Reflection of Comprehension Strategy Lesson Plans

My Comprehension Strategy Lesson Plan was an Introduction to Series. I used a warm up activity with making a sequence out of the number of cards in each row of a house of cards, and then found sums of rows to begin working with how series are used. I then had a dense chunk of text to read, which I made a graphic organizer in order to break the text into manageable chunks and digest the information. I found that the lesson went really well. The amount of text was an effective amount, and the organizer was a fun way to take notes and have everyone following along. If I were presenting this lesson again, I would possibly make a stronger emphasis on the series work that is done in the warm up. I would possibly go back to the warm up after the reading, and the students have written the definitions for the vocabulary, and have the students identify which are partial sums and which is the sum of the series. However, I think that the comprehension strategy part went smoothly, and I would definitely use a graphic organizer web like that again to tackle dense text and digest new vocabulary. The graphic organizers could even be sent home to guide students with readings that students could do prior to class, and allow more time to apply their vocabulary knowledge.

Chapter 2 Reading

Chapter 2 Reading: Learning with New Literacies

            Technology has absolutely transformed how students communicate, find information, and make understandings from this knowledge. Students can find answers and immediate feedback on the Internet so quickly that I believe it is an important time for teachers to take the time to reflect on how they’re teaching, and how this technology should be integrated into the classroom. In today’s society, what methods of teaching will be most effective given the way students are functioning outside of school? And what will student’s lives be in the workplace? Filled with technology.

            As a mathematics teacher, I reflect on how careers involving mathematics function. There will indefinitely be a computer program that will be utilized to make calculations. As one becomes familiar with working on graphing calculators and various mathematical computer programs, even if you have to learn a new program, each new program becomes easier to learn because of similarities, and also the familiarity with technology. Does that mean that students should abandon pencil and paper calculations? - Absolutely not. Students must understand how particular mathematics works, and be able to interpret results and ensure that the results are feasible. This deeper understanding comes from performing the computations manually. A deeper understanding also develops when using multiple representations and methods for solving. Thus, it is important for teachers to stress the importance of having technological understandings, but also teachers must describe why we learn how to solve on our own when we have such resources at our fingertips.

            Another idea that mathematics must emphasize in a word of technology is the importance of the process. The process of learning to problem solve is absolutely pivotal in almost every profession. Teachers must direct lessons to have student lead exploration into the material, and develop the ability to think critically. The Internet may be able to spit out certain answers for students, but it cannot give them the ability to be critical thinkers and problem solvers. That is something that teachers must facilitate and develop in their students.

            New literacy also involves not stressing on “right” answers. This can be a challenge for mathematics teachers. However, it leads me to think about how it is important to emphasize how there isn’t always just one “right” way to approach problems. As often in mathematics, teachers are looking for students to find a particular numerical value. However, students can perform write to learn strategies to comprehend and other activities, which do not involve one particular answer. There is also research on how literacy is a social practice. This reflects on how we know teens are social beings and it is important to be aware of this as we are trying to get them to gain understanding and retain knowledge. Having students create blogs and comment on each other’s blogs is a wonderful example of fostering this social aspect in literacy.

            In the text, there is a story regarding a fifth grade teacher who challenged himself to integrate technology into his classroom. It describes how he begins to use computers, he created a blog, and then had all his students create blogs, and eventually had them commenting on each other’s, and then moved into Twitter. I found that this anecdote was a good example of how teachers could involve technology in the classroom, but also a good lesson of how it is okay to progress into using new technologies and strategies. It’s okay for us to ease into it, and add or subtract as it works in your classroom and with your particular students. Especially if a teacher that has more traditionally taught, it is fair to work into adding more student led inquiries and problem solving activities. However, students may be caught off guard if the rhythm of the class takes an absolute one eighty, and they aren’t ready to facilitate all that you would like them to.

            It is important to remember that new literacies are embedded into content standards. It is crucial for students to be able to use multiple representations of information. Thus, teachers truly must strive to keep up with the technology that is available. It is what most students are familiar with, and it is important for school to be relevant in order for the most success possible. This will prepare students to become productive persons in society. As it is challenging, it is refreshing to renovate ones’ lessons and ways to convey material.

            Lastly, new literacies allow wonderful opportunities for differentiation. With no “right” answer, there are opportunities for students to have assignments that are best for them. Using technology could also lead to greater motivation and engagement with students that are often disengaged in academics. Then as with introducing anything new implemented in the classroom, expectations and scaffolding is important. New literacies are essential in the classroom today to allow students to have the best learning experience possible. 

Chapter 10 Writing

Chapter 10 – Writing for Tests and Assessments

            The text describes how math teachers have always strived for students to show their work, and not simply write down a mysterious number in which the roots are no where to be found. However, even if a student shows how they plugged numbers in to a particular formula that may not mean they understand the mathematical concept behind what they did.             Thus, “showing ones’ work” is not sufficient. This is where it is important to have portions of tests where students can thoroughly describe their reasoning in words. However, this cannot simply be something that students are expected to do thoroughly for exams. These types of writing activities must be frequently practiced in day-to-day classes for students to begin to effectively describe their thought process in writing for mathematics.

            In my field experience, the Algebra II students have just finished a unit on Probability. They were asked to write their reasoning if a certain scenario appeared theoretically feasible. Numerous students used knowledge outside of the mathematical evidence to describe if such an idea was reasonable. I cannot explicitly recall the problem, but it was something about if a student could possibly perform three activities or something, and the students were supposed to draw from the data in the earlier problems. However, many students described how students are often busy and participate in numerous activities- drawing on no mathematics at all! The directions to this problem were obviously not nearly clear enough, and I also believe that the students were not given enough practice to successfully tackle a writing problem in math class. I asked the teacher if they do a lot of writing to explain their reasoning, and she said they did not. Thus, students were likely thrown off on what they were being asked to do. It is important to remember that students need to have demonstrations, scaffolds, and practice with assignments, activities, and the types of problems they will be asked in assessments. Test day is not a time to introduce writing mathematical thinking.

            I loved the example on page 256, which had the students be the announcer for the swimmers, and describe what was going on in the race. The graph displays the swimmers race, and then the students are the interpreters. The students write what the graph tells them, and they have the chance to role play and be creative in their assessment. This is fun for the students – a fun test! As a teacher, I want to strive to constantly find these types of applications. Constant collaboration and research are necessary to continue to create curriculum, instruction, and assessment that take the material to another level of context and interest for students.

            

Chapter 8 Reading

4/7/13

Chapter 8 Reading: Developing Vocabulary and Concepts

            For my Mathematics Curriculum and Instruction Course, I am beginning to create a ten-lesson plan Unit Plan. I have decided to do it on Sequences and Series, so I can teach two of the lessons to the Algebra II students at Johnson High School. Students may have worked with number patterns before, however, it is likely that this will be the first time they will have applied the technical vocabulary words such as sequences, series, iteration, summation, recursive formula, explicit formula, arithmetic (accent third syllable) sequence/series, or geometric sequences/series. I have found it challenging to figure out how to introduce these concepts in context. I want to have the students discover the definitions and have meaning to the vocabulary. In addition, I have been trying to figure out the best order to introduce the vocabulary, without introducing too much at once. There is a lot of new terminology in this unit, and I believe it is important to ensure that connections are made for students to get the most out of the material, and it doesn’t become too overwhelming.

            In other chapters of reading, we have discussed how students need to ground their reading and learning into previous knowledge, otherwise they will be unable to understand and retain the material. This same idea is developed throughout this chapter on vocabulary. The technical vocabulary from ones’ content area cannot just be pulled from a textbook and defined with other complex terminology. The vocabulary needs to be integrated with prior knowledge and allow students to make connections and remember the meanings.

            While reading this chapter, I began to question. Vacca states, “Words are labels for concepts” (Vacca, 241). However, if my students understand how to take a geometric sequence, and formulate corresponding recursive and explicit formulas, does it matter if they don’t know what they’re called? Have they mastered the objective if they can do it without saying exactly what it is? I’m not entirely sure. I feel that if they are at that level of understanding with the concepts, associating the vocabulary name with the concept is a feasible expectation. Especially because many mathematical names are given for a reason, as they allow you to make a connection to another mathematical concept. Therefore, it is important for me to facilitate those connections being made and help students to organize their grasping of concepts with vocabulary.

            A method described in the book was graphic organizers. Thus, I immediately decided to apply this to method to develop connections amongst the vocabulary that I will be using with my students at Johnson. They will be doing the unit on Sequences and Series following their unit on Probability. Unfortunately, their isn’t too strong of a correlation between the two units and it is nice to have flow and connection between units. However, I decided to map the vocabulary using a counting principle method that is frequently used in probability, which is a Tree Diagram! One can see that there are eight different types of Sequences and Series that we will be able to tackle by the end of the unit. These types are identifiable by starting reading at the red. Thus, some of the types are infinite arithmetic sequences, finite arithmetic sequences, infinite geometric sequences, finite geometric sequences, infinite arithmetic series, and so on. It is nice to have all the terms organized as well as some addition notes I added at the bottom.

           

            

           

            The text also mentions that a five minute free write on an important vocabulary word/concept can be a beneficial method to get students to start making those connections to their previous knowledge. Brainstorming is another method, in which students could work in groups and formulate a list of ideas. There are also a couple methods that emphasis the grouping and labeling of words. As I am trying to apply these methods to my lesson planning, I think some sort of grouping activity with the vocabulary may actually work well. I would maybe even integrate example sequences and series to group with the vocabulary. There are numerous examples of mapping ideas and concepts together to make vocabulary more clear. It is important to demonstrate how to effectively create these maps, and scaffold so students are able to be creative and use their own thought process, yet, know how to go about making a useful learning tool.

           

           

             

Chapter 3 Reading

Chapter 3 Reading: Culturally Responsive Teaching in Diverse Classrooms

            As I began to read this text, I had the precursor in my mind of how I am confident that I will embrace diversity in my classroom. However, it is difficult to understand how to do this, or what this looks like. I also hadn’t fully understood what types of obstacles exist, which would prevent me from doing this. This chapter begins by presenting how a variety of languages and cultures are gifts in the classroom, with a variety of perspectives and ideas to create a rich and vibrant classroom environment. However, many of these students struggle with literacy and learning, and as a result, they are placed in low ability groups and are limited because of this obstacle. Then the strengths that can come from instructional situations with diverse learners never occur because of the restrictions placed on them. Thus, my purpose for this reading was to find several practices that I want to implement in my own secondary mathematics classroom in order to embrace diversity and help bring down barriers.

            The example of how a science teacher embraces diversity in his classroom gave numerous examples how he provides the learning environment for ELL students to be successful, and for students of all cultures to be embraced and add interest to the class. I thoroughly enjoyed this example and aspire to have a classroom like Tim Fitzpatrick’s. First of all, I enjoyed the activity that he used at the beginning of the year to develop a learning community that fosters discussion, and not regurgitation of facts. The activity was for students to create autobiographic sketches and share aspects of their life stories to one another. This is something I want to use with my diverse classroom that I will be teaching at Breakthrough Saint Paul this summer. I believe this will be a good activity for the first day. Students can be creative, and then describe themselves through pictures and words. Many teachers believe that these types of activities take too much time, however, they can create a learning environment that fosters beneficial classroom discussions that may not have occurred otherwise.

To provide aid to ELL students, he labels all of the tools. If there are ELL students in my classes, and this appears to be beneficial, I believe that labeling items around the room and integrating a second or third language into the class at various times is a feasible step for me to take. I have a minor in Spanish, and very much enjoy learning parts of other languages. This could be crucial in the comprehension of key concepts in a class. A student can entirely miss an objective because of a language barrier; thus, I will take steps to avoiding this.

            Another way in which, Tim Fitzpatrick, the High School Science Teacher embraces cultural diversity is to undergo studying scientific problems occurring around the world. Relating this to mathematics, I was thinking about how students could dip into statistics from other countries, and then develop mathematical understandings of topics regarding countries around the world. This could be a statistics project that allows students to use the transitive approach, which would allow the students to do statistical analysis (think critically) and then generate conclusions and opinions. I also would like to have posters of mathematicians from around the world, hanging in my classroom, as well as infrastructures with beautiful geometries. I believe that classroom decorations can also provide a wonderful opportunity to passively display how important fresh ideas of all cultures can be in a classroom.

            Mr. Fitzpatrick also is selective on the passages that he assigns students to read. It may only be a couple paragraphs, and he will even rewrite material for more clarity, and assure that the key concepts are dissectible. He states that he likes to keep it real. He places emphasis on portraying key concepts in the most simplistic ways possible. I think that it is important to be precise. If there is a key concept that you want to assure it portrayed in math or science, it isn’t beneficial to assign an enormous amount of text that may have a lot of additional fluff and difficult vocabulary. Clear and precise text is important for ELL students, and all students.

            I also believe that the idea of getting family or community members into the classroom to discuss their professions is an awesome idea. Activities like this can be memorable, and help students apply the material they are learning in class to the real world, and what they may want to do in the future. The idea presented in the text is to bring in a carpenter to discuss trigonometry, and possibly have them create a small frame. It would also be a good activity for students to devise the questions to ask the community or family member. Having those formulated ahead of time can assure good questions will be presented, and creating these can be an activity in itself involving research. Then there is reading, writing, speaking, and viewing all involved is learning. I really enjoy this example because it gives a clear example of how I can involve families, as these relationships are important.

            What sticks out as most concerning for me, is the amount of ELL students that are placed in lower-track classrooms. As many people may have seen the popular movie staring Sandra Bullock, The Blind Side, I have heard the same story from one of my current Mathematics Pedagogy Professors. Some students are unable to read the assessments set before them, and as they fail to have success, it may appear that they do not understand the material. However, once the assessment is read to them, they are able to describe their understanding. Thus, I will do my best to have numerous types of assessments, projects, and activities that will allow all types of students to display their understandings. It can be so easy to look past the idea that the student may still understand the concept even if they do not do well on the test, as we rely so heavily on students’ ability to read successfully. It is so important to have relationships with all ones’ students, and understand their learning, and what needs to be done to assure the best learning experience possible.