Reach 108 Differentiated Assessment

These reading were so powerful and generated a lot for me to think about. I am going to start writing and see where that takes me in this blog. More and more I am understanding the significance and power behing good diagnostic, formative, and summative assessments. I will get into my personal skill in this area later in the blog. As I started reading, I like the idea that reliable assessments come from multiple sources of evidence. I liked the comparison of viewing assessments like photo albums vs. single snapshots. I thought that was a clever way to phrase it. One single summative test at the end is less likely to provide a complete picture of student's learning than a collection of diverse evidence. I have always thought that we as a society (probably for political purposes) rely too heavily on those standardized tests to be the sole determining factor. My question has always been well then if we know that, then why do we still focus or continue to emphasize that one big standardized test? In my classroom, some children are going to do well on the paper unit assessments and others will not. As an example, the last unit I finished was almost two weeks ago, and I had worked really hard on this unit and decided to extend it a bit longer due to the fact that there were still a lot of students who during the formative assessments like teacher observation were still not showing understanding. While we were doing the fact families, some students were able to put the three numbers correctly in the right order to make correct number families, but they were falling short with that key understanding of how the inverse relationship between addition and subtraction to solve problems. I was determined to make sure that there was understanding of that concept and not just being satisfied with students providing the correct number sentences. During the unit, one of my lowest students in my first class and probably overall was showing through other means like board problems or through bellwork or other tasks that she had a good understanding of the inverse relationship between addition and subtraction. Peggy was even in my room to observe a lesson where I had pulled a small group, and she was dominating the group by answering quickly and quite vocally and drowing out some of the other students in that group session. It had become clear to me that she was exhibiting some understanding during that formative assessment (my observation) and a work sample of building 4 number sentences out of the three numbers given in the fact family extension lesson. Peggy even commented in her observation notes that she was providing a lot of answers and seemed ready to go back to her seat and "graduate" from that small group. I was excited each and every time before this particular day and after that she had made big steps in acquiring that understanding. Then came the unit assessment (big summative paper test), and she did not perform well on it. Should I use that one paper test as the only indicator of her understanding of fact families? Years ago I might have said that the one summative assessment cancelled out everything else, but now I see that my little "M" in the Broncos really does know a thing or two about fact families number sense that a paper test does not show.

We were all given a benchmark assessment to use for Math as the method for placing our Rocketeers at either far below basic, below basic, basic, proficient, and advanced. The test is pretty good, but now I am in a place to start to question if we should solely be using only the scores from that assessment to place our students at the end of the year? WHat about my "M" who clearly has some understanding about fact families because she has demonstrated it to me on numerous occasions? It will be interesting to see this next round how she will test on that piece of the assessment. Using this big end of the year test to prove what a student can and cannot due seems to be like putting all of your eggs in one basket. I am a bit uncomfortable because of those students like "M" who show understanding inother ways, just not on the paper test.

I liked the piece about giving feedback also. I wanted to take time to make a comment or two about that. I agree that we attach scores and percentages but those are not feedback. Feedback is exactly what the chapter metnioned which is giving students information about their strengths and weaknesses. I am familiar with rubrics and I have seen really good kid friendly rubrics in writing; however, I have never seen one for math. I would like to know if anyone has seen one or has an idea about how you might use one for math. Sometimes math can be so cut and dry because there is one right answer you are looking for unlike writing where one is able to be flexible and more creative. Could a math rubric be developed an if so what would you use it for and what would it include? I share to a certain extent feedback with my students. I probably do not do it in the most effective way, but I do share with them information about what they are doing in terms of showing their work that maybe is stumping them and which specific steps they might have confused or missed in working a problem. Maybe it was that they did not get the key word in a word problem which contributed to the wrong operation being applied. That would just be an example. I always stress for them to show their work and that means that there should be some kind of number sentence or equation or drawings or something there to prove it. I include that in the assessments because at the first grade level the math can be pretty simple and the really advanced ones are able to figure things out in their head without writing it down, but I stress the importance of them working every single problem out and proving it no matter how easy it can be done even if done in their head.

Right now I am so excited to see growth on the big benchmark assessment;however, I know that those kinds of tests even the unit assessments I have are not "fair." As the article mentioned some with be penalized by using that format and it will favor others. I have some pre-assessments and unit assessments in place and I am learning to use a variety of things for formative assessments which is good because I did not have those things going for me years ago. I am in a stronger place now as a teacher, but I need some serious work on creating even stronger diagnostics and summative assessments and that will be a work in progress.

REACH 108 Strategies

These chapters had so much information that I had to read a few pages at a time, stop, and then pick up and read again another day. The chapters listed a lot of different strategies, and I hope to talk about them more in depth during our sessions to get a better idea of how each one works because after reading, I don't feel I completely can envision what each one of these strategies looks like actually being implemented. I guess that says something about the kind of learner I am. I need to actually see things being done to fully understand them and be able to do them myself. The reading mentioned stations, agendas, complex instruction, centers, tiered activities, compacting etc. I really found it difficult to take this all in and make direct applications to math based on the examples that the reading provided. I can understand the concept of centers and stations as this is a target area for me to begin implementing very soon. I have already discussed with this with our coach and a little with our principal, and I am waiting to figure out maybe in which specific direction I can go with it. I have implemeted centers when I taught in another district, and the program we used required a minimum of 7 centers around a specific theme or unit of study. I think centers is the one strategy listed that I feel most comfortable and knowledgeable about. Jason, I know you finally implemented your centers this week, and I wanted to know how that worked out for you and the students. Based on your reaction the other day, it sounded like you had a considerable amount of success with it. I have wanted to ask for some collaboration time for us math teachers just to bounce some ideas off of each other in terms of differentiation, and I hope we can get the chance to discuss and make our math program even stronger. I guess one of the questions, I have for you would be which other strategies mentioned in this reading assignment do you feel would be most effective for math. I liked the compacting one as it relies on encouraging and emphasizing teachers to assess students at the beginning of a unit and those students who get at least three-quarters correct would not continue work on what they already know. I feel like I have made the grave error of falling into the trap of teaching it anyway even if they know it and I want to set this as one of my goals and start using those assessments in a better way to organize and structure my instruction for different groups and levels of students. I am sure I probably bored them a bit, but my rationale was well it will be good review or reinforcement for them. Another idea that I liked about differentiation is providing opportunities for children to make choices. I think this goes back to 105 and our discussion about how people learn, and choice is definately a piece of that. I am struggling a bit right now with the huge difference between the really high groups and the lower ones that are still struggling with number sense or number recognition. I hope we can have a deep discussion at our next session about issues we have and how we see differentiation working to as the author wrote, " the goal is for the teacher to meet a student where he is in knowledge, understanding, thought, planning, and presentation, and then to help the learner push forward." That was the quote that summarizes what we as teachers are trying to learn more about right now in this course.

REACH 109 ASSIGNMENT 2 STEP UP TO WRITING

I really loved the two articles given for the writing piece of 109. Years ago, I would have never stopped to think to incorporate so much writing into math, but through good training and excellent guidance by my school and my teacher program, I am starting to see the value in doing so. I push my students for oral explanations to their answers which is good, but I also understand that having a time and place for them to process their thinking and express it in written form would also give me great insight into their exact thinking process, their strengths and their weaknesses as mathematicians. I want them not to just give me the answer whether it is right or wrong, but I constantly push them to defend their answer to the "jury" the rest of the class. Going along with pushing them for oral answers, I could continue to expand on that and give them an outlet for writing it down and explaining it through words, sentences, and drawings. I do provide them with some ways in which they can write it down. One of the ways is to write it down in their math journals. Since they are only in First Grade, I have had to provide prompts to get them started, and I have asked them to write in their own words something that they either did today in class or learned, or reviewed that they can share. I provide vocabulary words in their unit assessments in which they have to provide a definition of the word and use it correctly in a math related sentence. I see that I can model more some think alouds and model the writing process more as it relates to their own thinking and answers so that they can see how that proces works and how they might apply it in their own process of understanding concepts in math. I think I could improve by asking this everytime we do an activity and it goes into their notebooks. I could ask for it also by choosing one or two math problems of the day on the board, and then upon going over the answer going a step beyond and modeling my thinking process and writing it on the board. I also think that I can incorporate more writing into their homework assignments even if it is writing down one thing that was easy or difficult about the homework and explaining why it was either easy or difficult. I think there are so many different ways a good teacher can incorporate more writing into math, and I am excited about improving and pushing them more and more in math but also with the literacy piece as it relates to math.

Reach 108 Self-Assessment

Differentiated instruction is such a powerful piece of a quality classroom. Being at Rocketship and in the Reach program is helping me to put the pieces together so that I can more effectively teach the diversity of learners all 82 of them who sit in my classroom everyday. At the beginning of the year, I had very little information about those 82 students and it has taken months to really grasp all of the factors that combine to make each student who he or she is. I began thinking about how I could possibly teach all 82, and know each one of them in specific ways relative to their socio-economic background, language, motivation, experiences, personal interests, and learning styles. There is so much information to consider when evaluating and creating differentiated instruction. Although I am no master at the grandiose task, I feel like my school and my teacher training program are guiding me in the right direction. I find that I am doing certain things right like carving out effective blocks of time to work in either small groups or one-on-one students. I am searching for appropriate ways to teach the curriculum and implement those strategies to ensure that all of my students are understanding the topic in relevant ways. I have looked at where I fall in terms of the continuum and I have placed myself professionally in between emerging and applying for TPE 4,5, and 7. In terms of TPE 2 and 3 Monitoring student learning during instruction, and interpretation and use of assessment, I again have placed myself between emerging and applying. After reading the articles, I am more aware each step of the way how important those pre-assessments are because they provide the information for alternative learning paths for students. These pre-assessments will guide me into the right direction of making sure instruction is where it should be for individual students. UbD planning will help me plan and focus on the "what" part of instuction, and the DI piece will focus on the who, where, and how. I am understanding that these two pieces of a quality classroom need each other, and even the best curriculum will falter if it does not address the who, where, and how. I look forward to growing professionally and developing my skills as a teacher to tap into combining UbD with Differentiated Instruction and finding effective strategies that meet the needs of a wide range of learners. I would like to challenge my students to achieve at their level and eventually moving over into more innovating teaching where as to guide my students to start making appropriate choices for their learning. I have a way to go on this road to mastery, but I am on the path and seek any and all support in that adventure.

105 Assignment # 3How Teachers Learn

I made a mistake on the last blog title. I put it as assignment 1, but it was really assignment 2, and this is the third one for 105 "How Teachers Learn." I really enjoyed reading this article because it was information for me to digest about myself as a learner and as a teacher. Even though I loved all of the chapter, and I would say that through the years, I have been involved in many workshops and trainings to learn a curriculum or a new strategy like GLAD, but this is not the type of professional development that this reading is talking about. The reading gave an example about a teacher who participated in a Math Their Way workshop, and even though this training gave this teacher new techniques to teach math. However this particular teacher did not start the process of rethinking her knowledge of math. This art of the reading made me stop and think about the book that our principal had us math teachers read over the summer by Liping Ma. After reading that book, I started to rethink my knowledge of math and how that in turn has prepped me for how I might teach math to my students. The book by Liping Ma, Knowing and Teaching Elementary Mathematics forced me to unlearn the old way I had been taught, and look at certain math concepts like regrouping in a fresh new way. So many workshops or training etc that we as teachers participate in do teach us new techniques and strategies, but do they tackle the deeper issue of challenging us to rethink our subject matter? For a teacher to step outside of their comfort zone and force himself to rethink his subject matter is indeed being vulnerable. I think it is hard for teachers to maybe grapple with the fact that maybe they do not know answers to some questions. Not until I read this book over the late summer, did I begin to take those steps to rethink my understanding of math, and how that translates into teaching my students. I think that process for teachers is very powerful.

I also found it interesting that districts spend only 1-3% of operational budget on professional development. The reading also mentioned that" this lack of investment is unheard of in leading corporations and other countries." I think that if we are to continue to make reforms in education and in teachers' professional developement this lack of funding must be addressed as well as the quality of the professional developments which need to target each teacher in a way that will best suit his or her needs for professional growth. Teachers are at different stages of their professional growth and to force each one in a district or school site to participate in the same one regardless of the necessity because it is dysfunctional.

Assignment 1:Reach 105 How People Learn

This chapter reminded me over and over again about the Understanding by Design book where it talks about the six facets of understanding. This chapter talks about how using new approaches in teaching can increase the possibility of of the majority gaining a moderate to deep understanding of material presented. One of the points stressed in this chapter was that the new science of learning emphasizes learning with understanding. I particularly became interested when in the chapter it discussed how memory has been favored over deep understanding, It gives the example of a typical multiple choice test question about arteries. This example is one that we see all to often just a series of m ultiple choice questions which are supposed to determine whether or not a student really has a deep understanding of a specific area. I am troubled by the emphasis on this types of tests as being the only true measure of understanding. I liked how the paragraph went on to talk about using learned material to solve other problems... in other words looking for evidence of trasfer. To me that is what we should really be after and not just a replay of certain facts but being able to target that trasferability in our students. I think back to my own education when I was younger and it would seem that those multiple choice tests were always favored. It was not until I went to college that I was able to hit what I knew and write papers, do projects, or create essays that I was able to apply what I knew to different situations.

Strategies that Work("Reading is Thinking" and "Reading is Strategic"

In these chapters, I started to think back again to when I was a beginning reader. I guess I was making those prior knowledge connections that the chapter talked about. I thought that this was a powerful reading because it made me think deeply about the process of reading which is so much more than decoding. Active readers interact with the text. I liked the example the author gave on page 13 when students were asked the essential question, What is reading? Answers like" figuring out words , spelling the words, knowing the letters" were all presented. Even though that is true, it was not until one student said, "when you read, you have to figure out the words and what they mean" that the real idea and purpose behind reading was given. The primary purpose for reading is understanding. I liked the part in the chapter where it talked about true comprehension being more than just literal understanding. Pushing students to interact with the text and go beyond just a literal understanding is the goal of any good teacher. I remember when I was in reading class all those years ago answering simple questions about what was in the story, but I do not remember ever being pushed at a young age to go beyond the literal meaning.

The reading selection goes on to describe the strategies that work to push for that deep comprehension into the text. First, activating background knowledge was described in the reading as being the foundation of our thinking. "We simply can't understand what we read without thinking about what we already know." p 17. Anytime I read a story to students or we prepare to read a selection, assessing their prior knowledge on the subject is always initiated first. Teachers should always guide students to make connections among their personal experiences, the world, and the text they are reading. The article makes the point that this connection of prior knowlede to new knowledge is the core of learning and understanding.

One piece of the reading that really stood out for me was the part that talked about the practice of schools not fostering questions by students. The reading suggested that the educational system requires or demands answers, the kind of answers that are straight forward for tests, and answers to math problems that involve no explanation. I know for my own personal experience teaching math, I am now requiring more and more explanation of their answers. For example a simple problem at the first grade level like 3+5=8 seems pretty straight forward, right? However, I ask them explain to me if you added or subtracted and tell me what tells you to add or subtract? I am referring to the math symbol +. I always am filled with questions even for the most basic problems because I want them to always be thinking about what it is they are doing and know how to explain it. I agree that questions are the heart of being able to move forward and the push they need to move their thinking forward. It made me remember the old saying, "There is never a dumb question."

Next, the reading went on to mention making inferences which I believe is very difficult for some children to do because an inference is not directly stated in the text. They have to dig deep and use their own information and the clues in the story to be able to do this. Visualization was mentioned in this selection as well. This involves a reader painting a picture in his or her mind. Personally this is one that I have always been pretty good at as a reader. I remembered reading Little House on the Prairie and making up my own pictures in the book in my own mind. I visualized the open praire andit was easy for me to do this because I grew up in southeastern Colorado which was flat and prairie. I visualized throughout the entire book, and that is a skill that has stayed with me throughout the years.

In addition, summarizing and sythesizing information were also provided in the reading. Summarizing being the skill to retell the information and sharing it in their own words. Students will have to sift through all of the information presented in the book and present those critical focal points and put them into their own thoughts and words.

As teachers we must be responsible and show our students what these strategies are and how to use them in their own reading. Constantly modeling those strategies for our students every step of the way. I am going to end this entry with a quote on page 21. " When we write we compose thoughts on paper. When we read, we compose meaning in our minds." Reading is so powerful because it opens the door to the world beyond.