were whole branches of mathematics that were invented just to try to solve the problem.
Another example is Pythagorean Theorem, the Greeks ran into trouble when they used the simplest unit on a right triangle and got a number that was irrational. The concept of irrational numbers was as hard to grasp for them as multiple dimensions are for us.
We force students to take summative fixed response tests. Their whole academic career, sometimes even graduation is based on this one test. Does the test tell you how a student thinks? No, it just tells you how many questions a student got right.
When I look at the test scores of my students I am disheartened because I know they can do math, they just have a difficult time taking fixed response tests. I dread to see the upcoming computerized tests. I have seen where students cannot browse through the test and answer what they know first and then go on to more difficult questions. They must answer each question in order. There are students that have test phobia. My granddaughter freezes up on computer tests. She says her mind just goes blank. She can't think of anything. She has an artistic personality and is used to drawing things to solve problems. Now there is no place to draw or write, no sketches. No paper allowed.
The process of solving a problem is more valuable to me than a fixed response. One thing that irritates me as a teacher having worked in the real world outside of academia is that there are no answer books in real life. The answer you give is the answer. My daughter worked for a large company that has massive numeral reports every quarter, She uses huge work books in Excel not just work sheets. The report she gives to her CEO is the answer. Is it right? She has to use problem solving abilities to prove to herself that her report is correct. If a student thinks an essay question is hard, wait till they get into the real world. My other daughter owns her own business, she has to figure profit ,loss, cost of goods sold, predictions about what market trends are coming up. No one can tell her how much to buy, how much to sell. She can't look it up in the back of a math book. She has to make decisions on her mathematics. The mathematics for which there is no answer book, no true/false, no little 4 part multiple choice question. She might have to analyze 20 different scenarios.to make a decision.