EDRD6530 – A Mile Wide but an Inch Deep

The first chapter from Content Area Writing: Every Teacher’s Guide surfaced quite a few “big ideas” that had meaning for me. The main issue that I want to discuss is the idea of teaching students content that is a mile wide but an inch deep. This is a problem in every subject area. In mathematics, teachers are pressed to convey so much content in such a short period of time that many students lack the ability to find meaning and relevance in their own lives. I think mathematics education could be far richer if there existed greater time for large-scale projects that connect multiple skills and integrate across content areas. I also think that projects could infuse a greater interest in mathematics and appreciation of its presence in our everyday lives.

One suggestion that the authors gave is “never add a new activity to your teaching schedule before you subtract something else” (pg. 16). I think this is a very useful tip. While planning lessons in my internship I’ve recognized a tendency to keep adding more information or activities to the daily lesson. This is because I value the depth of content and believe it important for my students to learn. The problem that I then run up against is lack of time and conveying information too quickly. Going into detail without adequate time isn’t beneficial either because kids can’t absorb new knowledge that quickly. Thus, the take-away lesson for me is; find something to discard before adding something new.

Daniels, H., Zemelman, S., & Steineke, N. (2007). Content-Area Writing: Every Teacher’s Guide. Portsmouth, NH: Heinemann.

EDU 6139 – Standard S

To view my meta-reflection on standard S check out my new page! This will be a work in progress as I grow in my internship and gather more data on student learning.

Standard S refers to…

Knowledge of Subject Matter and Curriculum Goals

Teacher Candidates positively impact student learning that is:

I. Content Driven. All students develop understanding and problem-solving expertise in the content area(s) using reading, written and oral communication, and technology.

II. Aligned with curriculum standards and outcomes. All studnets know the learning targets and their progress toward meeting them.

III. Integrated across content areas. All students learn subject matter content that integrates mathematical, scientific, and aesthetic reasoning.

EDU 6942 – September Experience

Actually going to school and observing teachers at work is one of the best learning approaches for me. I am a hands-on, “do-it-yourself” type learner and appreciate the chances I get to engage with students and teachers. I therefore really enjoyed the September Experience class which required 20 hours of observation and assistance time at the opening of the school year. I observed and assisted at a middle school with two seventh grade mathematics teachers. I’ve attached my reflective paper that discusses in detail my thoughts about what I saw and heard.

September Experience Paper

EDU 6139 – Week 2 Reflection

Week 2: What characteristics of lessons have been memorable, intriguing, or surprising to you? Why has this been the case and what characteristics do you deem worthy of emulating as you develop your own teaching style?

One aspect that I really enjoy about the lesson design, and will emulate in my own career, is that instructional time is kept to a minimum. “Research has shown that the typical teacher consumes 90 percent of the allocated time” (Wong & Wong). Unfortunately, when the teacher consumes the majority of classroom time students are not given the opportunity to practice, reflect on, or absorb the content. As I mentioned earlier, my mentor teacher has adopted complex instruction, which focuses on increasing the amount of “engaged” time on the part of the students and designing tasks that are group worthy.  In our classroom Instructional time occupies on average 10-15 minutes at the beginning of the period and engaged time occupies about 30-40 minutes. During engaged time students are working together in groups of three or four on challenging, thought provoking tasks. The teacher is rotating through the room observing student work, asking questions, checking for understanding, and ensuring on-task behavior.

On the whole, the level of commitment and participation by students in the group activities has pleasantly surprised me. Majority of students are working collaboratively together to complete assigned tasks and showing genuine interest and excitement in learning. I attribute the excitement to the fact that students are the ones doing the work. The teacher provides a short lesson on the material and essential knowledge, and then the students are given adequate time to practice, think, and discuss their learning. Every student is responsible for recording all work in his/her individual math journals. In addition, many tasks also incorporate a group product. The product is either an extension of a problem or an entirely new problem that requires extra effort or thought. For example, one product that students were asked to complete the other day was a “group think page” in the middle of the table. This product asked that students complete all problems in their own journals, but as a group they had to justify their thinking and record it on the shared page. For example, one problem asked students to order integers from least to greatest. Each student ordered the integers in his/her journal and as a group wrote or diagramed their reasoning on the shared page. Here is an example of one groups’ “think page.” I think this product is very powerful because it encourages students to reason why they do what they do, and practice explaining in mathematical language. It also gives the teacher a view into the students’ thinking. I’m really fond of incorporating a “product” into daily work. I believe group or individual products offer variety to daily lessons and support student growth in critical thinking and problem solving. It offers a different dimension to learning mathematics. I will definitely find ways to include various product ideas into my teaching practice.

Overall I think there are many positive aspects to the instructional style that my mentor teachers employ. I like direct instruction at the beginning of the lesson because there is always valuable information to impart and direct teaching is usually the most effective route. I also like that direct instruction is kept short to allow for plentiful student engagement. The emphasis on group worthy tasks is also an aspect that I wish to adapt because I believe mathematical problem solving is enhanced when students collaborate and share ideas. There are some aspects to the instructional style that I am still questioning and forming an opinion. For instance, I wonder if there should be more of a balance between group activities and individual activities. I have noticed that many students love the group interaction, but others clearly would prefer thinking and processing alone. I also think that individual processing time is necessary for students to check their own understanding.  Another aspect of the instructional style that I am questioning is the opportunity to assess student learning. Aside from the weekly homework quizzes and unit tests, this is done informally by the teacher as she rotates through the room to check in with groups. The problem that I am seeing is that students are more easily able to “piggy back” onto others work. This is of course always the case with group work. So, to counteract this, my mentor teachers and I are trying to create tasks and products that require input from all members. We also incorporate regular check-ins called “shuffle quizzes,” which are designed to encourage all students to be accountable for their own learning. For instance, as we rotate from group to group we shuffle the students’ journals and ask the chosen student to explain the steps involved to solve such and such problem. This process encourages students to stay accountable for their learning and ask questions if necessary. It also allows my mentor teacher and myself to randomly check for student comprehension. Although “shuffle quizzes” and “group think” pages are effective ways to assess student learning I do think there is room for improvement in this area. However, it is still early in the year so perhaps methods of assessment will become more visible to me as we move forward in the school year. Overall, there are many aspects to the teaching style that I am sure I will emulate in my own practice.

Wong, H.K., & Wong, R.T. (2005) The first days of school: how to be an effective teacher. Mountain View, CA: Harry K Wong Publications.

EDU 6132 – Family Involvement in School

A healthy interaction between school and parents is an important component for a child’s success at school. As a future secondary level math teacher (leaning towards middle school) I have considered how I can involve my parents in their child’s development. Sadly, parental involvement drops significantly once children enter middle school. This is unfortunate because middle school years are some of the most vulnerable and influential years for students, as many are going through the confusing time of puberty and questioning how “cool” school really is. I believe that more parental involvement can have a positive impact on both the social and academic development for children. Meece and Daniels (2008) tell us that parent involvement at school includes attending parent-teacher conferences and engagement in volunteer activities and school programs.

In my future math class I would like to include parents in as many aspects of student learning as possible. First, I would like to create a class blog, which I plan on updating daily so that parents are always familiar with their child’s learning for that day and aware of the short and long-term learning goals. I’ve encountered my parents who express a lot of frustration about not knowing their child’s schedule, when tests are, what projects or going on, etc. Many parents want to be involved but are not sure how to be involved without pestering the teacher. To me this is a faulty system because parents and teachers can best help the child by working together as partners (Meece & Daniels, 2008). Therefore, the more I can keep my parents informed the better they can help their child at home. This also includes having parent-teacher conferences and being flexible with the scheduling times.

In addition to keeping open lines of communication I would really like to see more parent involvement at school. I understand that many parents work but there may be some who have the flexibility to come into class. Ideally I would love to have a volunteer sign up sheet (on the blog) where parents can pick a time to come into class and help out. I would design certain roles for these volunteers, which may include leading small group discussion, rotating through the room to help students with classroom exercises, and perhaps working one-on-one with students who need extra help. This level of involvement would take a lot of organization on my part but I think it would be worth the effort. Meece and Daniels (2008) point out that classroom involvement can help parents “gain confidence in their own parenting abilities and in their abilities to help their children succeed in school.” This seems like a win-win to me.

In addition to individual teachers reaching out to parents the school can also help students by promoting healthy habits and modeling a balanced, healthy life style. As we read in chapter 8 of Medina stress has a detrimental effect on learning. Thus, the more the school can foster a healthy, stress free environment the better. Some actions the school may take are offering healthy food choices, placing an emphasis on exercise, fostering a supportive community within the school, providing more counseling, and offering more before and after school programs.

EDU 6132 – Positive Peer Relations

“Peer relations play an important role in fostering school engagement, motivation, and achievement” (Meece & Daniels). Sadly, forming friendships and establishing positive relations with peers can be very difficult for many children. Some children lack the necessary social skills to interact with others in a friendly, cooperative, and good-natured manner. Children who don’t form positive peer relations are either rejected or neglected. Both situations are costly to the students’ academic and social development (Meece & Daniels).

Teachers can help students who struggle with peer relations by developing and promoting a safe and inclusive classroom environment. If students feel comfortable in the classroom they will be better able to focus on the learning activities. My hope is that if students learn to respect each other and be kind in the classroom, they will carry over these attitudes into the lunchroom, other classrooms, and situations outside of school.

Creating a supportive and inclusive classroom takes effort on the part of the teacher. One strategy that I particularly like is cooperative learning groups because it benefits students both socially and academically (Meece & Daniels). When students work in groups they are able to discuss ideas, ask questions, share different viewpoints, problem solve together, and learn alternative modes of thinking. All of these activities help increase the students’ level of understanding about the topic. Participation in these activities also helps students recognize the strengths of his/her peers, which can help reduce certain prejudices and stereotypes. For example, when working on a group math project a student may struggle in developing an equation and solving for a solution by may be very proficient in designing a poster and graph to accompany the problem. Another student may be an excellent writer and offer a concise explanation and descriptive piece to accompany the project. The aim is that cooperative learning exercises will encourage students to learn from each other, help students recognize that everyone has something valuable to offer, and help reduce negative peer relations.

Although cooperative learning is a useful strategy for promoting positive relations between peers, it’s still necessary that teachers take an active role in supervising and guiding interactions to ensure that groups work constructively together (Preciado, 2011). Assigning students to groups does not automatically mean they will work in a positive way together. Students need guidance and support in order to learn what constitutes cooperative, friendly, and helpful behaviors. This may mean that teachers assign specific roles to make sure everyone is contributing, use flexible grouping, and intervene when necessary.

References

Meece L., J., & Daniels H., D. (2008). Child and adolescent development for educators. New York: The McGraw-Hill Companies, Inc.

Preciado, J. (Producer). (2011, May). Edu 6132 students as learners [Audio Podcast]. Seattle Pacific University.

EDU 6132 – Factors to Consider When Planning

What factors should you take into consideration when planning a lesson/unit in your discipline?

One major consideration that I will take into account when planning my lessons is that every brain is wired differently (Medina, J., 2008). According to Medina there are billions of multiple intelligences because no two brains are alike. Since I am interested in teaching secondary mathematics this means that I must be creative and flexible in my instructional approach. My goal is to incorporate many instructional techniques so that students have multiple opportunities to fill in their knowledge gaps. Math is a challenging subject for many students because brains interpret information differently.  The teacher might teach one way that makes sense for some students, but is completely confusing for others. If I encounter a moment like this, which I know I will, my objective is to spend time to ensure that all students are caught up. To do this I will have to use time and space flexibly to ensure the best outcome for learned knowledge. Some ideas I have are to create working stations; where students work in small groups on specific concepts. I can then scaffold so that some stations are more challenging and complex, and others are designed to re-teach and practice basic skills. I would like to structure my daily lessons in a way that provides students the opportunity to work on concepts that match their unique needs.

Medina’s concept of multiple intelligences also connects to Piaget’s theory of cognitive development; that children have their own logic and way of knowing things. Piaget believed that education should develop children’s ability to think independently rather then stifle it through the transmission of knowledge. He believed that “students must have opportunities to experiment, to question, and to create their own meaning through their own physical and mental activities” (Meece, L., & Daniels, D., 2008). This element of discovery is important in middle and high school mathematics because concepts become more abstract. Students need time to share and discuss ideas, collaborate with each other, and problem solve as a group. As the teacher my role is to facilitate discussion and pose challenging, thought provoking questions.

On the whole, I hope to incorporate discovery-based learning into my lessons and provide adequate time for students to absorb new information. My aim is to be sensitive to the different needs of students and recognize that each student brain is interpreting knowledge in his/her own unique manner.  Taking that into consideration, I will plan my lessons so that I use multiple strategies and instructional approaches. I will also plan the day to incorporate flexibility and adaptations into the lessons.

EDU 6132 – What kind of teacher would you like to be?

What kind of teacher would you like to be? Why?

As a prospective secondary level mathematics teacher I greatly appreciate Wu’s arguments about the false disconnect between basic skills and conceptual understanding. “Conceptual advances are invariably built on the bedrock of technique” (H. Wu, 1999). With this in mind, I want to be a mathematics teacher who teaches students algorithms in a manner that enables them to grasp the skill, in addition to the conceptual component that the skill embodies. I believe that memorization and mastery of basic skills is important, but only by way of teaching students the underlying ideas, or theories that back these skills. I often hear students express feelings of confusion and frustration associated with math. These feelings are usually connected to their lack of understanding about the concepts, and boredom with just memorizing formulas and solving numerous problems. I want to help students develop number sense and the ability to reason by effectively teaching them mathematical principles.  I believe that if students increase their conceptual understanding, they will in turn develop better mastery over the skills, and thereby utilize higher order thinking. My hope is that this will alleviate some of the negative feelings connected to mathematics study.

In addition to fostering academic growth in students I also want to be a teacher who inspires confidence in ones self. I want to teach my students that each and every one of them is capable of learning and succeeding in school and life. Taking into consideration Meece & Daniels (2008) this goal requires that I create a learning environment that supports child development. By increasing my knowledge of child development I will be more effective at shaping positive school experiences. One component of creating a positive experience is giving students positive affirmation.

The Early Catastrophe brought to light an astonishing statistic on the ratio of encouragements to discouragements from parents of different income groups. Sadly, the average child in a welfare family accumulated 1 encouragement to every 2 discouragements. With these thoughts in mind, I want to be a teacher who consistently works to understand all my students as individuals and makes every effort to create a positive, supporting learning environment.

EDU 6132 – Reflection #1

I really enjoyed reading Medina’s book, Brain Rules: 12 Principles for Surviving and Thriving at Work, Home, and School, because it was informative, humorous, and to the point. I found that the  “rules” were not necessarily new ideas, but they were well argued and supported by scientific research. For this reason, I found them enlightening and inspiring. The fact that “physically fit children…appear to concentrate better…and allocate more cognitive resources to a task and do so for longer periods of time” (Medina, J., 2008) made me wonder physical education does not have a greater presence and importance in schools and classrooms. It seems that simple changes could make a great difference. For example, teachers could plan lessons so that students move around during the class period. This could take the form of students rotating groups, working at the white board, utilizing alternative seating arrangements such as exercise balls to allow students to fidget in a constructive manner. Ultimately, we need to keep our students active in the classroom in order to stimulate blood flow to the brain.

Meece and Daniels (2008) was also a revealing introduction to the study of students as learners. The first chapter draws attention to fact that teachers are but one influence on child development. There are various other factors such as race, family structure, socio-economic-status, etc., that blend together to influence the development of a child. However, “adolescents spend approximately one-third of their waking hours in school” (Meece, J.,  & Daniels, D., 2008), which suggests that teachers can contribute significantly to the social development of students. This then necessitates that as a future teacher I need to be knowledgeable about child development and aware of the status of children today. Page 17 in Child & Adolescent Development for Educators presents a portrait of America’s children today. I was shocked by some of the statistics and the challenges they pose to both students and teachers.

A final piece of the reading from this week that I would like to discuss is the “Focus on Teaching” from Meece & Daniels (2008) found on page 10. Since I am an aspiring mathematics teacher I appreciated reading the comparison between mathematics classrooms in America from those in Japan. I think it can be very beneficial to learn from other cultures. The following two lessons I pulled from the excerpt on page 10 of Meece & Daniels (2008).

Lesson 1: American students spend most of their time in mathematics classes acquiring isolated skills through repeated practice. In contrast students in Japan spend as much time solving challenging problems as they do practicing skills.

Lesson 2: In America, the teacher’s role is to break down complex tasks into manageable pieces and to provide plenty of opportunities to practice. By contrast, Japanese teachers find challenging problems to begin the lesson and refrain from showing or telling students how to solve the problem.

Reading about these differences has inspired me to research more about differences in mathematics education across cultures. I believe there is a lot to learn from other cultures and perhaps experiment with different approaches to find what works well. I hope that there will be more readings during this course that discuss mathematics education because I thoroughly enjoyed all of the readings from this week.

Reference List:

Meece, J., & Daniels, D. (2008). Child & adolescent development for educators (3^rd ed.). New York: McGraw-Hill Companies.

Medina, J. (2009). Brain rules: 12 principles for surviving and thriving at work, home, and school. Seattle: Pear Press.

EDU 6130 – My Personal Philosophy on Classroom Management

After reading and discussion various experts’ philosophies and methods for classroom management I was asked to craft my own philosophy on discipline. I must admit this was a harder task than I expected. I found myself liking many approaches and had a difficult time synthesizing them in a way that would merge with my own personality. After much thought I was finally successful in creating a temporary classroom management plan. The details can be read in my philosophy on discipline paper.