The learning goal the students were most successful with was simply writing ratios. Although writing ratios is a simple skill it is a gateway requirement for being able to write proportions and think on a more critical level. Students seemed to be successful with writing the ratios because it was a lower level skill.  It did not require much critical thinking ability to achieve success at the basic level.   It requires students to identify the comparison and structure of a fraction and correctly placing the numerator and denominators to show a comparison between two quantities.  Furthermore, what makes this skill multifaceted is that it can be any stated in several ways.  All students were able to master this learning goal at a rate of at least 7 out of 10 times.

       The success of this learning goal is attributed to the fact that the students were able to function on a very basic level.   On this most basic level of understanding students are more able to show mastery.   Because of instruction required student to use the ratios they created to make proportions; students were constantly able to fine tune their ability to write ratios. 

    During instruction it was a challenge in teaching student to write proportions; they were not so careful to follow the order of the ratio and more often they followed the order of the words and had to be redirected to write the ratios and proportions correctly.  Students were given the cue to write the ratio in word first in order to avoid this pitfall that tripped up a good number of students.    

     Once the students were instructed and taught the relationship and how to state ratios, students were able to recreate the skill on their own.  By increasing to the learning goal of writing and solving proportions this continually allowed for assessment of the students’ ability to write ratios. 

     Also, I believe the student performed well because of the increasing level of difficulties the learning goals put in place.  The learning goals built on the prior skills.  The initial goal of writing ratios is a necessary skill in order to write and solve proportions.  Students were given several ways to solve the problem and were not restricted to any one way of the teacher.  Students were guided to information and not necessarily provided with the information.  The instructor tried to build in healthy struggle in order to expand the student’s thinking beyond what they already knew. 

      Another reason that seems to have allowed the students to be successful in writing ratios was their prior knowledge.  Students had been exposed to fractions in elementary school.  The ability for the students to grasp the fractional format of ratios was engrained in them prior to their arrival in the sixth grade.

     Initially, during instruction the students were able to discuss and make connections with prior knowledge to understand ratios.  Again, by moving on to proportions students were able to practice ratios to the near conclusion that students could prepare the ratios most of the time. 

     As shown in the assessments students were able to draw on their prior knowledge of fraction to use ratios to show mastery.  Thus, students were able to both use prior knowledge and their ability to get additional scaffold practice to acquire and master the skill.

     The students will be able to use proportions to solve real world applications was the learning goal that the students were least successful with  65% of the students reached the level of proficiency of solving problems. 

     The lack of success can be contributed to a lack of concrete and abstract thinking and very ambitious learning goals; can be sited as a couple of possible reasons for the lack of success.  Furthermore, in retrospect lack of substantial educational support for ELL and Special education students may also have contributed to some of that population’s inability to perform on a more proficient basis.

    Some students have not acquired the necessary deductive reasoning skills in order to process higher order information.   Also, students lack of ability to see the links between mathematics and their success beyond middle school.  This leaves a student somewhat apathetic about the process of learning mathematics.  I think this notion could be diverted by using more relevant example to the students’ lives when writing and examining instruction in the classroom.  Incorporating more modern terms; tweets, social media sites, additional technological lingo and verbiage in mathematics may make the buy in for students more interesting to them.  Maybe, stop calling them work PROBLEMS and maybe just call them mathematical situations.  

     Instruction can try to address and lay a foundation for the students who have not yet developed abstract reasoning.  All students should come with some level of concrete thinking that allows the educator to build upon even though the students may not reach the level of thinking totally abstractly.  Instruction can be more tailored to assisting the students in being able to use their minds eye to see things they cannot touch. 

     Assessments were appropriate based on this factor because the standards are that the students will be able to move towards thinking on that level.  Therefore, the big idea is that even though students may not have the necessary ability to achieve proficiency in the given assessment they still have to be move forward in their learning.

     I believe the instruction for the special needs students could have supported the students more.  Based on the instruction, if there were key words that could make the English language learners better understand the word problems, I believe that would have enhanced the performance of those students. The task of writing ratios were basic for the students; however, once we began working within the word problems to set up proportions, the English language learners and special education students were beginning to lose pace with the rest of the class.  It is my belief that these students were at a serious disadvantage because of their lack of a grasp on the English language.  Therefore, the goals were within reach for the students,

      Assessment can be redesigned to better allow opportunities for students with individual needs to perform on a more proficient level.  Students with learning disabilities and ell learners may be given alternate assessments to allow them to show their proficiency level where as the use of word problems in English may have prevented their ability to show mastery. 

     Therefore, it is my belief that these students would have benefitted from have the test red to them or having the word problem in both English and Spanish.  Moreover, I would try to make the lessons with more Spanish in setting the learning goals, tailoring instruction and in writing assessments.

     I would do more with manipulative and hands on activities to allow students to see the relationship between ratios and proportions.  I would like to give students more guided practice so they can feel a level of achievement which will influence positive thoughts on math.