Are you PREpared?

Starting at the beginning of October in 2013, the Professional Readiness Exam was instated within Michigan. The bottom line of this test is to measure students' knowledge and understanding that the state demands within the education system. Within the state of Michigan, there have been laws that mandate a test to be given to students' as part of the teacher certification process. Throughout the student body, mix feelings start to spread questioning the reliability and validity of the selected material on the test. During my time at Grand Valley studying education, discussions upon discussions have arose within  the classrooms relating to standardized tests and how many feel as if they have to teach to these standardized tests because their jobs rely upon them. We, as a community of experienced and newly structured teachers, need to stray away from this idea as a whole. Standardized tests are not the answer within the educational world. The methods and measures that are derived from these methods are not an accurate description of the students knowledge as well as falling back on the teaching strategies that are structured within the classroom. As we attempt to move away from the idea of teaching to standardized tests, the state mandates the Professional Readiness Exam, (*standardized test*), to assess students' understanding that are trying to go into a field in which they should not be teaching to these standardized tests. A tad bit hypocritical if I do say so myself.

Those who are studying Elementary as well as Secondary Education take the same test prior to going into the College of Education here at Grand Valley State University. This test includes sections Reading, Mathematics, and Writing. These sections assess the students' understanding and knowledge that they will need in order to teach within a Michigan classroom. Is this test showing understanding and knowledge of the content, or is this showing test-taking skills? Public information about the PRE states that this test focuses on the students' ability to show their knowledge and understanding of the concepts that are covered as well as test-taking skills. Why? What is important about test-taking skills that is needed for the teacher to bring into a Michigan classroom? Do we need these because the community of teachers needs to teach test-taking skills to the students? The test-taking skills does not provide sufficient evidence of the students' understanding and knowledge of the concepts that we, as teachers, are teaching to them.

Briefly, lets focus on the mathematics portion of the PRE test. The subarea test areas included are: quantitative literacy and logic, algebra and functions, geometry and trigonometry, and statistics/probability. Within colleges across the state, there are different requirements for each student to take math classes. These requirements could range from only needing one class to multiple classes. If you were one of the students who were only required to take one math class through their whole college career, are they going to be well PREpared for this test? Not only do they need to focus on all of their other classes in order to obtain good grades so that they graduate in a good manner than just skimping by, but they need to teach themselves these concepts all over again that they haven't had experience within 3 or more years. Sound fair?

 So, why make these points? If Education is a path that one decides to travel, shouldn't they just have to do what they are told and take the test? I feel as if there is more to it than just that. We have been taught for years that assessment gives justification for understanding. We are able to take the time in class or outside of class and assess one's skills. The PRE does just this so it places a teacher in the student's shoes. Since we have to take the test to further our education in the field in which we have wished to go into, we must make the best of it. It may seem like a lot of work, but everyone should be able to gain something out of it. Test taking skills are essential in education as it sits today. As one studies for the PRE, they typically remind themselves of concepts that they had learned years ago. One benefits from regaining knowledge, thus making them a better overall teacher. Also, concepts that had been learned years previously might make more sense during the present time. Students would be able to make more connections to the concepts and would be better teachers in the end.

The point of this was not to bash the PRE test for the new teachers that are coming through the educational system within the state of Michigan because I do not have a simple solution to bring to the table. However, my point that I hope was elaborated was the fact that the test seems to lack reliability and validity in assessing students' understanding and knowledge. It is a test that points more in the direction of assessing test-taking skills in which the state believes that teachers will then bring into the classroom. That is what the community of teachers is trying to move away from though. We are coming into a new mindset where teaching to the standardized tests is hindering our own students' understanding and knowledge. The same is happening to us when we are mandated to take the PRE test in order to further our studies within the educational world. We need to move away from test-taking skills and standardized tests in order to enhance our students within the classroom above and beyond what they have in past history. 

Spacing out on Proportions and Fractions

As we progress through our education and enhance our knowledge, we then must take a step back and place ourselves within the shoes of students. What are some strategies and tools that they would use to understand a problem? How would they go about solving it? Little did I know that this would be one of the hardest things to do within my college classes. During a recent class, we focused on problems that were related to proportions and fractions. The strategies that we used were on a level that middle grade students would have a hard time wrapping their mind around. The real issue is that we need to realize that the ways that we solve a particular problem may not be on the same level as our students. We, as teachers, need to have enough tools to formulate multiple strategies for our students in order for them to master the concepts presented to them. This post has been created to put in writing certain strategies and tools that I plan to pass along to my students referring to proportions and fractions so that they are not simply getting frustrated and spacing out.

Within the recent class period, the problem referred to the diluting of blue chemicals for blue jeans. The problem was asking which solution was "bluer" based on how many blue bottles and clear bottles were in each solution. The strategy that I found most useful was cancelling to find out what was left in the larger solution to see which one was "bluer." However, I soon realized that this is not a well thought out strategy to use. By using this manipulation, the proportions are changed which would be hard for a student to understand and realize. Although it worked for me and I was able to determine which solution was bluer, if I were teaching this to students, it would not be the strategy that I would focus on to teach. So what are some other ways that students would be able to have "click" in their head? After this class, some thoughts raced through my mind that I would try to implement into my lesson plans.

The use of examples that do not have an emphasis on numerical values. One of the main problems that have rose to the surface through my volunteering and observations of classrooms and other mathematical education activities, is the emphasis on correct numerical answers. What if we used questions that required more reasoning? Consider an example that talks about the concentration of orange juice. When mixing with 3 cans of water, would a container of orange juice with 3 cans of orange concentrate have more or less compared to a container with 4 cans of orange concentrate? These types of questions require much more in-depth understanding and comprehension compared to a question asking strictly about a comparison of numbers.

When I was in mathematics classes, nothing excited me more than money. Since this was the case I sincerely believe that by including more examples that the students would be able to relate to and be excited about, they're more apt to stay within the learning part. An example including this would be an exchange rate. The students would be able to use hands on money that have different exchange rates. They could then write out proportions and fractions that model what they are trading with one another based on a system that tells which exchanges they are allowed to make. For example, we could say that 3 US dollars are exchanged for 2 British pounds. As described in the previous strategy and example, the students would have a more in-depth understanding and comprehension by using these hands-on activities regarding proportions and fractions. Below are a few examples that could be used throughout the activity. It is important to note that planning questions are not concrete. Students may struggle or fly through specific parts of an activity, which is why the teacher must be adaptive.

1.  Represent the exchange rates as fractions for US currency and British Pounds. 
2. How many US dollars would you have if you had 14 British Pounds? 
3. How many British Pounds would you have if you had 26 US dollars? 
4. If you had 1 British Pound, how much US dollars would you have? 
5. Create your own proportion. 

Overall it is known that proportions and fractions are a hard concept for a lot of students to wrap their head around. It is our responsibility as teachers to provide different strategies and tools to our students so that they are able to comprehend at a deeper level. Using the above strategies and many more that are not elaborated on within this post, the students would be able to manipulate more on their own with the problems and be able to apply the correct operations when working with non-numerical and numerical problems.