A Technology-based Grant for Transformative Learning
Context Romeo High School is a suburban High School, north of Detroit, Michigan. Its student population is one of socio-economic and ethnic diversity. In our school, we have a mixture of students that come to us with a varied amount of prior knowledge and skill. Many students move frequently; some are the children of migrant workers, some are recent immigrants, some have moved from urban areas because of school-of-choice, while others have grown up in poverty and are feeling the affects of the economy on our small town that is powered by a Ford plant and little else. And yet, other students drive to school in fancy cars and go home to million-dollar houses. The range of students’ socio-economic situation, race, ethnicity, and religion is about as varied as it comes. As a secondary school, we have a high percentage of our students that receive free-and-reduced meals, and those that do not have access to a computer, let alone the Internet, at home, while other students tote around their Coach® bags and iPhones®, where they have the world of information at their fingertips. Regular access to technology in and out of the classroom can be limited and disparate. It is important to keep in mind while teaching that many of the students, although coming from an overall affluent suburb, often face everyday struggles of poverty and hunger.
The gap that exists between these students reaches far and wide. With the lack of sameness in our community, each classroom teacher can be expected to have a variety of learners; English as a second language students are provided with assistance from an ESL certified teacher and students with special needs have accommodations and special arrangements for classroom assessments such as tests and quizzes. Each classroom consists of thirty to thirty five students. All teachers are provided with a PC in the classroom, however student access to computers is only available in the Media Center or computer labs and must be arranged ahead of time. In addition to a PC, I have an ELMO document camera, Epson digital projector and a set of twenty TI-84 Plus calculators in my classroom. |
Overview
Transformation
the Total PaCKage
Evaluation
Implications
Resources |
Content
For generations, students have been faced with the task of learning factual information to achieve their most immediate goal, the test, and then their memory of that knowledge fades away as they turn their focus to the next set of information to learn for the next test, and so on in a cycle of learning and forgetting. But today more than ever before, students need to able to think critically and innovatively about their experiences. In our 21st Century world, learning needs to move beyond knowing facts to understanding larger ideas and concepts, and being able to apply those ideas to the world around them, as 21st Century learners and professionals. Levstik & Barton said that, “simply knowing more facts does not necessarily mean greater understanding…even though they know plenty of ‘math facts,’ they don’t know enough about what the operations mean to use them in real situations.” (Levstik & Barton, 1997).
Geometry is much more than using formulas and applying them to shapes in a textbook; it is a mathematical understanding of the concrete world that is proven through rational thought and proof. In many ways, teaching of geometry has been minimized to its most rudimentary facets, and through the integration of instruction that builds on students’ prior knowledge, is scaffolded, is learned through disciplined inquiry and integration of technology, students will be able to “see” math as a logical process.
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"Learning flourishes when... it is shared, tested, examined, challenged, and improved." -L. Shulman |
Technology
The TI-Nspire™ Calculator and Navigator™ System is a flexible technology that allows students and teachers many different and unique experiences in one device and system. The TI-Nspire™ functions as a traditional TI-84 Plus graphing calculator, but additionally, with the Nspire software and faceplate, the calculator functions more similarly to a handheld computer. With TI-Nspire™ calculators, students are more easily able to make connections to the concepts or meanings that underlie the facts, rules, formulas, or definitions being taught. Students will benefit because the TI-Nspire™ software allows students to "take action on a math object to observe the consequence and…reflect on math…interact with multiple mathematical representations to develop understanding in a way that extends beyond paper and pencil" and "grasp the concepts they struggle with most". (Texas Instruments, 2009).
By implementing the wireless TI-Nspire™ Navigator™ system with the TI-Nspire™ calculators, students will have the opportunity to interact in a collaborative, interactive classroom environment by enhancing student interactions, focusing attention, and providing opportunities for peer and self-assessment. With the TI-Nspire™ Navigator™ system, teachers have the ability to see what the students are accomplishing and in return hold students to a high level of accountability. The TI-Nspire™ Navigator™ system has several features that are used in the classroom setting; the quick poll and learning check allows for the opportunity for formative assessments of students. Screen capture can be applied to increase formative or conceptual knowledge. Finally, the activity center allows students to explore and develop conceptual knowledge all done wirelessly through the TI-Nspire™ Navigator™ system.
Research shows that instructional software has positive effects on student achievement in mathematics when compared to instruction without such technology (US Department of Education, 2008). TI-Nspire™ calculators and the Navigator™ System allow students to visualize mathematics and take a hands-on approach to their mathematical learning (Texas Instruments Educational Technology, 2009). |
This full system includes:
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Pedagogy
“Learning mathematics involves skill
acquisition, drilling, repetition, and instruction by an authority. It also
involves independent construction of knowledge, connection to physical or real
world situations, reflection by the learner, and independent reapplication to
new situations.”
~Jonathan Halabi, New York Public Schools math teacher.
In addition to “traditional” methods of teaching, I strive to vary my approaches and methods to meet the needs of my students. As Jonathan Halabi said, learning mathematics involves not only traditional instruction, but also the opportunity for students to construct knowledge and apply that knowledge in rich and meaningful ways (Halabi, 2007). Effective teachers provide students with opportunities to work both independently and collaboratively to make sense of ideas, but also that effective teachers enable students to build on existing proficiencies, interests and experiences (Anthony & Walshaw, 2009). Many have heard the old adage that you do not know where you are going unless you know where you have been, and the same is true of mathematics; without accessing and using students’ prior knowledge, a teacher cannot effectively guide students to greater learning and understanding. By engaging prior knowledge, students become a resource for further learning and therefore can make more meaningful connections to the content and application of mathematical theories.
~Jonathan Halabi, New York Public Schools math teacher.
In addition to “traditional” methods of teaching, I strive to vary my approaches and methods to meet the needs of my students. As Jonathan Halabi said, learning mathematics involves not only traditional instruction, but also the opportunity for students to construct knowledge and apply that knowledge in rich and meaningful ways (Halabi, 2007). Effective teachers provide students with opportunities to work both independently and collaboratively to make sense of ideas, but also that effective teachers enable students to build on existing proficiencies, interests and experiences (Anthony & Walshaw, 2009). Many have heard the old adage that you do not know where you are going unless you know where you have been, and the same is true of mathematics; without accessing and using students’ prior knowledge, a teacher cannot effectively guide students to greater learning and understanding. By engaging prior knowledge, students become a resource for further learning and therefore can make more meaningful connections to the content and application of mathematical theories.
Additionally, by engaging students in learning geometry more collaboratively, students will be able to work with one another to build a socially constructed understanding that they will then, take ownership of and reapply to other situations. As stated in Vygotsky’s Social Development Theory, social interaction is important for learning because higher mental functions such as reasoning, comprehension, and critical thinking originate in social interactions and are then internalized by individuals (Woolfolk, 2001). According to Vygotsky, “social interaction plays a fundamental role in the development of cognition,” and social activity—of which scaffolding is certainly an example—is crucial to a child’s development as a learner of these higher-level mental functions that are at the core of this DreamIT project (Lawson, 2002). In my geometry teaching, the use of cognitive and social learning approaches seem to be most effective; by engaging students’ prior knowledge, increasing opportunities for social learning to occur and scaffolding instruction, students will have greater opportunity to work with their geometric knowledge to build a deeper, richer understanding of geometry as a process of logic and reason.
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Bringing it all together . . . the Total PaCKage
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When thinking about technology, pedagogy and content, these three knowledge bases can be found in different areas of education. At the intersection of all three is Technological Pedagogical Content Knowledge (TPaCK), the “sweet spot” of technology integration that is deeply rooted in both best practices in pedagogy and a deep understanding of the content. Through this DreamIT, the proposal of using the TI-Nspire™ calculators and the Navigator™ System in the classroom has not been selected for its technological capabilities alone. I have selected the TI-Nspire™ calculators and the Navigator™ System in spite of the fact that it reinforces the ideas of cognitive and social learning theories and lends itself to teaching reasoning and logical processes of geometric concepts.
TI’s Math Nspired online resource provides a wide variety of pre-developed math and science applications and activities free for educators to download, as well as online professional development. A major part of this DreamIT will be to utilize these resources that have been developed by professionals in the field of education by using scientific research and corresponding these activities to one or more of the Standards for Mathematical Practice included in the Common Core State Standards for Mathematics. Additionally, “each activity is designed to have high fidelity mathematically, cognitively, and pedagogically” which includes questions to stimulate reflection and sense-making, demanding high cognitive function of all students. (Dick and Burrill, 2009).
Without the use of the TI-Nspire™ calculators, the hundreds of activities would not be accessible or reasonably easy to use. Other similar geometric technologies, such as Geometer’s Sketchpad or Geogebra are wonderful resources for in-depth exploration to the savvy user and mathematician, however, both programs require the user to develop their mathematical explorations from scratch and without a predetermined frame of reference; which can be both daunting and time-consuming. The Math Nspired activities allow students to move through the pre-constructed activities with the predetermined information already set, saving time and allowing student’s to accurately manipulate multiple representations of the mathematics. As students build their knowledge, they activities and applications have been designed to remove the guides and scaffolding to allow greater student independence and discovery; a process that would be impossibly daunting to teacher and student alike to develop on their own.
In using the TI-Nspire™ system, students can work individually, in the classroom, without having to pre-schedule lab time to utilize the computers, meaning that students can have more time with these mathematical activities than would otherwise be provided to them. Also, the use of the TI-Nspire™activities in the classroom, allows students to “discover” the rules of mathematics and geometry, and provides great opportunity for group and whole-class discussion for the “why’s” of mathematics, letting learning become a more social process within the classroom, and moving away from the traditional lecture and drill technique of presenting mathematics. The TI-Nspire™ Navigator™ System additionally functions as a classroom response system which research has demonstrated can significantly affect both the quality of students’ discussion and what they learn from the discussion, as well as support manipulating dynamic notations and models are important in mathematics understanding. Overall, the “classroom use of TI-Nspire™calculator and the TI-Nspire™ Navigator™ System can enhance student engagement, collaboration and learning” and with a tablet PC, can enhance teacher monitoring of student progress to more accurately meet the needs of every student (Center for Technology in Learning 2004).
To view sample TI Math Nspired activites, follow the links below and click on "Try the Lesson":
TI’s Math Nspired online resource provides a wide variety of pre-developed math and science applications and activities free for educators to download, as well as online professional development. A major part of this DreamIT will be to utilize these resources that have been developed by professionals in the field of education by using scientific research and corresponding these activities to one or more of the Standards for Mathematical Practice included in the Common Core State Standards for Mathematics. Additionally, “each activity is designed to have high fidelity mathematically, cognitively, and pedagogically” which includes questions to stimulate reflection and sense-making, demanding high cognitive function of all students. (Dick and Burrill, 2009).
Without the use of the TI-Nspire™ calculators, the hundreds of activities would not be accessible or reasonably easy to use. Other similar geometric technologies, such as Geometer’s Sketchpad or Geogebra are wonderful resources for in-depth exploration to the savvy user and mathematician, however, both programs require the user to develop their mathematical explorations from scratch and without a predetermined frame of reference; which can be both daunting and time-consuming. The Math Nspired activities allow students to move through the pre-constructed activities with the predetermined information already set, saving time and allowing student’s to accurately manipulate multiple representations of the mathematics. As students build their knowledge, they activities and applications have been designed to remove the guides and scaffolding to allow greater student independence and discovery; a process that would be impossibly daunting to teacher and student alike to develop on their own.
In using the TI-Nspire™ system, students can work individually, in the classroom, without having to pre-schedule lab time to utilize the computers, meaning that students can have more time with these mathematical activities than would otherwise be provided to them. Also, the use of the TI-Nspire™activities in the classroom, allows students to “discover” the rules of mathematics and geometry, and provides great opportunity for group and whole-class discussion for the “why’s” of mathematics, letting learning become a more social process within the classroom, and moving away from the traditional lecture and drill technique of presenting mathematics. The TI-Nspire™ Navigator™ System additionally functions as a classroom response system which research has demonstrated can significantly affect both the quality of students’ discussion and what they learn from the discussion, as well as support manipulating dynamic notations and models are important in mathematics understanding. Overall, the “classroom use of TI-Nspire™calculator and the TI-Nspire™ Navigator™ System can enhance student engagement, collaboration and learning” and with a tablet PC, can enhance teacher monitoring of student progress to more accurately meet the needs of every student (Center for Technology in Learning 2004).
To view sample TI Math Nspired activites, follow the links below and click on "Try the Lesson":