Saturday, March 15, 2008

Schools that Change

In Schools that Change: Evidence-Based Improvement and Effective Change Leadership, Lew Smith describes schools with a commitment to change:

"In these schools, 'satisfaction is derived from professional work accomplished together and from the achievement of students' (Ogden & Germinaro, 1995, p.7). In these schools, the principal served as an instructional leader, making sure everyone understood the message that all students could achieve. Conversations about students, teaching, new ideas, and vision were encouraged and valued. The staff welcomed research findings and found great merit in professional development. Time was provided to ask the hard questions, research and reassess, and take risks. These collegial schools constantly raised the bar for all students and staff."

I wonder how many teachers can identify all of these qualities in their schools? I wonder how many students would say their schools fit this description?

Monday, January 28, 2008

This I Believe

I was blessed with both good teachers and truly outstanding teachers in elementary school. In middle and high school, the educational experiences that impacted me the most didn't occur in traditional classroom settings but at summer camp, where I experienced hands-on learning at its best, and at the Governor's School I attended half-day from grades 10-12, where a month of the school year was devoted to scientific research we conducted on our own.

My classroom will be a place that respects students as authors, book reviewers, mathematicians, problem-solvers, scientists, explorers, and individuals. At my Governor's School, students roaming the halls were not cause for alarm because the teachers knew us. They knew that we were on a mission-- to the computer room, to another teacher's lab to get equipment, or even to the student lounge for a snack to keep us going through a rigorous day of working as a scientist would-- no bell schedule or quizzes in sight, but on task because what we were doing was important. We worked hard because our teachers treated us respectfully, instructing us in the scientific method but letting us choose our own question to research, arming us with the tools we needed to be researchers but letting us learn from our mistakes and triumphs as we worked independently.

Students should be learning to value that *process* of learning, not the grade they receive. A numerical score or letter grade has little meaning if students don't know how it was achieved or how to apply their skills across situations and disciplines. As a student, I was proud of a math assignment when I had struggled to solve a real-world problem, like how long it would take for grain to drain from a silo, not when I quickly crunched numbers.

I am a certified Project Learning Tree teacher; this environmental education curriculum "helps students learn how to think, not what to think, about the environment," and I look forward to integrating PLT lessons into my curriculum. I am interested in learning more about other EE programs like Urban Sprouts.

The best language arts experience I had as a student was "translating" a text into a journal, then into an abstract painting, then into a play-- it challenged me in a way no other assignment had. I grew up with a great small-town librarian, who talked to me like I was a peer in the world of books, constantly recommending books to me. I love, love, love really good children's literature, and would rather read Young Adult Fiction by authors like Sarah Dessen, Scott Westerfield and Laurie Halse Anderson than books written for women my age. I fantasize about what my classroom library will look like. It will look inviting and relaxing, a place to curl up and read because reading enriches our lives, not because there's a test on Friday.

Can you tell I can't wait for this fall to come?

Wednesday, January 23, 2008


This semester I am studying differentiation in a course with Carol Tomlinson. I will be using this blog, which I previously used for Teaching With Technology.

- What IS Differentiation?

Tuesday, February 20, 2007

Reuters Article: Math Anxiety Saps Ability to Do Math

By Julie Steenhuysen

SAN FRANCISCO (Reuters) - Worrying about how you'll perform on a math test may actually contribute to a lower test score, U.S. researchers said on Saturday.

Math anxiety -- feelings of dread and fear and avoiding math -- can sap the brain's limited amount of working capacity, a resource needed to compute difficult math problems, said Mark Ashcraft, a psychologist at the University of Nevada Las Vegas who studies the problem.

"It turns out that math anxiety occupies a person's working memory," said Ashcraft, who spoke on a panel at the annual meeting of the American Association for the Advancement of Science in San Francisco.

Ashcraft said while easy math tasks such as addition require only a small fraction of a person's working memory, harder computations require much more.

Worrying about math takes up a large chunk of a person's working memory stores as well, spelling disaster for the anxious student who is taking a high-stakes test.

Stress about how one does on tests like college entrance exams can make even good math students choke. "All of a sudden they start looking for the short cuts," said University of Chicago researcher Sian Beilock.

Although test preparation classes can help students overcome this anxiety, they are limited to students whose families can afford them.

Ultimately, she said, "It may not be wise to rely completely on scores to predict who will succeed."

While the causes of math anxiety are unknown, Ashcraft said people who manage to overcome math anxiety have completely normal math proficiency.

© Reuters 2007. All Rights Reserved.

Monday, February 12, 2007

thoughts on NCTM standards

Reflections on the NCTM Principles and Standards for School Mathematics:

Six Principles:

1. Equity- holding high expectations and offering strong support for all students.

2. Curriculum- should be coherent, focused, and well articulated. Math instruction should be constructed around "big ideas" of mathematics. Math should be treated as an integrated whole, not as a list of isolated bits and pieces.

3. Teaching- Teachers should develop an understanding of what their students know and need to learn, and challenge and support them as they learn content *well.* Teachers should have a firm understanding of how children learn math as well as an awareness of each students' development as an individual.

4. Learning- Students actively build knowledge from experience and prior understanding. Students should evaluate their own ideas and those of others and should make and test conjectures. According to Van De Walle, trust must be established with an understanding that it is okay to make mistakes; students will realize that errors are an opportunity for growth.

5. Assessment- should not be something that is done *to* students, but should be done *for* students to guide and enhance learning. Teachers should use feedback to establish and adjust goals.

6. Technology- Is an essential part of contemporary mathematics. Technology influences what is taught and enhances learning.

Content Standards:
- Number and Operations (numbers and number sense, computation and estimation, counting and writing numbers, interval counting and patterns, comparing greater than and less than, fractions and decimals, rounding)
- Algebra (patterns and functions)
- Geometry
- Measurement
- Data Analysis and probability (statistics)

Process Standards:
1. Problem Solving- students will build new knowledge, solve problems, apply and adapt a variety of appropriate strategies, and monitor and reflect upon the processes they use. Van De Walle describes problem solving as "the vehicle through which children develop mathematical ideas."
2. Reasoning and Proof- Students recognize reasoning and proof as fundamental elements of doing mathematics, make and investigate their conjectures, develop and evaluate their own arguments and proofs and those of others, and select and use various types of reasoning and proofs. Providing an argument or rationale becomes an integral part of every answer.
3. Communications- Students will organize and consolidate their thinking, communicate thinking coherently and clearly, analyze and evaluate the thinking and strategies of others, and use the language of mathematics to express ideas precisely. Students will talk about, write about, describe, and explain mathematical ideas.
4. Connections - Van De Walle offers that students are practicing reflective thought when they connect related ideas. Students will recognize and use connections among ideas, understand how ideas interconnect and build on one another to produce a coherent whole, and recognize and apply mathematical ideas in other contexts. Students will gain "real world" understandings of the roles of mathematial concepts and integrate mathematical ideas into other content area work.
5. Representation- students will organize, record, and communicate their ideas, select, apply, and translate concepts to solve problems, and use various representations to model and interpret phenomena. Students will gain the understanding that mathematics is a way of communicating ideas.

Professional Standards:
1. Worthwhile mathematical tasks - knowledge of students' understandings, interests, and experiences and of the range of ways that diverse students learn mathematics. The teacher should pose tasks that promote communication about mathematics and promote the development of all students dispositions to do mathematics. Tasks should stimulate students to make connections and develop a coherent framework for mathematical ideas.
2. Teacher's Role in Discourse- The teaher should ask students to clarify and justiy their ideas orally and in writing; Van De Walle recommends that teachers encourage reflective thought by requiring explanations and justifications in addition to answers. Teachers should decide when and how to atttach mathematical notation and language to students' ideas.
3. Students' Role in Discourse- listen to, respond to, and question the teaher and one another. The teacher should promote discourse in which students try to convince themselves and one another of the validity of particular representations, solutions, conjectures, and answers. Van De Walle suggests that when students try to make sense of the explanations of others, ask questions, and make explanations for or justify their own ideas, they are using reflective thought. Van De Walle points our that Vygotsky's concept of internalization is the transfer of external ideas exchanged in the social environment to those that are internal, personal constructs.
4. Tools for enhancing discourse- the teacher should encourage and accept the use of invented and conventional terms and symbols; computers, calculators, and other technology; metaphors, analogies, and stories; written hypotheses, explanations, and arguments; and oral presentations and dramatizations.
5. Learning Environment- Foster the development of mathematical power by consistently expecting and encouraging students to take intellectual risks by raising questions and formulating conjectures. Van De Walle states that students must come to understand that mathematics makes sense - there is no need for the teaccher or other authority (like the back of the book) to provide judgment for student answers.
6. Analysis of Teaching and Learning

According to Van De Walle, the Professional Standards move us:
1. Toward classrooms as mathematics communities
2. Toward logic and evidencce as verification and away from the teacher as sole authority for right answers.
3. Toward mathematical reasoning and away from mere memorizing procedures.
4. Toward conjecturing, inventing and problem solving and away from an emphasis on mechanistic finding of answers.

Monday, February 05, 2007

Learner.Org Annenberg Media Video: Domino Math

In this Annenberg Media Teaching Math K-4 clip, Mrs. Wright, a teacher at William Monroe Trotter School, leads a multi-grade classroom of first and second graders in a number facts activity. Wright uses dominos and stickers as a manipulative to demonstrate using counting to understand the properties of sums. The students observe as Mrs. Wright demonstrates using the dominos and stickers to identify different combinations of numbers that produce the same sum, then break into groups of three to work on finding different sums. The students are given challenges and an extension activity, writing number sentences, as they finish their work.

Mrs. Wright's activity uses problem solving to teach "a lesson that doesn't need the teacher up front" (her own words) as described by Van De Walle in"Elementary and Middle School Mathematics: Teaching Developmentally." As Mrs. Wright points out, the activity uses questions that are open ended, with no one right answer. Students work cooperatively to produce correct responses and explain why their answers work using number facts. The groups are carefully arranged with at least one strong counter in each, and second graders can be observed helping first graders clarify their ideas -- something I enjoyed as a third grader in a multi-age classroom when I was in elementary school. Wright encourages conversation using prompts like, "tell me what's missing," and circulates the room both to keep students on task and to encourage extended thinking. The dominos and stickers might also be a useful tool when teaching other whole number concepts.

Monday, January 29, 2007

Mathematical Processes: Place Value Centers

For our Elementary Math methods course with Professor Robert Barry, our first assignment involves a series of Annenberg Media videos available online at The first video used in our tasks is "Place Value Centers," based around a first grade lesson taught by Ms. Vigstrom at Palla Elementary in California.

Ms. Vigstrom's lesson is well-aligned with the three-step lesson planning approach associated with teaching through problem solving, but is more teacher-centered at its outset than many problem solving lessons. Early in the video, Vigstrom describes her goals for the lesson: familiarizing students with place value and building their readiness for double-digit addition, subtraction, and associated number patterns through the practice of exchanging ones and tens.

Ms. Vigstrom begins her lesson with a "lead-up activity" drawing on the students' prior knowledge based on their experience of counting their days in school using sticks and bundles. Vystrom transfers this idea to her "giant place value mat," substituting sticks and bundles with cubes and rods, and demonstrates the use of this manipulative using students' ages as a personalized example. She further transfers the concept of grouping tens from the model to a written format. During her introduction, Vigstrom draws on her students to explain strategies such as counting from ten.

The second element in Ms. Vigstrom's lesson plan is a set of four activity centers the students work in pairs to complete. The centers connect the idea of grouping ones into tens using a measuring activity, a sorting activity, an illustrating activity, and a race to connect, group, and count cubes. In the illustrating activity, students interpret a written number using blocks. The number is shown in the context of a 100-number chart (we have seen these charts used for addition, subtraction, and even multiplication activities in other videos, I think one will be a must-have item for my future classroom shopping list!).

The measuring activity seems to be the most exciting ones for students, who are heard making comments such as, "Please measure me, I can't wait all day!" and comparing their respective heights based on the lengths of the rods they create with cubes. I really like the idea of using measurement to explore place value because connections are made between units of measure and counting units.

Extension Questions: Why did Ms. Vigstrom have students work at centers?
What is the value of using different manipulatives to explore the same concept?

Vigstrom shares her idea that using different manipulatives in centers is helpful because each student approaches the topic from a different background and will develop an understanding of the concept of place value differently than a peer will. During their center work, Vigstrom circulates the classroom asking extension questions such as "can you tell me what you did?" and "What is the nine for?" in order to prepare students for class discussion. The students convene to discuss their discoveries and the connections made during the center activities. They test their discoveries in other contexts based on prompts from Vigstrom, who asks general questions as well as more specific concept-related prompts such as "what does the number on the left side [of a written two-digit number] stand for?"

The lesson on Place Value Centers includes the NCTM standards of number sense, measurement, and connections.

i'm back!

I've decided to use this blog again to post my thoughts on technology used both to illustrate pedagogy and to enhance students' experiences in the field. As a fourth-year Elementary Education major in the Curry School of Education at UVa, it will be interesting to compare my reflections as a new education major to the way I think now as a preservice teacher with a growing field experience and knowledge base.