HOPE Reflection H2 – Honor Access to Content

H2 – Honor student access to content material. Teacher candidates use multiple instructional strategies, including the principles of second language acquisition, to address student academic language ability levels and cultural and linguistic backgrounds. Many regard mathematics as a second language. Mathematica notation and use of mathematical vocabulary areLessonPlan LessonPlan 1essential to learning this topic. At the school where I work, all students are fluent english language speakers, it is unusual to encounter a language barrier in communication. Most of the language acquisition problems are through the understanding of mathematical language. To address this HOPE standard, math teachers must make the mathematical language more accessible by planning in vocabulary acquisition and teaching concepts and then naming the concepts.

The evidence I am presenting is two photocopies of some lesson plans where I am introducing two new topics. The first I am introducing students to sequences and series. In this lesson, students start with the Entry Task (ET) and are asked to complete “the list of numbers”. Since these are the teacher’s notes, the ideas are just brief notes. After the entry task, the plan is to formally put a name to “a list of numbers” which we will call a sequence. Similarly, as the lesson continues, I plan on clearly indicating and showing students the notation and the vocabulary for the notation about how to write a sequence. When I introduce combinations and permutations on the second lesson plan, I first mention “what are the possibilities of rolling two dice?” This removes technical language, the words “combination” and “permutation” and “the basic multiplication principle” are not even mentioned until the next day in class when students have acquired the conceptual understanding.

By removing the barrier of technical language students feel more comfortable with the content. The teacher will avoid the use of confusing language, but if a student uses improper language (such as the note about the difference between probability and odds in the lesson plan), the teacher will address the students misuse of language and avoid confusion of the vocabulary in the future. The HOPE standard is met because the teacher is planning for proper language acquisition and preparing students to understand content and then later naming that content when students struggle for a word to name the idea.

Over the course of my teaching internship, I have build knowledge and understanding of how to introduce new ideas to students without complicating the matter. From creating lessons that revolve around language acquisition and notation, I have learned that while I may have a deeper, technical understanding of mathematics, many students do not, and become intimidated by advanced language. By using lower level language, many of my challenged students become engaged.

Since many students are apprehensive about mathematics, this technique for introducing new ideas is helpful for students who are overwhelmed by math language and concepts. Providing instruction in an order that is helpful not to overwhelm students is important, especially in mathematics where there is a risk for pushing students away from the topic. To improve my understanding of this program standard, I will need to interact and prepare planning for more students who have different language needs, especially english language learners or those who lack significant mathematical skills. Since this HOPE standard is similar to Differentiation, I hope to address language acquisition, use of language and assisting english language learners as an improvement to my practices in differentiation.


A Day in the Life of a Student

Today’s goal was to follow the school day of a sophomore student throughout their day. To protect the identity of this student they will be called MW. The goal was for me to observe five different classrooms during a six period day. Within each class, I was looking for teaching strategies and tools to use in my own classroom. At the end of the day, I asked MW some questions about their day. While the student interview was only a case study, MW provides several helpful suggestions to improve their learning experience.

The morning classes include Math, English and Biology. Within all of these classes, I noticed good responsive listening. Teachers would ask student questions and then summarize what the student said and repeated the comment to the class so all could hear. In English, the instructor was careful about making smaller comments to encourage conversation in class. The activity in English was to analyze a short story, a topic which can be shallow or deep depending on the students’ understanding. The instructor contributed to the classroom discussion as well to prompt students to analyze the short story more deeply. At the end of the classroom discussion, the teacher make a more sophisticated analysis than the students were able. This exposed the students to higher expectations. The teacher used OneNote to distribute materials to students and students were able to access copies of the teachers journal.

In math class, students started with an entry task to summarize their homework and clarify questions. The class activity was to debrief a challenging problem from the homework and clarify understanding of the basic elements of trigonometric ratios. Students had questions to prepare for a quiz the next day. The activity included a worksheet where students needed to use prior work to plot data and discover a relationship of a sine wave. The end of class, summarized their understanding of “accuracy” and careful procedures for getting more reliable results.

Biology was a very busy class, the lesson was very engaging and highly differentiated. One comment about the lesson that I particularly enjoyed was the presentation of the entry task. The day’s objective was clearly posted on the board and students were able download a copy of class activities from OneNote. Student’s shared out the Initial Thinking questions by popcorn method, students would choose others to “keep the conversation going.” The instructor was clear about the importance of understanding the Carbon Cycle and other biological systems and stated that this would be tested on the End of Course Assessment (EOC). The class activities included a dice game and students would mimic a carbon molecule in the journey throughout the day. Students seemed to enjoy the activity and learned about the many processes of the carbon cycle. Students were able to articulate what happens to a carbon atom as it moves from the sun to plants and then into animals and back into the atmosphere. The activity was followed by a debrief so students could articulate their learning. After the debrief, students watched a video that repeated the material again. This instructor was very smart about providing many learning opportunities for important content. The class ended with an exit slip that informally assessed students learning from the day. Students were instructed to make a carbon cycle as homework to use to prepare for their EOC test in the spring.

After lunch, MW was schedules to attend Current World Problems, Spanish and Health. Mostly, this class period was work time for students to finish a group project about government systems since 1500. MW shared with me the group project and the required elements for a grade. Before work began, students the teacher had a student present a “SHIELD” which allowed the student to comment about their past present and future. The intention of the exercise if for the class to know each other better. Students can share about their interests and goals. Next the teacher gave instructions of work time, he was very clear about presenting a product at the end of the period and made suggestions for groups to produce exemplary work (i.e. Review each other’s papers, get organized and then work together to produce a product). Essentially, the teacher anticipated potential shortcomings and took preventative measures to work through the project. We also talked about some of the functionalities of the grading system to optimise its use.

Next was Spanish in which students entered the class and listened to the instructor through an immersion lecture. The teacher spoke little english when teaching the material, but frequently broke into english to emphasize important points. He continued to discuss why immersion was used and why he believed in this philosophy for language acquisition. Most of this period was direct instruction and lecture based. Students did not respond frequently and when they did, it was brief.

The last class was Health where there was a lot of individual work time. Some of the lesson was direct instruction where students had access to a OneNote document to help follow the lesson and take notes. The period was an introduction to nutrition and involved the explanation of a project. The teacher clearly displayed the objective and the required elements of the project so that students knew what was expected of them throughout the unit. Many students who were in previous classes were also in this class. It was interesting to note the difference in classroom dynamic because of these students. Those who were quiet in the morning, we not more rambunctious and hard to get back on task. Teachers should consider this when teaching.

Finally, after the day, I asked MW some questions about their day. This student liked the biology lesson because there was an activity where she could move. She mentioned this was uncharacteristic of her typical day, but when she moves around, she claims she remembers more. Typically, she enjoys her math class because there are clear instructions and she tends to work hard. MW is also in a robotics class (which I did not attend) but this takes up a lot of her time. Sometimes teachers don’t understand that this is a challenging workload. Along these lines, MW claims that she becomes overwhelmed when projects are overlapping and she does not have the tools to manage this better. MW recommended teaching students in advisory time management and note taking skills. She also would like a space after school to get some work done and manage her schedule. Throughout the day following the student, I realized that the school has very high expectations for the students and teachers don’t often repeat information. This school expects students to understand verbal instructions the first time, which is a challenging skill for many people, even adults.

Annotated Bibliography: Mathematical Literacy

What is an Annotated Bibliography?

Our class was provided ten peer-reviewed journal articles discussing various techniques about math and student literacy. The following document provides the sources for the articles and my commentary about each article. Each commentary is divided into three paragraphs. Paragraph one summarizes the article. Paragraph two assess the utility in my classroom, ratings are on a scale of 1 (I could use this tomorrow) to 3 (this research will not affect my teaching) and commentary is added to discuss reasoning. Paragraph three is a reflection on the application within the classroom or reasons why the research is not useful.

Annotated Bibliography Document

Cited Articles:

  1. Alsina, C. (2002). Too Much is Not Enough, Teaching Maths Through Useful Applications with Local and Global Perspectives. Educational Studies in Mathematics , 50, 239-250.
  2. Bintz, W. P. (2010). Fibbin With Poems Across the Curriculum. The Reading Teacher , 63 (6), 509-513.
  3. Checkley, K. (2001, October). Algebra and Activism: Removing the Shackles of Low Expectations. Educational Leadership , 6-11.
  4. Draper, R. J. (2002). School Mathematics Reform, Constructivism, and literacy: A Case for Literacy Instruction in the Reform-Oriented Math Classroom. Journal of Adolescent & Adult Literacy , 45 (6), 520-529.
  5. MacBride, R., & Luehmann, A. L. (n.d.). Capitalizing on Emerging Technologies: A Case Study of Classroom Blogging. School Science and Mathematics , 108 (5).
  6. Mancil, G., & Maynard, K. L. (2007). Mathematics Instruction and Behavior Problems: Making the Connection. Beyond Behavior , 24-28.
  7. Martinez, M. E., & Peters Burton, E. E. (2011). Cognitive Affordances of Cyberinfrastructure for Science and Math Learning. Education Media International , 48 (1), 17-26.
  8.  Özgen, K., & Bindak, R. (2011). Determination of Self-Efficacy Beliefs of High School Students towards Math Literacy. Educational Sciences: Theory & Practice , 11 (2), 1085-1089.
  9. Phillips, D. C., Bardsley, M. E., Bach, T., & Gibb-Brown, K. (n.d.). “But I Teach Math!” The Journey of Middle School Mathematics Teachers and Literacy Coaches Learning to Integrate Literacy Strategies Into Math instruction. Integrating Literacy Strategies… , 129 (3), 467-472.
  10. Singer, D. (2007). Discourse Time! Developing Argumentative Literacy in the Math Classroom. Coalition of Essential Schools .


Bloggary #1: The Problem with American Textbooks

Through many years of standardized education, textbooks have become the quintessential teacher tool. Powerhouse textbook companies are able to customize book topics to align with state and federal standards for students.  This process has not only driven out less dominant publishers, but also created singular authority on what should be taught and how teachers should teach. The problem is that students receive a disproportionate amount of their learning from a single source, a practice highly discouraged in academics. Additionally, these textbooks are so dense with material and core themes that essential topics are often glanced over to favor covering a wide variety of topics rather than truly integrating strong understanding of a single subject. Even worse, textbooks leave gaps in curriculum further challenging student comprehension of what they read and disengages learners. (Daniels & Zemelman, 2014)

What can be done about the textbook conundrum? Diversify! Textbooks are a great place to start, especially within the STEM fields, but should be used with caution strictly as reference books to start the conversation. Math and science are not closed fields and research continues to be conducted regularly. Classroom conversations should follow student interest, which is why external sources are essential in creating a diverse classroom learning environment. They engage student interests through investigation by research. Traditional math classes are operated by first using lecture, then textbook readings and finally homework problems from the textbook. Real math does not happen this way. Math is a way of logically representing real world scenarios with numbers, so the topic should be taught the same way. Learning through the history of math not only provides cultural perspectives, but encourages literacy. There are interesting stories about economics, stealing, cheating and even crazy people in bathtubs (Archimedes). While most of the new research is far too complex for students to study, learning how to take real world ideas and apply content concepts encourages students to implement their knowledge in a useful way distancing the use of textbooks.

Application allows students to learn about how other subject fields operate. Math is a support for almost every field, so reading and discovering fields outside of mathematics increases student application. One criticism by Daniels & Zemelman (2014) is that textbooks are secondary sources of information, recompiling first or even secondary sources to create a flowing article or document. Using secondary sources for research provides an incomplete picture of the topic area and generally does not help understanding. Math journals and research are not accessible to students and often primary sources are too difficult or dry to provide meaning for them. I believe textbooks are good at breaking down concepts into manageable bite size pieces for students. From here a student can solve mechanical problems. Conversely, the steps are often too simple and solutions are being spoon fed to students. There is sometimes no room for students to think or problem solve. Any math teacher would tell you that mechanical regurgitation of computer like output is not the desired outcome for students. We want real world questions to guide which mechanical concepts are needed to learn and use math techniques to answer those questions.

In general, the content should make sense and students should be able to reconstruct concepts from the ground up. Removing the textbook from the classroom can help with this. Students grow confident knowing that they played a part in their own understanding of topics rather than having a textbook tell them what to know. Integrating real world topics creates a guide to know how to proceed. Teachers can help by nudging students to asking the right questions and directing them to find the right mechanics for solving problems. Daniels and Zemelman suggest many literary reading strategies teachers use to build understanding. Many, but not all, of these techniques are directly applicable to understanding math concepts and becoming literate in the language of math. Sources: Daniels, H., & Zemelman, S. (2014). Subjects matter: Exceeding Standards Through Powerful Content-Area Reading (Second ed.). Portsmouth, NH: Heinemann.

Entry Reflection:

(1) This blog entry demonstrates the HOPE principle O2 – Offer appropriate challenge in the content area. (2) The entry was made with many references to authors Daniels & Zemelman, who wrote “Subjects Matter: Exceeding Standards Through Powerful Content-Area Reading. This entry summarizes much of their work and discussion around the impact of textbooks within the classroom. (3) Teachers should be able to recognize content as valuable or invaluable to students based on the sources of the information and the challenge offered to the students. A textbook may offer information deemed appropriate for the student, however sometimes student have a challenging time understanding the meaning behind what they read. By removing the textbook and creating many sources of information for a student, teachers differentiate their teaching style and engage many learners.

(4) Until reading the critiques, I did not understand the problem textbooks posed for many students, especially those tho are underachieving because of an inappropriate match of learner to reading. (5) Further, I learned that by extending the textbook reading by including more sources of information, teachers are able to differentiate their teaching to meet students needs for optimal learning. (6) The responses in the blog entry have helped me think about how to use alternate sources of information in my classroom. I hope to use textbooks as a reference for students to learn about the technical methods of mathematical processes. I hope to include external sources of information to guide the direction of what to teach in my classroom.

Pre-Course Student Development Reflection

Psychologists provide some insight to understand the development of humans. Educators can take advantage of psychological research by analyzing how human development impacts student’s learning. Through my undergraduate psychology courses I have learned about several developmental influences on students and humans in general. In this reflection, I will focus on three which I am most familiar with, they include schema theory, types of memories and the Atkinson-Shiffrin modal model of memory.

First, through my introductory Psychology course, I learned about schema theory (Riordan, 2014). This theory claims that ideas and theories are formed by an individual’s experiences and then are adjusted when new information is presented. For example, children develop a theory, If i pull this string, the attached toy will follow. Other things that have string like qualities (such as the tail of a cat) could also be pulled with the hopes of the cat moving in the desired direction. However, the child may soon learn that the cat does not like their tail being pulled in a direction and may hiss or scratch at the child. New schema was then developed for the child. They have learned that string like objects will only move in my direction if they are not alive. Schema based learning can be extended to a secondary classroom when students learn about topics over a long period of time. They will need to continually add new concepts to their pool of current knowledge and develop a more rounded view of the topics.

Next, in a cognitive psychology course (Hyman, 2014), I learned about the various forms of memory systems and techniques. With many classroom demonstrations,  we covered the distinct differences between semantic and episodic. In class, we discussed how students tend to remember episodic experiences better than semantic knowledge. Because the human brain prefers events over pure knowledge, we are inherently better at retaining knowledge based in concrete examples rather than intangible ideas or feelings. (Hyman, 2014) Relating this back to teaching, students are more likely to remember an event that was engaging rather than a concept read and memorized for exam purposes. Helping students create episodic memories in the classroom can help increase their understanding and development in subject content.

Finally, the Atkinson-Shiffrin modal model of memory (1968) prescribes and outline of how humans interpret events and store them in their memories. Human’s use their senses (e.g. sight, sound, touch, smell) to intake new memories in the sensory memory. Then, some, but not all, information from the sensory memory is transferred to the short term memory store. Within the next few seconds, our brains transition the short term memory into the long term memory where information is stored indefinitely. Many arguments surround the retrieval of long term memories or the validity of this model, but that is outside the scope of this topic. One agreed upon element is rehearsal increases the ability to retrieve information (Atkinson-Shiffrin 1968). Rehearsal in the classroom can come in many forms, testing encourages rehearsal to increase the ability to retrieve information in a stressful situation. Additionally, simply reviewing ideas within a classroom can help student dedicate the semantic knowledge into their long term memory for easy retrieval. While this ideas of the modal model sound complex, the process is surprisingly natural for humans. (Hyman, 2014)

Developing understanding for how the brain is able to acquire new information in the form of memory helps educators understand how to best assist students. In line with the HOPE standards, by better understanding how humans learn, educators can honor student diversity and development (H1) as well as provide efficient access to content material to encourage subject understanding (H2).