# e-book Teaching to Intuition: Constructive Implementation of the Common Core State Standards in Mathematics

Promoting productive mathematical classroom discourse with diverse students. The Jounral of Mathematical Behavior , 22 1 , Professor Dorothy White contrasts typical, direct teaching methodology with two classrooms that emphasize discourse in the classroom. White describes education in African American and Hispanic classrooms as geared toward repetitive problems meant to keep the class occupied and under control. The classes in the article portray an environment where the students thinking process is what is valued, far more than the correct answers.

Ediger, M. Quality teaching in mathematics. In this article, Ediger stresses the importance of having high quality teachers teaching mathematics. This is due to the fact that students will use mathematics in everyday life. Teachers should allow for active learning in the classroom, and need to reinforce mathematical vocabulary.

Teachers need to understand the mathematical knowledge and skill level of their students. The teacher should also be knowledgeable in the content and know how to improve self efficacy in mathematics. These are just a few of the suggestions that Ediger points out in this article. Elk, S. Is calculus really that different from algebra? A more logical way to understand and teach calculus. Elk goes through specific examples of each case, and shows how blindly applying rules such as never divide by 0 leads to confronting contradictions.

Although the article does not go into how to solve the problems, it does shed light on some algebraic origins of the definitions of these elementary calculus concepts. Gutstein, E. In this article, Eric Gutstein summarizes his experience using mathematics for social justice approach in two Chicago-area schools over several years.

Gutstein admits, at the beginning, it was hard to generate any mathematical interest among students. But as soon as he starts to link math to different societal, economical, political etc. Gutstein tries to bridge the gap between Mathematics and Social Justice in his classroom. Later he had his students research various topics and explore those from mathematical point of view.

Journal for Research in Mathematics Education, 34 1 , Hersh, Reuben Proving is Convincing and Explaining. Educational Studies in Mathematics, 24 , In this article, Hersh explains how proof plays two different roles, one in mathematical research and the other in the classroom.

Mathematical proof can convince and can explain. In research, its role is to convince. In a classroom, convincing students is not a problem. Students are always convinced. In a classroom, the primary role of proof is to explain. This article presents three meanings of proof. The first colloquial meaning is to test the true state of affairs. The second mathematical meaning is an argument that convinces qualified judges. Here Hersh makes a point that proof in a classroom is a tool for the teacher and class, whereas for mathematician it is a tool of research.

Karimi A. Journal of the Indian Academy of Applied Psychology , 35 2 , Karimi and Venkatesan investigate the affects of cognitive behavioral therapy on mathematics anxiety. The sample was a group of year old Iranian students who tested high on mathematics anxiety. The experimental group was administered a fifteen 1.

They were also given a workbook with a summary of session material with and home practice problems. The post test demonstrated that a significant decrease in anxiety in both the mathematics test and the numerical tasks categories. The paper concludes that this paper and related research indicates that CBGT and other research can be highly effective at reducing mathematics anxiety for both genders.

Lubienski, S. Research commentary: On gap gazing in mathematics education. Journal for Research in Mathematics Education, 39 4 , Her two main arguments are using gap analyses for shaping public opinion and policy and informing mathematic education research and practice.

Toward the end of her article, she suggests future directions for gap gazing through 1 hierarchical linear modeling, 2 cross-classified models, and 3 propensity score matching. Reys, R. Assess the impact of standards-based middle grades mathematics curriculum materials on student achievement.

This article is about a research study 2 year study done to determine the impact of standards-based curriculum materials on the success of students. The standards focused on in this research study were created by the National Council of Teachers of Mathematics. It was conducted on eighth grade students in six school districts in Missouri. The researchers were looking at the types of textbooks the students used in school. They compared students who used standards-based textbooks with students who did not use these types of materials. The researchers analyzed the scores of the Missouri Assessment of Performance MAP Mathematics Examination to determine if the materials helped students improve.

This article also shows tables of the comparisons of scores between schools that used the standards-based curriculum and those that did not. Soucie, T. Making Technology Work. Mathematics Teaching in the Middle School, 15 8 , The authors in this article mention several benefits of using technology in the classroom.

For example, technology can motivate students and can help them visualize the mathematics. Technology often involves real-life application of mathematics. Before using technology in the classroom, the article identifies some purposes for using it appropriately. This article also provides examples of how certain technology was used in the classroom; student remarks were included to provide the reader with a bright picture of the successes technology can bring into the classroom.

One of the examples included in the text was an activity where students worked in pairs — one individual would calculate by hand while the other individual could use a calculator. What really surprised students were actually testing that mental math can sometimes be much easier and faster than relying on a calculator.

Following this activity, teachers now have a stable opportunity to discuss the best opportunities to use technology and when not too. Throughout this article, it is apparent that technology should improve the quality of mathematics taught. Tomlinson, C. Mapping a Route Toward Differentiated Instruction. Educational Leadership , 57 1 , This article compares two different classrooms. Both teachers are covering the subject of ancient Rome. One classroom is teacher centered and is mostly lecture based.

His students are disengaged, but memorize facts and do well on quizzes. The second teacher believes she is running a differentiated classroom. Her students are having fun and learning about a different topic on ancient Rome. Although her students are enjoying class, the second teacher has no end goal.

### Learning Forward

Neither teacher has an effective learning environment. She then introduces a third teacher. This article gives a good idea of what differentiation should and should not look like. Yerushalmy, M.. Solving equations in a technological environment. Mathematics Teacher 90 2 , The authors also ask if the use of technology alone is enough to convey meaningful mathematics. To answer these questions, they tested an alterative algebra course in Israel that incorporated technology. The students in this course were assessed using tasks that included both familiar and novel problems.

In the article, the authors discussed the solutions several students provided on two of these tasks. Research study. Read the abstract first. Burns, M. Nine Ways to Catch Kids Up. Marilyn Burns, founder of Math Solutions Professional Development, writes about her successes in developing lessons that help intervention students catch up and keep up in learning mathematics.

She recalls that these helpful suggestions might not be useful for all students, but for the students who are truly at risk of failure, these things can change the ways in which students can learn and achieve greater success. Three timing guidelines for offering instruction intervention to support floundering students can be before, during, or after the lesson of topic is discussed and taught. Here, Burns mentions pros and cons of each. She also clearly states that providing extra help to struggling learners must be more than just extra practice. Rather, in nine effective and unique ways, teachers can provide extra help to students without doubling the amount of work.

Burns includes a short conversation she had with a student who was struggling with multiplication. What the reader is able to learn from this example is that many students are struggling because they lack connections between prior knowledge and have difficulty building a strong foundation of mathematics. Cobb, P. Reflective Discourse and Collective Reflection. Journal for Research in Mathematics Education, 28 3 , The authors studied discourse in a first-grade classroom to analyze the relationship between classroom discourse and mathematical development.

They focus on reflective discourse, by analyzing two classroom episodes. The children were able to reflect, through participation in discourse, on the previous activity. Although there was collective discourse, it is up to the individual students to reflect and form ideas. In addition to individual students playing an important role in reflective discourse, the teacher is also key.

In addition, the symbolic representations the teacher used help to guide the discussion. This article provides examples of reflective discourse that make it clear what they are describing. I also agree with the notion that discourse does not cause learning, but allows the possibility of learning. Gravemeijer, K. Context problems in realistic mathematics education: A calculus course as an example. Instead of a procedural or entirely graphical approach, which the authors believe may leave the students unable to understand the whole picture or unable to connect concepts to formal mathematics, this method suggests that teachers employ guided reinvention, often by considering the historical origins of the concepts.

The idea is to keep the gap between where the students are and what is being introduced as small as possible by designing a hypothetical learning trajectory for the students to be able to reinvent formal mathematics. The article gives some examples of how to use this method by considering time, velocity, and distance as the context for learning derivatives.

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Mathematics Teacher 99 4 , In this article, Herzig discusses why diversity is important in mathematics and what it takes to succeed in mathematics. Herzig cites equitable opportunity, intellectual climate of the classroom, and economic necessity as reasons why diversity is important. Leonard, J. Journal of Teacher Education , 61 3 , In this article Leonard et al. Leonard et al. Oberle, E. Relations among peer acceptance, inhibitory control, and math achievement in early adolescence.

Journal of Applied Developmental Psychology, 34 , For middle grades students years , relationships are the heart of positive academic, social, moral, and emotional development. This article aims to combine cognitive, social, and academic learning through a research study that reveals the connections between peer acceptance, inhibitory control, and math achievement in early adolescence.

In summation, higher inhibitory control leads to more peer acceptance and more math success. McKinney, S. Embracing the principles and standards for school mathematics: an inquiry into the pedagogical and instructional practices of mathematics teachers in high-poverty middle schools.

This article is about the principles and standards for mathematics in middle schools that are labeled as high poverty schools. The authors focused on instructional practices in high-poverty middle schools. The authors were concerned that teachers were not using up to date methods to teach mathematics to middle school students. Therefore they completed this study by analyzing the instructional practices of diverse in-service teachers.

## EMAT 7050 Mathematics Instruction

In the beginning of the study they found that many teachers were very traditional and used the drill and practice method. They found that inquiry-based methods increased student achievement. Schoenfeld A. Journal for Research in Mathematics Education , 20 4 , Schoenfeld takes a sample of high achieving 10 to 12th grade mathematics students. His team observes their classes and gives them a survey to determine their attitudes toward success in mathematics, classroom mathematics, and their attitudes toward mathematics. At the forefront of the articles discussion was the seeming disconnect from classroom practices of the students and their beliefs about the subject itself.

The students considered most memorization of rules and doing two minute problems to be at the forefront of learning mathematics. However, they also believed that mathematics was great for strengthening their creativity and logical skills, which Schoenfeld identifies as a stark contradiction. He posits that this disconnect between classroom and subject perceptions is due to rhetoric the teachers espouse about the merits of doing mathematics.

He claims that more admirable goals have been set and talked about in the classroom, but little has been done to actually make the learning of mathematics a deeper experience for students. Steffe, L. New York, NY: Springer. The first and the second hypothesis existed in the literature. Steffe came up with the third hypothesis. The first one is separation hypothesis where study of whole number is considered in the context of discrete quantity and the study of fraction is in the context of continuous quantity.

The second hypothesis is the interference hypothesis where it is believed that whole number knowledge interferes with the learning of fractions. He then describes two basic ways to understand the reorganization of the prior scheme. Truxaw, M. Lessons from Mr. Larson: an inductive model of teaching for orchestrating discourse. The Mathematics Teacher, 4 , Mathematical discourse is an important part of instruction as contunually indicated by the NCTM. There is often discrepancy of what type of discourse is most useful.

This article introduces the two types of discourse: univocal and dialogic. The article follows a teacher in an eighth grade algebra class and includes the discourse that took place in one of his lessons. The "inductive model" was the label given by Truxaw and DeFranco in their observations of this teacher. At several points, they discuss the teacher's actions as developing "metacognition. Another point made by Truxaw and DeFranco is that the teacher's disposition toward mathematics -- activing doing mathematics -- may influence the classroom discourse.

This is an interesting point. What research is there to demonstrate any relationship between the teacher's disposition toward mathematics and creating a discourse oriented classroom?

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Bartell, T. Journal for Research in Mathematics Education, 44 1 , The article talks about how to learn and implement techniques to teach mathematics for social justice. There has been a lot of research done in inequity and social justice in mathematics classroom. But there have been few research that actually teaches the preservice teachers how to implement social justice in their classroom. Bartell stress that more work needs to be done for preservice teachers that increases understanding and expand their assumptions about the goals of mathematics education and the knowledge required of teachers negotiating various aspects of such practice.

Bartell works with 8 secondary mathematics teacher in a graduate level mathematics course. Those students were divided into 2 groups. These two groups went from defining mathematics for social justice to development of lesson plans and analyzing the results of their lessons. Later Bartell summarizes her findings and suggests improvement in this area. That panel included. That special issue was made available online in The individual articles from can still be found with a Google search.

Here is a link to the Introduction to the special issue that was written by the Editorial Panel. It is a very interesting overview. Although, the claim is made that the print versity has the complete online materials, it is clear from just the abstract of Bartell's article that some editorial changes were made between and Huinker, D. The author, Huinker, writes about two urban school classrooms that devote their lessons to encouraging fifth grade students to problem solve by inventing their own algorithms. The teachers take on this challenge despite prior concerns about student performance on state-wide testing.

Included in that article are five main guiding principles for teachers to consider as they initiate problem solving in such a creative way.

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Given are multiple scenarios and glimpses of actual student-teacher conversations as this type of problem solving approach was implemented in this fifth grade classrooms. Emphasizing on the big ideas was an important key ingredient for success with this approach. This study used fraction strips as a tool for students to visual fractions. Students were also encouraged to record their thinking in writing. In this study, these students constructed intuitive qualitative understanding of fraction concepts and operations p.

Johnson, B. Of the four groups they tested all had high anxiety scores, but elementary education students had the least anxiety starting out, and were the only ones who had a statistically significant decrease in anxiety from taking the freshman content course aimed at deeper understandings of elementary mathematics. The special education pre-service teachers had the second lowest anxiety to start out with by a slim margin, but seemed to be relatively unaffected the classwork.

The article points out that there would probably more appropriate courses or interventions for certain groups, namely the special education pre-service teachers. Kaplan, R. Using technology to teach equivalence: Reflect and discuss. Teaching Children Mathematics, 19 6 , Lang, X. CAI and the reform of calculus education in China. This article presents the development of computer-assisted instruction CAI in China in Lang emphasizes the role of the computer as a tool, not a replacement for brainpower, and notes that good problems should encourage the students to think deeply.

Lang gives a couple of examples of problems used in the laboratory courses, and encourages collaboration amongst teachers to construct new meaningful problems. Lang wishes to avoid the traditional lecture and memorization of relevant rules that was a common practice in China prior the attempt to reform undergraduate instruction in the early s emphasizing the importance of practical problems. Manouchehri, A. Inquiry-discourse mathematics instruction. The NCTM encourages the use of student inquiry and mathematical discourse.

Inquiry based instructions allows for students to come up with mathematical ideas and discoveries on their own. When a teacher uses inquiry based instruction they are creating a mathematical environment where students are given opportunities to expand mathematical investigations. A teacher should be able to connect ideas and facilitate discourse in the classroom. In this article, the author reflects on a project they did in a classroom.

The project the students were given was the cereal box problem where they were to come up with displays of cereal boxes with different amounts of boxes. The article goes through the thought processes of each group of students and demonstrates how successful the discourse that took place was in promoting understanding of deeper mathematics.

Norton, A. In Teaching Children Mathematics, 14 1 , Here the components of a scheme are discussed and it is shown how schemes are different from strategies. Five different mental actions are discussed prior to the introduction of the fraction schemes. The five fraction operations are: unitizing, partitioning, disembedding, iteration, and splitting. Based on these mental actions, various fractional schemes are discussed here. They are: simultaneous partitioning scheme, equi-partitioning scheme, part-whole scheme, partitive unit fractional scheme and partitive fractional scheme.

This article will give the reader a quick understanding of the fraction schemes. Phillips, D. Education, 3 , This article focused on how mathematics and literacy teachers could incorporate literacy strategies into a mathematics classroom. A project was designed for mathematics and literacy teachers. This project received money through a grant given by the US Department of Education and was specifically tied to middle school teachers.

The project consisted of 2 phases: 1 teachers discussed learning needs, goals and concerns; 2 development of strategies and creation of resources needed to increase literacy in mathematics. In the end, the mathematics teachers became more confident when incorporating literacy strategies and saw the need for the strategies in their math classrooms. They were not able to assess the impact the strategies had as of when the paper was written. Therefore, they could not determine if these strategies improved comprehension and mathematics scores on the state tests.

Ross, A. School Science and Mathematics 11 2 , The study involved seven seventh and eighth grade teachers and their students. During the duration of the study, 16 algebra lessons were taught. The study found some sub-categories of representations, constructivist approaches, and student engagement increased learning, while others decreased learning. For example, the study found that iconic representations, independent thinking, problem-centered lessons, and expression and justification of ideas resulted in a decrease in learning.

Schiefele, U. Journal for Research in Mathematics Education, 26 2 , Does interest in a particular subject better predict outcomes of experience and achievement than general motivation? Does motivation and quality of experience predict achievement independent of ability? Researchers studied freshmen and sophomore students with high ability in at least one subject area. Higher achievement was correlated to higher mathematic ability, while interest did not play much of a role at all. Results also show that interest and experience are related, as well as interest and achievement.

The relationship between interest and experience, however, is stronger. There are many suggestions made for future research based on this study. Dogan, H. Dogan compares two groups of pre-service teachers taking a class in rational numbers, geometry, measurement and problem solving. The traditional group learned the material through lecture. The cohort group learned the material through discourse.

Each group was given a pre and post-test measuring aspects of their mathematical perception, emotions, confidence, and course expectations. More pronounced was the improvement in emotion than in perception. Fear, frustration, and difficulty decrased for those in the cohort class, and enjoyment increased.

The students in general were confident in their ability to learn mathematics. A notable result was that both groups were significantly less enthused about teaching math after the course. Faulkner, V. There is evidence that strong teacher knowledge and understanding of content impacts student gains on standardized measures. Faulkner and Cain conduct research testing the effects of 40 hours of professional development has on the following:. Kober, N. This is an article on the progress of using the common core state standards and the challenges that schools and teachers have had when implementing them.

The second page of the article lists and explains the findings so far when using these standards.

## Educating Everybody's Children: We Know What Works—And What Doesn't

This is the third year that these standards have been implemented. Therefore, the authors wanted to determine the process after the second year. This article includes many tables that show the results of surveys from each state and the timeline for implementation of the standards. Kober and Rentner state that a challenge that still exists is aligning tests with the common core state standards.

Niess, M. Preparing Teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. According to Niess, how teachers learned their subject matter is not necessarily the way their students will need to be taught in 21st century. The study examined the TCPK of 22 graduate students in a multidimensional science and mathematics teacher preparation program that integrated teaching and learning with technology.

According to Niess, if implemented effectively, TCPK can be a very useful tool for teachers to engage their students in more in depth studies in science and mathematics. Dunston, P. Mathematics Teaching in the Middle School, 19 1 , Professor Dunston, a literacy educator, and Professor Tyminski, a mathematics educator, at Clemson University came together to write this article about how teaching vocabulary instruction to middle school students can enhance conceptual understanding and set the foundation for appropriate mathematical discourse.

In this article, they focus on three research-based vocabulary instruction strategies that are very effective in a middle school mathematics class. The authors make a strong argument to conclude explicitly teaching mathematical vocabulary is essential for conceptual understanding and appropriate mathematical language for young adolescents.

Middleton, J. Journal for Research in Mathematics Education , 30 1 , Middleton and Spanias compile the findings of many studies on motivating students in mathematics. They talk about motivation from several different theoretical points of view including: behavioral, attribution and learned helplessness, goal, and personal-construct theories. The authors generalize the findings of studies done in each of these areas and relate them to each other. Though motivation has yet to be linked to a specific cause, findings show strong correlations between motivation and perceived success.

Researchers have also found that motivations develop at a young age and are relatively stable, but can be impacted by teachers. Simon, M. In this article, Simon discusses a constructivist model for teaching. He justifies the need for a model by discussing how the ideas of constructivism alone are not enough to implement constructivist teaching. This model was based off of his pre-existing notations of social constructivism and the data he gathered from a three-year teaching experiment.

The hypothetical learning trajectory outlines a path from a teachers learning goals, to their planned learning activities, to their hypothesis of the learning process. A key to this model is modification. This article deals with three parts. The first part presents the constructivist perspective of school mathematics. Here he talks about the difference between invention and construction. According to Steffe, invention is the production of unknown by the use of imagination without social interaction, whereas construction involves interaction. In the second part, Steffe describes first- and second-order mathematical knowledge.

It is indicated by what they do as they engage themselves in mathematical activities. The third part deals with the structure of the scheme. Tall, D. Mathematics Teaching , , This article discusses how the author, Tall, moved from written calculation, to graphing calculator, to the software AREA to discover the pattern of integration. After the students learn the techniques of building up areas with small intervals by hand, and larger intervals via the graphing calculator, Tall directs the attention of his students to the computer. Using the graphs from partial sums, the students are guided to guess possible general area functions and interpolate known points.

Tall gives multiple examples to use this type of method to determine positive and negative areas, the fundamental theorem, and the role of continuity. Walshaw, M. Review of Educational Research , 78 3 , I found this article to be the most useful article that I have looked at thus far.

It supports the use of classroom discourse in the mathematics classroom because studies show that classrooms where students are given opportunities to explain, defend, and argue mathematical ideas create more productive learning environments. They emphasize on the quality of classroom discourse in classrooms and not just the quantity. The article also includes implications for mathematics teachers such as what discourse works, how it works, and why it works.

Blanton, M. Mathematics Teacher , 2 , This article is about an observational study that was done in a mathematics classroom with a year long objective of developing better proof-writing and understanding skills among students. The class was taught by one of the authors and the classes were videotaped and then analyzed. Most people are familiar with the practice of medical rounds, in which interns and mentoring physicians visit patients in an institutional setting, observe their various conditions, discuss what they observed, and analyze possible treatment options and outcomes.

In the medical profession, making these rounds is viewed as a significant and highly important form of professional learning. While medical rounds for physicians and instructional rounds for teachers — called Teacher Rounds to distinguish it from the practice of rounds by administrators — are not precisely the same, the comparison is a shortcut way to begin thinking about what constitutes this kind of school-based professional learning.

Teacher Rounds is a strategy many schools use as part of a comprehensive program for improving teaching and learning. Teacher Rounds is based on these core assumptions about what it takes to create a culture of professional growth and learning:. Teacher Rounds is an advanced form of critical colleagueship — a professional learning environment that helps teachers expose their classroom practices to other educators and enables them to learn from data-driven feedback offered from a stance of inquiry.

During Teacher Rounds, teachers teach individual lessons while other teachers in their rounds group observe. Through rounds, more experienced practitioners can pass on knowledge and experience to the less experienced. There are opportunities for both veteran and novice teachers to learn, and those opportunities are encouraged.

Schools will hire outside experts to provide workshops and other events designed to help teachers learn how to change their practice in order to implement the Common Core. But there is little chance that this professional learning will help teachers figure out how to embed the Common Core State Standards into their practice — and professional learning will certainly not focus on how teacher collaboration can play a central role in teachers learning how to teach to those standards.

This does not guarantee that all teachers will be equally effective. By design, Teacher Rounds is perfectly positioned to give teachers the tools, skills, strategies, and supports they will need in order to align their practice with the Standards for Professional Learning and thus open the door to the Common Core State Standards. The table on p. Build in time for reflection and mutual support among those planning, running, and facilitating Teacher Rounds. They have identified a problem of practice, which they developed after agreeing that their math students lack persistence and perseverance in using mathematical discourse.

After discussion, they understand that this problem is closely aligned to a Common Core Standard: constructing viable arguments and critiquing the reasoning of others. This key practice becomes the focus of their Teacher Rounds group, and they use the following strategy. Teachers do not consistently provide daily differentiated rigorous tasks that encourage students to explain their mathematical thinking and build math fluency.

How do we use Number Talks a newly adopted math program in the school district to plan math discussions that enable students with different math abilities to explain their thinking and build fluency? The host teacher completes a host teacher preparation form. A sample of this form is at right. The teachers convene a Teacher Rounds debrief meeting using a Debriefing Protocol see box on p. Wonderings: Teachers wondered about these things that could impact their practice. The next Teacher Rounds meeting begins with records of practice that teachers bring to report on their commitments.

Two examples:. Video 1: The teacher videoed a student who had had trouble participating in Number Talks. Her video shows her escorting him to the white board and tutoring him by practicing a Number Talk. She felt that individual attention could build his confidence.

This is evident on the video, her record of practice. In a subsequent record of practice, she showed that some of the more silent students participated more actively in the whole group activity. Video 2: The teacher is working on pacing, and there is a picture of solutions on the white board. The question she is working on is finding a balance between brisk pacing vs.

She said she is particularly interested in this because she teaches students in the bottom third of math performance for the grade. This artifact was supplemented by a second artifact — a photograph of the whiteboard. The teachers see that taking the time to work a handful of high-yield strategies into their routines brings significant gains to their students. Successful schools — whether charter, traditional, or independent — have features in common: a clear mission, talented teachers, time for teachers to work together, feedback cycles that lead to continuing improvements.

Vivan Troen vtroen comcast. Katherine C. Achieves the highest levels of return for teachers and students through a low-cost, high-impact professional learning initiative. Evaluates professional learning by using records of practice as a focus tool for teacher learning. Encourages teachers to voice their concerns about their teaching; teachers are receptive to learning from one another. Provides ongoing professional learning for teachers regardless of years in the field; recognizes the importance of continuous improvement for all teachers.

Students show a visual cue when they are ready with a solution, and students signal if they have found more than one way to solve the problem. This form allows students to think, while the process continues to challenge those that already have an answer. Students share their strategies and thinking with their peers. Learning Forward. Definition of professional development. Standards for Professional Learning.

Mizell, H. Troen, V. However, it can be a challenge to implement. This book focuses on View Product. Blessings From The Dust. Thomas and Betty Jones grew up in the coal mining camps of southwestVirginia, a dusty, Thomas and Betty Jones grew up in the coal mining camps of southwestVirginia, a dusty, barren place where people had to work hard just to survive. Both their fathers were coal miners, as were many of the early African-American men who Commitment Precocious, naive Darla Mae Deacons often wakes up screaming in her rural Virginia home about her visions of a fiery pit, a redheaded woman, and a white-gloved hand.

Her secrets could tear her family apart! She fears going to Improving Literacy by Teaching Morphemes. With reports from several studies showing the benefits of teaching young children about morphemes, this With reports from several studies showing the benefits of teaching young children about morphemes, this book is essential reading for anyone concerned with helping children to read and write. By breaking words down into chunks of meaning that can be What happens when creative writing meets the maker space? Writing and making collide, revealing the Writing and making collide, revealing the genius inside of even the most reluctant writers.

She spills you