As the math teacher, my daughter reaps the “benefits” of daily math facts flashcard practice. Although neither of us particularly looks forward to the drill and kill exercises, my experience of working with students in eighth grade who have not yet mastered basic computations reinforced the importance of such activities. Regardless of the level of enjoyment, it is absolutely critical to establish a strong foundation in basic mathematical skills in order to increase the likelihood of success in higher level math courses.
Bransford, Brown, and Cocking state that mastery and memorization are significant components of traditional education. However, research on development of expertise in a subject matter requires more than the recollection of facts. The child must have the opportunity to construct learning through inquiry-based instruction. Not only must teachers work to develop mathematical knowledge, but they must cultivate the students’ general problem solving skills.
I constantly look for everyday, hands-on activities that incorporate math skills. Simple actions such as working with my daughter in doubling a pancake batter recipe or keeping an accurate Yahtzee scorecard indirectly highlight the importance of performing mathematically-sound arithmetic operations. I find the integration of hands-on algebraic activities more difficult because algebra is infrequently used in everyday life experiences.
With the increase of technology and computer-based education however, relevant and engaging resources are becoming more widely available, although the quality of such tools is not guaranteed. Prior to using a program (web-based particularly), I ensure that the program is legitimate and worthy of the devotion of instructional time. To teach about slope and equations of linear and quadratic functions, I utilize a software program called Green Globs. I use Study Island, a web-based instructional tool aligned with state standards, to prepare students for PSSA testing. The Utah State University developed interactive algebra activities in its National Library of Virtual Manipulatives that are aligned with the National Council of Teachers of Mathematics Standards. This site includes activities that mimic classic games such as Peg Puzzle or Switch or Stick and the feedback is given immediately on the same screen.
Bransford, Brown, and Cocking advocate the practice of incorporating real-life problems and simulations into the classroom. In addition, they encourage opportunities in which learners receive feedback – whether it be from computer-based or directly from a teacher. These are just two of the numerous ways mentioned in “Conclusions and Recommendations for Research” chapter in which technology can assist with the establishment of effective learning environments.
As I continue to work to develop my algebra students’ mathematical abilities using a wide range of resources, I take great interest in assisting in the development of my daughter’s mathematical foundation by continuing the daily flashcard practice (against her wishes!) Although the world of virtual manipulatives, web-based tutorials, and Green Globs is remarkable, without a solid base in arithmetic operations, the activities are entirely ineffective.
References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
Thursday, November 20, 2008
Thursday, November 13, 2008
Blog#9 - Oh No! Here Comes the SMART Board!
Nine years ago, I was perfectly content using my blackboard and chalk at the front of my first classroom. I invested in dust-free chalk and the best erasers I could find. Two years later, I cringed when our technology professional wheeled in a fancy overhead projector and installed a white screen above my beloved chalkboard. I remember wheeling the cart to the back of the room until I received a pre-observation notice in my mailbox and reluctantly began to use the projector.
Although at first my complaints, such as blocking students’ views and fan noise, outnumbered my perceived benefits, it was not long before using the overhead became practically second nature. Before I knew it, my chalk was tucked away and I had officially and successfully integrated technology in the classroom. As stated in Bransford, Brown, and Cocking’s “Technology to Support Learning” chapter, even though the chalk was “old”, it was still useful. I used the overhead for guided instruction and the chalkboard for students to display their independent practice.
By year six of my teaching career, my math course binders were extraordinary. Not only was each lesson planned accordingly, but my color-coded overhead transparencies were organized to perfection. Other than the occasional incorporation of a new teaching strategy, my planning was essentially complete…until I received word that I was the lucky recipient of one of three SMART Boards in the school.
The learning curve was steep and I tried deciphering the functions myself, but the task of operating the SMART Board seemed overwhelming. I initially treated it as an untouchable (intimidating) piece of equipment and continued using the overhead projector as long as I could, but eventually I took the plunge and connected the SMART Board.
After three years, I can state convincingly that utilizing this technology has significantly impacted student interest and motivation to learn. Students no longer have to mentally visualize geometric transformations. This powerful too allows them to see the rotations and reflections in action. Not only is the SMART Board colorful and dynamic, but it is interactive and reaches students with various learning styles. The vast majority of available research supports the view that interactive whiteboards have the potential to have a positive impact on teacher pedagogy and learner engagement.
Bransford, Brown, and Cocking agree that new technology extends possibilities and creates new learning environments. According to Snowman & Biehler (2006), the National Board for Professional Teaching Standards proposed that teachers be “members of learning communities.” Likewise, Bransford, Brown, and Cocking endorse the establishment of electronic collaboratories, virtual learning communities that link students with field professionals. All of this is possible with a SMART Board!
Soon, the SMART Board will be considered an ancient artifact just like my chalk box seven short years ago. Another fascinating and more efficient piece of equipment will replace it and I actually look forward to the opportunity!
References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
Snowman, J., & Biehler, R. (2006). Psychology applied to teaching, (11th ed.). Boston: Houghton Mifflin.
Although at first my complaints, such as blocking students’ views and fan noise, outnumbered my perceived benefits, it was not long before using the overhead became practically second nature. Before I knew it, my chalk was tucked away and I had officially and successfully integrated technology in the classroom. As stated in Bransford, Brown, and Cocking’s “Technology to Support Learning” chapter, even though the chalk was “old”, it was still useful. I used the overhead for guided instruction and the chalkboard for students to display their independent practice.
By year six of my teaching career, my math course binders were extraordinary. Not only was each lesson planned accordingly, but my color-coded overhead transparencies were organized to perfection. Other than the occasional incorporation of a new teaching strategy, my planning was essentially complete…until I received word that I was the lucky recipient of one of three SMART Boards in the school.
The learning curve was steep and I tried deciphering the functions myself, but the task of operating the SMART Board seemed overwhelming. I initially treated it as an untouchable (intimidating) piece of equipment and continued using the overhead projector as long as I could, but eventually I took the plunge and connected the SMART Board.
After three years, I can state convincingly that utilizing this technology has significantly impacted student interest and motivation to learn. Students no longer have to mentally visualize geometric transformations. This powerful too allows them to see the rotations and reflections in action. Not only is the SMART Board colorful and dynamic, but it is interactive and reaches students with various learning styles. The vast majority of available research supports the view that interactive whiteboards have the potential to have a positive impact on teacher pedagogy and learner engagement.
Bransford, Brown, and Cocking agree that new technology extends possibilities and creates new learning environments. According to Snowman & Biehler (2006), the National Board for Professional Teaching Standards proposed that teachers be “members of learning communities.” Likewise, Bransford, Brown, and Cocking endorse the establishment of electronic collaboratories, virtual learning communities that link students with field professionals. All of this is possible with a SMART Board!
Soon, the SMART Board will be considered an ancient artifact just like my chalk box seven short years ago. Another fascinating and more efficient piece of equipment will replace it and I actually look forward to the opportunity!
References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
Snowman, J., & Biehler, R. (2006). Psychology applied to teaching, (11th ed.). Boston: Houghton Mifflin.
Thursday, November 6, 2008
Blog#8: Teacher Learning...in Atlantic City?
Upon reflecting upon my education, I now remember fondly not the most popular mathematics teachers (whose nicknames were typically something along the lines of “Easy A (fill-in-the-blank)” or were just plain cool), but those who were structured, disciplined, and truly mastered the art of teaching. The teachers I now recall most favorably are those who challenged me and those from whom I learned the most mathematical content. These teachers could easily be identified by gauging my progress early in the following school year when we reviewed the previous year’s concepts and I felt confident and not especially in need of the review.
It is amazing how maturity influenced my assessment of pedagogical practice. After reading Bransford, Brown, and Cocking’s “Teacher Learning” chapter, I began to contemplate all of the factors that affect teaching practices such as self-reflective abilities, prior experiences, professional development opportunities, and post-graduate education. It is difficult to compare teachers, as no two teachers I have had are all that similar in practice or demeanor. These differences exist as a result of many factors, including past educational experiences, teacher preparation programs, frequency of incorporation of self-inquiry and reflection exercises to improve practice, quality and quantity of profession development opportunities, and continuing education. These aspects result in an educators’ melting pot. Experience forms the person and likewise influences teaching methodologies.
While several of these factors are inherent, the one area in which schools are directly responsible is professional development. New teachers in my district are required to attend 60 hours of professional development seminars and courses during their first year (6 additional hours required in the event of each snow day). After the first year, the number of hours required for professional staff is 18. There exists a comprehensive (and impressive) professional development program within the district that offers many interesting opportunities for growth. However, loopholes in executing the professional development plan often cause the cancellation of these quality programs due to lack of interest. Most teachers I know “earn” their hours through summer team meetings (in Atlantic City or at the local pub) or other non-professional development events such as website maintenance and compiling team clothing orders, practices which have been approved year-after-year by building administrators ever since I joined the district five years ago. Although these activities build rapport and organizational skills, in my opinion, they do not enhance teaching and should not count towards the teacher’s mandated hours.
Professional development is an area in which every educator in the melting pot may be inspired to grow, or in the least, encouraged to reflect upon current practices which promotes self-improvement. If professional development trends remain similar, my hypothesis is that the popular “Easy-A” teachers back in the day may have frequented the same establishments as some of my colleagues for their so-called professional development. I cannot help but wonder how many of the teachers who positively impacted my life actively participated in professional development opportunities during their career.
References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
It is amazing how maturity influenced my assessment of pedagogical practice. After reading Bransford, Brown, and Cocking’s “Teacher Learning” chapter, I began to contemplate all of the factors that affect teaching practices such as self-reflective abilities, prior experiences, professional development opportunities, and post-graduate education. It is difficult to compare teachers, as no two teachers I have had are all that similar in practice or demeanor. These differences exist as a result of many factors, including past educational experiences, teacher preparation programs, frequency of incorporation of self-inquiry and reflection exercises to improve practice, quality and quantity of profession development opportunities, and continuing education. These aspects result in an educators’ melting pot. Experience forms the person and likewise influences teaching methodologies.
While several of these factors are inherent, the one area in which schools are directly responsible is professional development. New teachers in my district are required to attend 60 hours of professional development seminars and courses during their first year (6 additional hours required in the event of each snow day). After the first year, the number of hours required for professional staff is 18. There exists a comprehensive (and impressive) professional development program within the district that offers many interesting opportunities for growth. However, loopholes in executing the professional development plan often cause the cancellation of these quality programs due to lack of interest. Most teachers I know “earn” their hours through summer team meetings (in Atlantic City or at the local pub) or other non-professional development events such as website maintenance and compiling team clothing orders, practices which have been approved year-after-year by building administrators ever since I joined the district five years ago. Although these activities build rapport and organizational skills, in my opinion, they do not enhance teaching and should not count towards the teacher’s mandated hours.
Professional development is an area in which every educator in the melting pot may be inspired to grow, or in the least, encouraged to reflect upon current practices which promotes self-improvement. If professional development trends remain similar, my hypothesis is that the popular “Easy-A” teachers back in the day may have frequented the same establishments as some of my colleagues for their so-called professional development. I cannot help but wonder how many of the teachers who positively impacted my life actively participated in professional development opportunities during their career.
References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
Thursday, October 30, 2008
Blog #7: Am I an Effective Teacher?
According to William Glasser, a notable psychiatrist and educational theorist, “Effective teaching may be the hardest job there is.” In this age of technology and testing, balancing the demands of accountability in No Child Left Behind while maintaining the attention and interest of the digital natives in the classroom is quite a challenge.
Bransford, Brown, and Cocking advocate that teachers must meet two criteria to be effective. First, the teacher must possess a deep understanding of the subject matter. As an eighth grade mathematics teacher, I feel that I not only thoroughly understand algebra, but I also have a solid background in prealgebra (for remediation), as well as geometry, trigonometry, and calculus (for enrichment or to appropriately relate current algebraic topics to future learning). It is an extraordinary moment observing students realize that the study of mathematics is an interconnected puzzle that all fits together, not a series of disjointed courses. I enjoy responding to, “Where are we ever going to use this in real life?” and having research and experience to back it up. Once the first brave student asks, I take an entire period to share the wonderful world of mathematics – and to excitedly inform them that algebra is just the beginning!
The second requirement of effective teachers is a thorough grasp of the pedagogical knowledge of how students learn. This includes adapting instruction to meet needs of students with various learning styles as well as creating activities that engage students through inquiry-based learning. Reflecting on my own teaching, this is an area in which I strive for constant improvement.
As an undergraduate, I earned my Bachelor of Science in mathematics. Fast forward to graduation and my decision to work as a technical analyst at Accenture, when my father took the opportunity to tell me that life is too short to do what you do not want to do. Later that summer I learned about New Jersey’s Alternate Route to Certification Program and I started teaching two weeks later. No educational background and here I was teaching America’s future Algebra and EARTH SCIENCE! (I can state with confidence that Bransford, Brown, and Cocking would not have wanted their own children in my Earth science class.)
As the school year progressed, I learned a great deal and I worked hard to become not just a purveyor of knowledge, but a teacher, through reading, studying, observing, collaborating with my amazing principal, and completing coursework through Alternate Route.
Eight years later, I hope that Glasser, Bransford, Brown, and Cocking would deem me an effective teacher. As illustrated by the model teachers in chapter 7 of How People Learn, effective teachers continually work to revise practices and ensure that each learner receives an education suited to meet his or her needs. I support Glasser’s assertion that truly effective teachers are in one of the toughest professions out there.
References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
Bransford, Brown, and Cocking advocate that teachers must meet two criteria to be effective. First, the teacher must possess a deep understanding of the subject matter. As an eighth grade mathematics teacher, I feel that I not only thoroughly understand algebra, but I also have a solid background in prealgebra (for remediation), as well as geometry, trigonometry, and calculus (for enrichment or to appropriately relate current algebraic topics to future learning). It is an extraordinary moment observing students realize that the study of mathematics is an interconnected puzzle that all fits together, not a series of disjointed courses. I enjoy responding to, “Where are we ever going to use this in real life?” and having research and experience to back it up. Once the first brave student asks, I take an entire period to share the wonderful world of mathematics – and to excitedly inform them that algebra is just the beginning!
The second requirement of effective teachers is a thorough grasp of the pedagogical knowledge of how students learn. This includes adapting instruction to meet needs of students with various learning styles as well as creating activities that engage students through inquiry-based learning. Reflecting on my own teaching, this is an area in which I strive for constant improvement.
As an undergraduate, I earned my Bachelor of Science in mathematics. Fast forward to graduation and my decision to work as a technical analyst at Accenture, when my father took the opportunity to tell me that life is too short to do what you do not want to do. Later that summer I learned about New Jersey’s Alternate Route to Certification Program and I started teaching two weeks later. No educational background and here I was teaching America’s future Algebra and EARTH SCIENCE! (I can state with confidence that Bransford, Brown, and Cocking would not have wanted their own children in my Earth science class.)
As the school year progressed, I learned a great deal and I worked hard to become not just a purveyor of knowledge, but a teacher, through reading, studying, observing, collaborating with my amazing principal, and completing coursework through Alternate Route.
Eight years later, I hope that Glasser, Bransford, Brown, and Cocking would deem me an effective teacher. As illustrated by the model teachers in chapter 7 of How People Learn, effective teachers continually work to revise practices and ensure that each learner receives an education suited to meet his or her needs. I support Glasser’s assertion that truly effective teachers are in one of the toughest professions out there.
References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
Wednesday, October 22, 2008
Blog#6: The Design of Eighth Grade Pre-Algebra
The general design process begins with an identified issue in need of resolution. It proceeds through a structured series of phases beginning with the acquirement of relevant research. Designers then reflect upon the information and utilize it to brainstorm possibilities until an optimal solution is determined. Instructional designers follow the same structured strategy, although the goal is more specific in that the process applies principles of learning to lesson planning.
In my Pre-Algebra class of 27 students, thirteen scored basic or below on the 2007 Mathematics PSSA. The remaining fourteen were on the borderline proficient. Eleven have IEPs, three are ESL, and one is deaf. The overarching goal, as dictated by administration, is to do whatever it takes to “get these kids proficient”.
I am fortunate enough to work in a district that has the resources to support students. There are four additional staff members assigned to this course and this amazing 5.4:1 student to staff ratio guarantees that students receive attention.
Bransford, Brown, and Cocking explain their four views regarding design of learning environments - learner centered, knowledge centered, assessment centered, and community centered.
The instruction is learner centered in that prior learning is recognized and built upon, using results of pre-tests and grouping students according to their current levels of understanding. Groupings change constantly.
Although I have always been “Ms. Yudt”, I am now “Miss”. We discuss that this term is one of deference and we marvel that yes – we can take the textbooks home to do homework! We emphasize the importance of being sensitive and respectful to all cultures.
Following the gauging of the students’ readiness levels, I design instruction that meets various learning styles. A recent lesson on angles was innately mathematical-logical, but I extended it linguistically (a-cute baby, obtuse moose), kinesthetically (“Aerobic Angles”), visual-spatially (pretzel stick angles), and musically (singing “All about Angles”– not especially popular with the eighth graders!). These knowledge-centered activities enhance the curriculum by engaging the learners in something other than textbook exercises, and the utilization of progressive formation ensures that the activities are developmentally appropriate.
Students have the opportunity to demonstrate understanding on summative assessments (1 quiz/test per unit) as well as on standardized tests. Formative assessments, such as a 3-2-1 tickets out and math jeopardy games, provide valuable, immediate feedback to both the students and me.
Parental involvement and support are key components to a successful working relationship with the students. For every “bad” call I make home, I make one “good” call. If parents are on-board, students are more likely to put forth effort in studying mathematics. We work as a community to increase the likelihood of success in the classroom.
Designing quality instruction takes time and energy. However, the investment is well worth it as students benefit and learning increases with effective teaching and clear, measureable goals, all incorporated into the instructional design process.
References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
In my Pre-Algebra class of 27 students, thirteen scored basic or below on the 2007 Mathematics PSSA. The remaining fourteen were on the borderline proficient. Eleven have IEPs, three are ESL, and one is deaf. The overarching goal, as dictated by administration, is to do whatever it takes to “get these kids proficient”.
I am fortunate enough to work in a district that has the resources to support students. There are four additional staff members assigned to this course and this amazing 5.4:1 student to staff ratio guarantees that students receive attention.
Bransford, Brown, and Cocking explain their four views regarding design of learning environments - learner centered, knowledge centered, assessment centered, and community centered.
The instruction is learner centered in that prior learning is recognized and built upon, using results of pre-tests and grouping students according to their current levels of understanding. Groupings change constantly.
Although I have always been “Ms. Yudt”, I am now “Miss”. We discuss that this term is one of deference and we marvel that yes – we can take the textbooks home to do homework! We emphasize the importance of being sensitive and respectful to all cultures.
Following the gauging of the students’ readiness levels, I design instruction that meets various learning styles. A recent lesson on angles was innately mathematical-logical, but I extended it linguistically (a-cute baby, obtuse moose), kinesthetically (“Aerobic Angles”), visual-spatially (pretzel stick angles), and musically (singing “All about Angles”– not especially popular with the eighth graders!). These knowledge-centered activities enhance the curriculum by engaging the learners in something other than textbook exercises, and the utilization of progressive formation ensures that the activities are developmentally appropriate.
Students have the opportunity to demonstrate understanding on summative assessments (1 quiz/test per unit) as well as on standardized tests. Formative assessments, such as a 3-2-1 tickets out and math jeopardy games, provide valuable, immediate feedback to both the students and me.
Parental involvement and support are key components to a successful working relationship with the students. For every “bad” call I make home, I make one “good” call. If parents are on-board, students are more likely to put forth effort in studying mathematics. We work as a community to increase the likelihood of success in the classroom.
Designing quality instruction takes time and energy. However, the investment is well worth it as students benefit and learning increases with effective teaching and clear, measureable goals, all incorporated into the instructional design process.
References
Bransford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
Tuesday, October 7, 2008
Blog#5: Mind and Brain: Early Language Immersion Programs
Southern Lehigh School District was the first district in Pennsylvania to offer a Spanish immersion program to its elementary students in grades 1-5 beginning in 1989. All core subject teachers in math, science, social studies, and language arts instruct students in Spanish. I recall reading in The Morning Call about the immense popularity of the program amongst the parents in the community. The article included pictures of numerous parents camping out in the school’s parking lot prior to the enrollment day in order to guarantee a slot for their children.
As the mother of a seven-year-old, I wish my daughter had the opportunity to experience a Spanish immersion program. If it existed in her school, I would most likely be pitching a tent in the parking lot - just like the parents in Southern Lehigh. Why? Bransford, Brown, and Cocking explain that young children learn new languages faster than older students because their synapses develop at a faster rate. Although most of the brain's cells are formed prior to birth, the majority of connections among cells are made in infancy and early childhood. This is the optimal time for developing and establishing language skills.
Bransford, Brown, and Cocking assert that synapses increase through learning and are shaped by experience. Exposure to new situations allows for the formation of more complex synapse structures, another benefit the children enrolled in the Spanish immersion program receive. Since more complex environments have a greater impact on development of the brain, the brains of the children enrolled in the Spanish immersion program produce an increased number of intricate synapses compared to those in less complex environments, such as traditional English-speaking classrooms.
I wonder why other local districts have not offered similar immersion programs. Has long-term research been conducted on the effects of enrollment in the Spanish immersion program? Since the immersion ceases in sixth grade, do students lose the synapses developed in the earlier grades? Or, is it a simple matter of cost-effectiveness within the district?
I am interested in learning not only how to consistently increase synapses (through learning and experience), but in determining how to prevent deterioration of the brain, such as dementia. I often hear that the elderly people complete crossword or Sudoku puzzles daily to keep their brains active. Does this truly work? The infamous “Nun Study” conducted by Dr. David Snowdon, an epidemiologist at the University of Kentucky, and his colleagues found, among other things, that that early language ability as demonstrated by more detailed early autobiographies written by the nuns, may lead to lower risk of Alzheimer's later in life.
The mind and the brain are truly fascinating topics. The importance of lifelong learning and experience new events amplified upon reading this chapter. Even though my daughter did not have the opportunity to enroll in a language immersion program, I will work with her to stay active – both physically and mentally – to ensure that her brain develops to the fullest extent possible during these critical early years.
References
Brandsford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
Snowdon, D., Kemper, S., Mortimer, J., Greiner, L,. Wekstein, D., & Markesbery, W. (1996). Linguistic ability in early life and cognitive function and Alzheimer's disease in late life: Findings from the nun study. Journal of the American Medical Association, 275(7), 528-532.
As the mother of a seven-year-old, I wish my daughter had the opportunity to experience a Spanish immersion program. If it existed in her school, I would most likely be pitching a tent in the parking lot - just like the parents in Southern Lehigh. Why? Bransford, Brown, and Cocking explain that young children learn new languages faster than older students because their synapses develop at a faster rate. Although most of the brain's cells are formed prior to birth, the majority of connections among cells are made in infancy and early childhood. This is the optimal time for developing and establishing language skills.
Bransford, Brown, and Cocking assert that synapses increase through learning and are shaped by experience. Exposure to new situations allows for the formation of more complex synapse structures, another benefit the children enrolled in the Spanish immersion program receive. Since more complex environments have a greater impact on development of the brain, the brains of the children enrolled in the Spanish immersion program produce an increased number of intricate synapses compared to those in less complex environments, such as traditional English-speaking classrooms.
I wonder why other local districts have not offered similar immersion programs. Has long-term research been conducted on the effects of enrollment in the Spanish immersion program? Since the immersion ceases in sixth grade, do students lose the synapses developed in the earlier grades? Or, is it a simple matter of cost-effectiveness within the district?
I am interested in learning not only how to consistently increase synapses (through learning and experience), but in determining how to prevent deterioration of the brain, such as dementia. I often hear that the elderly people complete crossword or Sudoku puzzles daily to keep their brains active. Does this truly work? The infamous “Nun Study” conducted by Dr. David Snowdon, an epidemiologist at the University of Kentucky, and his colleagues found, among other things, that that early language ability as demonstrated by more detailed early autobiographies written by the nuns, may lead to lower risk of Alzheimer's later in life.
The mind and the brain are truly fascinating topics. The importance of lifelong learning and experience new events amplified upon reading this chapter. Even though my daughter did not have the opportunity to enroll in a language immersion program, I will work with her to stay active – both physically and mentally – to ensure that her brain develops to the fullest extent possible during these critical early years.
References
Brandsford, J.D., Brown, A. L., & Cocking, R.R., Eds. (1999). How people learn: Brain, mind, experience and school. Washington, D.C.: National Academy Press.
Snowdon, D., Kemper, S., Mortimer, J., Greiner, L,. Wekstein, D., & Markesbery, W. (1996). Linguistic ability in early life and cognitive function and Alzheimer's disease in late life: Findings from the nun study. Journal of the American Medical Association, 275(7), 528-532.
Tuesday, September 30, 2008
Blog #4: How Children Learn (Better!) in Algebra
As a middle school mathematics teacher, I often struggle with the fact that over 90% of the eighth grade students enroll in Algebra 1 or Algebra 2. Are all of these children ready to learn this complex mathematical language at the ages of twelve or thirteen?
This past summer, I reconsidered my approach to grading. In my nine years as an algebra teacher, I came to the realization that some students are simply not ready for the rigorous curriculum involving variables, systems, and the quadratic formula, and other complicated concepts. This school year, I decided to place a larger weight on practicing algebraic skills than I ever had in the past. My new policy is that if a student completes every homework assignment in the marking period (following guidelines such as showing all steps of work), he or she will earn at least a B- in the course, regardless of the accuracy or correctness of the assignments. My modification in the grading scale supports the findings outlined in Bransford, Browning, and Cocking’s “How Children Learn” chapter in which the authors not only emphasize the importance of experience, but assert that practicing is also a critical component of skill development.
I have already noticed positive changes in my algebra students’ approach to learning. Students demonstrate increased motivation and determination, as well as higher homework grades than ever before. I have made very few calls home this year due to a lack of effort. A shift has occurred: My students have transformed from entity theorists to incremental theorists. The students have learning goals and understand that if they put effort into attempting the problems, they will be rewarded. Additionally, a surprising effect has surfaced: the averages on the first three assessments are significantly higher than in past years.
Although I modified my grading scale, I have not changed the responsibility placed on the students, nor have I changed the curriculum. Each student is expected to complete homework and perform well on assessments. I believe the focus on the practice aspect of algebra has reduced the so-called math fear or test anxiety within the classroom environment and allowed the student to concentrate on what is really important in math – skill development and independent problem solving. I find that the students ask better questions and are motivated to explore and understand the processes, rather than simply getting an answer.
I encourage the students to “find a better way” to solve problems and I look forward to receiving emails from proud students wondering if their particular method of solving has been used before and/or if it is allowable. These senses that learning is a process and practice is as important as experience have proven successful thus far.
My students are participants in their own learning, no longer spectators, as stated by Bruner in Bransford, Browning, and Cocking. I only hope that the persistence continues throughout the school year while the students set out to improve their mathematical abilities, one practice opportunity at a time.
This past summer, I reconsidered my approach to grading. In my nine years as an algebra teacher, I came to the realization that some students are simply not ready for the rigorous curriculum involving variables, systems, and the quadratic formula, and other complicated concepts. This school year, I decided to place a larger weight on practicing algebraic skills than I ever had in the past. My new policy is that if a student completes every homework assignment in the marking period (following guidelines such as showing all steps of work), he or she will earn at least a B- in the course, regardless of the accuracy or correctness of the assignments. My modification in the grading scale supports the findings outlined in Bransford, Browning, and Cocking’s “How Children Learn” chapter in which the authors not only emphasize the importance of experience, but assert that practicing is also a critical component of skill development.
I have already noticed positive changes in my algebra students’ approach to learning. Students demonstrate increased motivation and determination, as well as higher homework grades than ever before. I have made very few calls home this year due to a lack of effort. A shift has occurred: My students have transformed from entity theorists to incremental theorists. The students have learning goals and understand that if they put effort into attempting the problems, they will be rewarded. Additionally, a surprising effect has surfaced: the averages on the first three assessments are significantly higher than in past years.
Although I modified my grading scale, I have not changed the responsibility placed on the students, nor have I changed the curriculum. Each student is expected to complete homework and perform well on assessments. I believe the focus on the practice aspect of algebra has reduced the so-called math fear or test anxiety within the classroom environment and allowed the student to concentrate on what is really important in math – skill development and independent problem solving. I find that the students ask better questions and are motivated to explore and understand the processes, rather than simply getting an answer.
I encourage the students to “find a better way” to solve problems and I look forward to receiving emails from proud students wondering if their particular method of solving has been used before and/or if it is allowable. These senses that learning is a process and practice is as important as experience have proven successful thus far.
My students are participants in their own learning, no longer spectators, as stated by Bruner in Bransford, Browning, and Cocking. I only hope that the persistence continues throughout the school year while the students set out to improve their mathematical abilities, one practice opportunity at a time.
Wednesday, September 24, 2008
Blog #3: Learning and Transfer and the PSSA
During a recent meeting with a concerned parent of a struggling eighth grade student, my team of teachers and I brainstormed strategies in which we could assist the student in learning and grasping information, an area in which she has historically experienced difficulty. As we shared our ideas and drafted accommodations, the language arts teacher’s comment surprised me. She stated that it takes twenty-six exposures for a student to commit a term to memory.
Following the meeting, I researched her statement. Although her fact was a bit off, I did find some validity to it. According to Paul Nation (1990), a concept must be introduced five to more than sixteen times before it is learned. This notion supports the Chase and Simon (1973) and Klausmeir (1985) findings cited in Bransford, Brown, and Cocking that it takes a substantial amount of time to learn, regardless of the talent level of the individual, especially if the application or meaning of the information is unapparent.
The Pennsylvania System of School Assessment (PSSA) and its impact on transfer of learning would be an interesting study. Students are tested annually in mathematics in grades 3-8 and 11 to determine their ability to transfer learning in one context (classroom) to another (standardized test) that shared similar characteristics (numbers and operations, measurement, geometry, algebraic concepts, and data analysis and probability). Thorndike and Woodworth (1901), as cited in Bransford, Brown, and Cocking would contend that success of the transfer is dependent upon the learning task and transfer task elements in terms of how well they match. Based on this research, the answer to the question of whether or not the teacher should “teach to the test” is an unequivocal “yes”. The greater the elements match, the greater the success of the transfer. Since transfer of learning typically occurs when a student applies previous knowledge to a new situation, there is a common thread between problem solving and transfer of learning.
Eighth students considered at grade-level in mathematics enroll in Algebra I. Prior to the PSSA, the curriculum did not include probability, geometry, measurement or data analysis. After No Child Left Behind, committees overhauled traditional Algebra I curricula to include a month-long review of tested mathematics concepts. As a result, current Algebra I students lose one month of pure algebraic study, or 10% of the Algebra course. The short-term effects include rushing through the final units and/or not getting to them at all. However, the long-term effects are staggering: These at grade-level students no longer have the opportunity to take Calculus as a senior in high school. Last year, the school district changed the course progression because high school teachers argued that the students were not completing earlier courses to the fullest extent, and therefore, lacked the necessary skills to successfully complete Calculus. High stakes testing interfered with higher level mathematics courses to the extent that an entire course has been removed from the sequence. Priorities, priorities, priorities!
Nation, I.S.P. (1990). Teaching and learning vocabulary. New York: Newbury House.
Following the meeting, I researched her statement. Although her fact was a bit off, I did find some validity to it. According to Paul Nation (1990), a concept must be introduced five to more than sixteen times before it is learned. This notion supports the Chase and Simon (1973) and Klausmeir (1985) findings cited in Bransford, Brown, and Cocking that it takes a substantial amount of time to learn, regardless of the talent level of the individual, especially if the application or meaning of the information is unapparent.
The Pennsylvania System of School Assessment (PSSA) and its impact on transfer of learning would be an interesting study. Students are tested annually in mathematics in grades 3-8 and 11 to determine their ability to transfer learning in one context (classroom) to another (standardized test) that shared similar characteristics (numbers and operations, measurement, geometry, algebraic concepts, and data analysis and probability). Thorndike and Woodworth (1901), as cited in Bransford, Brown, and Cocking would contend that success of the transfer is dependent upon the learning task and transfer task elements in terms of how well they match. Based on this research, the answer to the question of whether or not the teacher should “teach to the test” is an unequivocal “yes”. The greater the elements match, the greater the success of the transfer. Since transfer of learning typically occurs when a student applies previous knowledge to a new situation, there is a common thread between problem solving and transfer of learning.
Eighth students considered at grade-level in mathematics enroll in Algebra I. Prior to the PSSA, the curriculum did not include probability, geometry, measurement or data analysis. After No Child Left Behind, committees overhauled traditional Algebra I curricula to include a month-long review of tested mathematics concepts. As a result, current Algebra I students lose one month of pure algebraic study, or 10% of the Algebra course. The short-term effects include rushing through the final units and/or not getting to them at all. However, the long-term effects are staggering: These at grade-level students no longer have the opportunity to take Calculus as a senior in high school. Last year, the school district changed the course progression because high school teachers argued that the students were not completing earlier courses to the fullest extent, and therefore, lacked the necessary skills to successfully complete Calculus. High stakes testing interfered with higher level mathematics courses to the extent that an entire course has been removed from the sequence. Priorities, priorities, priorities!
Nation, I.S.P. (1990). Teaching and learning vocabulary. New York: Newbury House.
Sunday, September 14, 2008
Blog #2: Coach Kopp - An Expert Teacher
I have been blessed with many teachers who cared for my well-being and deserve recognition for their part in helping me achieve my goals. However, there was one teacher who set himself apart by displaying principles noted by Bransford, Brown, and Cocking.
Michael Kopp is a veteran basketball coach, ready to begin his 29th year of coaching the Central Catholic High School girls’ team. He has amassed over 600 wins and is recognizable state-wide for his accomplishments. Not only is he an extraordinary coach, he is a humble man who shies away from the spotlight and teaches greater lessons than basketball to his players.
Flash back to 1995, my senior year: My teammates and I were decent players, but none of us were superstars, 1000 point scorers, or even Division 2 prospects. It was deemed to be a “rebuilding” year at CCHS.
Coach Kopp undoubtedly knew the “talent” he was inheriting, but he quietly began his quest for another winning season. Coach, a mathematics teacher by day, noticed patterns – who worked with whom best and in what situation, which defense to play when certain players were on the court, and whom to play during key moments of the games. Coach Kopp’s choices reflected his deep understanding of the game of basketball. His knowledge was conditionalized and transformative, dependant upon the opposing team’s strategy.
At the end of a game, Coach Kopp coolly and confidently retrieved knowledge in answering reporters, only of course after he expressed his pride in his team.
Coach Kopp led us to the AAAA State Basketball Championship Game at the Hershey Park Arena, a feat which no one predicted of at the onset of the season. This “rebuilding” year team knocked down powerhouse teams with Division I prospects and went all the way to the top. How? We were led by an expert.
Coach Kopp organized his thoughts around the “big ideas” that Bransford, Brown, and Cocking noted – how to work together as a great team to beat five (more) talented individual players. A novice coach may require the memorization of plays, but an expert like Coach Kopp taught his players how to read defenses and trusted us to alter offensive plays, especially when the other team had our offensive scheme committed to memory.
Coach Kopp’s playbook was not “a mile wide and an inch deep”, a criticism of curricula by the Third International Mathematics and Science Survey within Bransford, Brown, and Cocking. He kept it simple – five offensive plays and four out-of-bounds plays – and did not change his approach during my four years at CCHS. His vast knowledge confirmed that good execution of a few plays was more critical than having numerous plays in the book.
Coach Kopp understood the game of basketball more than any other coach with whom I have worked. He is an expert in coaching and I only hope he stays in the game long enough so that my daughter is able to experience his greatness firsthand.
Michael Kopp is a veteran basketball coach, ready to begin his 29th year of coaching the Central Catholic High School girls’ team. He has amassed over 600 wins and is recognizable state-wide for his accomplishments. Not only is he an extraordinary coach, he is a humble man who shies away from the spotlight and teaches greater lessons than basketball to his players.
Flash back to 1995, my senior year: My teammates and I were decent players, but none of us were superstars, 1000 point scorers, or even Division 2 prospects. It was deemed to be a “rebuilding” year at CCHS.
Coach Kopp undoubtedly knew the “talent” he was inheriting, but he quietly began his quest for another winning season. Coach, a mathematics teacher by day, noticed patterns – who worked with whom best and in what situation, which defense to play when certain players were on the court, and whom to play during key moments of the games. Coach Kopp’s choices reflected his deep understanding of the game of basketball. His knowledge was conditionalized and transformative, dependant upon the opposing team’s strategy.
At the end of a game, Coach Kopp coolly and confidently retrieved knowledge in answering reporters, only of course after he expressed his pride in his team.
Coach Kopp led us to the AAAA State Basketball Championship Game at the Hershey Park Arena, a feat which no one predicted of at the onset of the season. This “rebuilding” year team knocked down powerhouse teams with Division I prospects and went all the way to the top. How? We were led by an expert.
Coach Kopp organized his thoughts around the “big ideas” that Bransford, Brown, and Cocking noted – how to work together as a great team to beat five (more) talented individual players. A novice coach may require the memorization of plays, but an expert like Coach Kopp taught his players how to read defenses and trusted us to alter offensive plays, especially when the other team had our offensive scheme committed to memory.
Coach Kopp’s playbook was not “a mile wide and an inch deep”, a criticism of curricula by the Third International Mathematics and Science Survey within Bransford, Brown, and Cocking. He kept it simple – five offensive plays and four out-of-bounds plays – and did not change his approach during my four years at CCHS. His vast knowledge confirmed that good execution of a few plays was more critical than having numerous plays in the book.
Coach Kopp understood the game of basketball more than any other coach with whom I have worked. He is an expert in coaching and I only hope he stays in the game long enough so that my daughter is able to experience his greatness firsthand.
Tuesday, September 9, 2008
Blog#1: Grassroots Video & McLuhan
The Horizon Report (2008) was both exciting and intimidating at the same time. I was instinctively proud (which admittedly felt a bit strange!) when I realized that I incorporate grassroots video in my classroom, without previously knowing the technical name “grassroots video”. I use Teacher Tube, a downloadable educational video site that offers video lessons, groups, and teacher blogs. It is a good resource to use if a student has been absent for several days and needs to hear and see a particular mathematics lesson in progress, instead of copying and reading notes in order to catch up with the class again. The videos are also useful for a substitute teacher to play for the class on a large screen. In general, I am not a proponent of showing videos when I am absent. However, it is very difficult to find substitutes for math classes, and showing a short math lesson video and following up with a check for understanding activity may increase the likelihood of the substitute returning to a math classroom and increase student knowledge using a different teacher resource.
In my opinion, Marshall McLuhan would argue that grassroots video, in this capacity, extends the mathematics teacher. Instead of instructing one-hundred and fifty students in one classroom each school day, these online videos allow the teacher to reach thousands or even millions of learners across the world. Learners experience the lesson in real-time and follow along as if they were members of the actual classroom. However, McLuhan states that each extension mitigates another component. I believe he would contend that grassroots video has the ability to make teachers and physical classrooms obsolete – a frightening prospect.
As a result of grassroots video, learners retrieve a sense of control over their pace of education, traditionally dictated by the classroom teacher and/or district curricula. A learner could potentially complete Algebra I in one week, instead of an entire school year! If overextended though, McLuhan may hypothesize that grassroots video would negatively impact communication and collaboration skills of the learners. Since the videos are one-way (not interactive), learners lose the ability to ask questions to remediate or enrich the lesson. In addition, learners would not have the opportunity to be grouped homogenously or heterogeneously to supplement learning and to gain the important skills and benefits associated with group work.
The Horizon Report (2008) validates the importance of staying current with technology trends, both personally and professionally. The report left me wondering what is possibly out there for future technologists to design. We must proceed with caution, however. As a Japanese proverb states, "Better than a thousand days of diligent study is one day with a great teacher."
In my opinion, Marshall McLuhan would argue that grassroots video, in this capacity, extends the mathematics teacher. Instead of instructing one-hundred and fifty students in one classroom each school day, these online videos allow the teacher to reach thousands or even millions of learners across the world. Learners experience the lesson in real-time and follow along as if they were members of the actual classroom. However, McLuhan states that each extension mitigates another component. I believe he would contend that grassroots video has the ability to make teachers and physical classrooms obsolete – a frightening prospect.
As a result of grassroots video, learners retrieve a sense of control over their pace of education, traditionally dictated by the classroom teacher and/or district curricula. A learner could potentially complete Algebra I in one week, instead of an entire school year! If overextended though, McLuhan may hypothesize that grassroots video would negatively impact communication and collaboration skills of the learners. Since the videos are one-way (not interactive), learners lose the ability to ask questions to remediate or enrich the lesson. In addition, learners would not have the opportunity to be grouped homogenously or heterogeneously to supplement learning and to gain the important skills and benefits associated with group work.
The Horizon Report (2008) validates the importance of staying current with technology trends, both personally and professionally. The report left me wondering what is possibly out there for future technologists to design. We must proceed with caution, however. As a Japanese proverb states, "Better than a thousand days of diligent study is one day with a great teacher."
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