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‎Seesaw is the best platform for empowering students to demonstrate and share their learning. Students use powerful tools in the Seesaw app to create, reflect and demonstrate learning. When students share their learning in their Seesaw portfolio, teachers and families gain valuable insights into what...

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Education Week has tracked states' testing plans in math and English/language arts since 2014. This year's survey found a continued, steady erosion in the number of states using the PARCC or Smarter Balanced common-core-aligned tests: five fewer than in 2017. The number of states requiring students to take college-admissions tests, or pass an exit exam to graduate, is holding steady. (For an interactive breakdown of states' 2016-17 testing plans, click here.)

Below are highlights from the latest survey of testing plans. Scroll down to see the full results for 2019.

Which States Use PARCC or Smarter Balanced?

Only ONE-THIRD of the states use the PARCC or Smarter Balanced tests.

Fifteen states and the District of Columbia will administer PARCC or Smarter Balanced tests in the spring of 2019. That's five fewer than in 2016 and 2017.

Thirty-two states use tests they designed or bought.

Three states give hybrid tests. Two mix their own questions with items from the PARCC/New Meridian item bank, and one adds its own questions onto the full Smarter Balanced test.

Read more about the current state of common-core tests.

Learn more about the states using PARCC or Smarter Balanced tests.

Learn more about the states using non-consortium tests.

Learn more about the states mixing PARCC and Smarter Balanced with their own items.

Which States Require Students to Take the SAT or ACT?

Requiring the ACT or SAT is HOLDING STEADY after a rise in popularity.

Twenty-five states require students to take the SAT or ACT, the same number as in 2016 and 2017. That number had been climbing steadily-from seven states a decade ago- as states looked for ways to encourage students to go to college.

Learn more about the states that require SAT or ACT.

Which States Require Exit Exams?

Requiring exit exams is HOLDING STEADY after a decline.

Thirteen states require students to pass a test to get a high school diploma, one more than in 2017. In some states, students can use projects or portfolios to meet this requirement. Exit exams used to be more popular: In 2002, more than half the states required them.

Learn more about the states that require exit exams.

What tests are states requiring in 2018-19?

Below is a complete breakdown of results from our state survey.

Design & Visualization: Stacey Decker & Vanessa Solis

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Education Week has tracked states' testing plans in math and English/language arts since 2014. This year's survey found a continued, steady erosion in the number of states using the PARCC or Smarter Balanced common-core-aligned tests: five fewer than in 2017. The number of states requiring students to take college-admissions tests, or pass an exit exam to graduate, is holding steady.

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The concept of free and accessible learning materials is not new to education, but a national movement called #GoOpen is accelerating the creation and sharing of open educational resources (OER) by educators, and helping to improve equity in the process.

Launched in 2015 and led by the U.S. Department of Education Office of Educational Technology, the #GoOpen initiative continues to support states and districts in the curation and creation of OER. As of January, 110 districts and 20 states have officially participated in #GoOpen by downloading, editing and sharing lessons, curricula and texts for free.

#GoOpen participants commit to replacing at least one textbook that is due for renewal with an openly licensed educational resource. Administrators can then reallocate funds previously spent on books to support the transition to digital learning, such as for technology infrastructure and deeper professional development.

#GoOpen help builds 'culturally responsive' materials

OER use can save districts money. Another big benefit is the opportunity to freely adopt course materials, texts, videos and software that are more relevant to a diverse group of learners and are less static than traditional learning resources, says Kristina Ishmael, a former K12 open education fellow at the U.S. Department of Education Office of Educational Technology.

"The teaching force still does not reflect the students in our classroom, but OER use is a way to ensure that our instructional materials do," Ishmael says. Resources and supports exist to help educators find OER that fit specific content areas and grade levels, says Ishmael.

For example, as district leaders curate existing materials and create new ones as part of the #GoOpen program, they participate in a community that shares learning resources and best practices. The #GoOpen ambassador districts also mentor newcomers.

States joining the initiative must develop a statewide repository for openly licensed materials, and create a webpage to document progress.

'Sharing and freedom'

OER use boosts equity, saves money and promotes the use of timely and relevant resources, says Molly Yowell, digital content creator for the Indiana Department of Education's Office of eLearning. Also, new leadership roles for teachers have emerged because they usually join the #GoOpen teams that vet and create OER.

"As a teacher, OER use allows you to have ownership of your content, and shows that your district trusts you to use the instructional materials necessary to help every student learn in your classroom," Yowell says. Use of OER also provides flexibility for teachers to customize their classrooms each school year or semester.

In making the shift to digital, administrators should embolden teachers to own their curriculum, and remind them that they are the content experts who know what their students need, Yowell says.

"Teachers who make the transition to OER use need to see it as an opportunity rather than a burden, and need to embrace a culture that promotes sharing and freedom," says Yowell.

OER professional resources

* The U.S. Department of Education Office of Educational Technology's #GoOpen District Launch Packet offers advice for implementing OER materials.
* New America's Making Connections: PreK-12 OER in Practice project site includes a map of districts using OER and a repository of openly licensed tools and professional learning resources.

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#GoOpen accelerates digital curriculum buy-in and boosts equity | District Administration

# data[].attributes.attachment_link.description
The concept of free and accessible learning materials is not new to education, but a national movement called #GoOpen is accelerating the creation and sharing of open educational resources (OER) by educators, and helping to improve equity in the process. Launched in 2015 and led by the U.S.

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NEA provides the latest education news and tells the stories of the educators making our public schools work. Learn more about our activism on key issues facing our 3 million members, and hear what those members have to say about the current events that affect them.

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Learning with Zearn helps math make sense. Students explore math through pictures, visual models, and real-life examples. Log in to your Zearn account.

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http://article.sciencepublishinggroup.com/html/10.11648.j.ajap.20160502.11.html

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Clustering Analysis on Teachers' Perceptions of Mathematics Pedagogical Content Knowledge

Department of Mathematics, University of Taipei, Taipei City, Taiwan

Email address:

(Yuan-Horng Lin)

(Yuan-Shun Lee)

To cite this article:

In the last decades of the 20th century, the content and the way mathematics is taught are definitely changed from the traditional curriculum. The traditional method of teaching mathematics relies on the assumption that students acquire knowledge and skills by observing a teacher's explanations and practices. Nowadays, learning mathematics is viewed as an active process in which students construct their knowledge by engaging in meaningful and purposeful activities [ 9]. Most findings from earlier research on the relationships among teachers' mathematical knowledge, their teaching, and student learning indicate connection between teachers' knowledge and student achievement. It shows the role of teachers' mathematics teaching knowledge in their teaching is important. However, some literature indicates the role of teachers' mathematical knowledge in their teaching is not clear [ 15]. Therefore, clustering on teachers' perceptions of mathematics pedagogical content knowledge to further investigate its features should be prospective. In this study, it aims to investigate primary school teachers' perceptions of mathematics pedagogical content knowledge (MPCK). Questionnaire of MPCK is to evaluate teachers' perceptions. Fuzzy clustering is adopted to cluster the response data of perceptions. The optimal clustering could display the features of MPC for each cluster. The relationship between features of MPCK and experience of in-service could be discussed further. Results could be references to promote the professional development of primary school teachers.

2.1. Teaching and Learning Mathematics

It is important to clarify what the teachers need to know and be able to do mathematically in order to be effective in teaching mathematics for understanding [ 2]. They developed the practice-based theory of for teaching and they clarified [ 1] .

In addition to general pedagogical knowledge and knowledge of the content, teachers need to know things like what topics children find interesting or difficult and the representations most useful for teaching a specific content idea. Pedagogical content knowledge is a unique kind of knowledge that intertwines content with aspects of teaching and learning (p. 4).

An understanding of the different kinds of perspectives that mathematics teachers hold on teaching mathematics can help to highlight some of the key characteristics of instructional practices that teachers' professional development aim to support.

Many definitions of pedagogical content knowledge begin with L. S. Shulman when he stated that pedagogical content knowledge in one's subject area [ 19]. As L. S. Shulman stated [ 20] .

The key of distinguishing the knowledge base of teaching lies at the intersection of content and pedagogy, in the capacity of a teacher to transform the content knowledge he or she possesses into forms that are pedagogically powerful and yet adaptive to the variations in ability and background presented by the students. (p. 15)

An argument that highlights the role of mathematics teachers in promoting educational improvement can be found in the research on school leadership. School leaders are increasingly considered as mediators of policies to support teachers' professional development of mathematics instruction [ 6]. Frameworks on teacher knowledge for mathematics teaching create a foundation for educational researchers who investigate the interaction of knowledge occurring in the classroom. The knowledge is multifaceted practice which is a challenge to decompose, evaluate and analyze the type of mathematics pedagogical knowledge.

Since teachers' mathematics knowledge greatly becomes an important issue throughout the past several decades, numerous approaches and methodologies have been undertaken in an attempt to identify the relationships among teachers' mathematics knowledge and student learning [ 16]. Studies using proxy measures have been mainly sought to demonstrate a relationship between teachers' demographic variables and teachers' mathematical knowledge. Another studies using direct measures to assess teachers' mathematics knowledge consider teachers' knowledge will influence student achievement [ 12]. Another lines concerning teachers' effectiveness tend to investigate and observe teachers' mathematical knowledge while they are teaching [ 10]. This study adopts clustering analysis to reveal the features of teachers' mathematical knowledge should be a prospective approach.

2.2. Dimensions of Knowledge for Mathematics Instruction

L. S. Shulman and P. L. Grossman refined the concept of pedagogical content knowledge and developed five subcomponents: knowledge of alternative content frameworks, knowledge of student understanding and misconceptions of a subject, knowledge of curriculum, knowledge of particular content for the purpose of teaching, and knowledge of topic specific pedagogical strategies [ 21]. In accordance with this point, one is clearly understood what knowledge mathematics teachers' should have.

Several other scholars have also attempted to identify components of teacher mathematics knowledge. To summarize the viewpoints, their common suggested components include four categories of knowledge: knowledge of mathematics, context specific knowledge, pedagogical knowledge, and knowledge of learners' cognition in mathematics [ 8]. In addition, mathematics teachers' beliefs are partly of their components [ 23]. Besides, the above four components of teachers' knowledge each influences one another.

P. Mishra and M. Koehler consider ed the development of technology ha d influenced the usage in educational environment, they provide d the concept of technological pedagogical content knowledge . The complicated relationships are shown in Figure 1.

H. C. Hill, D. L. Ball and S. G. Schilling proposed three types of subject matter knowledge (SMK) and three types of pedagogical content knowledge (PCK) [ 11]. As to mathematics teachers, the knowledge is non-overlapping categories in the domain of mathematical knowledge for teaching. It is shown in Figure 2.

Teacher knowledge is strongly related to individual experiences and contexts [ 25]. A major conclusion from literature is that an understanding of teacher knowledge may be useful to improve teacher professional development and to make educational innovations more successful.

Some literature investigated effects of teachers' mathematical knowledge for teaching on student achievement. H. C. Hill, B. Rowan and D. L. Ball used a linear mixed-model methodology to explore whether and how teachers' mathematical knowledge for teaching contributed to gains in students' mathematics achievement [ 12]. The data included the first and third graders' mathematical achievement gains over a year which was nested within teachers, who in turn were nested within schools. Results showed that teachers' mathematical knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates. This finding provided suggestions to improve students' mathematics achievement by improving teachers' mathematical knowledge.

2.3. Fuzzy Clustering and Its Application in Education

L. A. Zadeh developed fuzzy theory and it flourishe d methodologies in many fields. In recent years, fuzzy theory has became one approach of data analysis methodology [Suppose is a fuzzy set and is membership function with the membership value , 4, 27]. A . represents the degree that belongs to fuzzy set A

The most widely-used fuzzy clustering algorithm is the fuzzy c-means algorithm (FCM). J. C. Bezdek combined fuzzy theory and clustering technique and he innovated fuzzy clustering greatly since he brought the membership into the objective function [. This f uzzy clustering is also called fuzzy c-means which allow s For a data matrix variables, the membership matrix and the group center matrix 3] partial memberships of data points in the clusters. It is suitable to cluster data base so that population of dataset could be classified into some subpopulation s . Fuzzy clustering is a useful technique which helps to enrich the semantics of the data by revealing patterns in database. N subjects and M . The following objective function with optimization problem is applied as follows, with are unknown under group number C

(1)

where and , could be acquired by iteration with convergence.

Decision on number of cluster is the issue of clustering validity. There are some indices to help select the optimal number of cluster. Two popular indices, which are partition coefficient partition entropy, are used in this study. The formulas are as follows [ and 3].

(2)

(3)

Within the range of possible clustering number, the best partition is that corresponding to the highest partition coefficient. As to the partition entropy, the best partition is that corresponding to the lowest partition entropy [ 26].

Fuzzy clustering has been adopted to identify and classify at-risk students at an early stage of their academic career so that teachers can develop plans to improve their performance [ 13]. Those at-risk students were classified into weak, average and good clusters. The findings could help educational managers monitor the performance of various groups of students and improve academic achievement. Clustering analysis was also adopted to investigate the knowledge that experienced science teachers have of models and modelling in science in the context of a school curriculum innovation project in which the role and the nature of models and modelling in science are emphasized [ 24]. In their study, two instruments of questionnaires are used collect response for clustering analysis. Results showed that different clusters had varieties of the teachers' knowledge of models and modelling in science. H. S. Siller, S. Kuntze, S. Lerman and C. Vogl investigated the big idea on the mathematics classroom for teachers to be aware of this big idea related to a variety of curricular contents. They study concentrated on views of Austrian and German pre-service teachers about the significance of modelling as a big idea. Clustering was adopted to analyze the ratings of the big ideas about results concerning the pre-service teachers' perceptions [ 22]. Its findings indicated the various features of big idea for different clusters. In according to the above the clustering application in education, it is concluded that clustering analysis should be beneficial to probe the mathematics pedagogical content knowledge of teachers.

3.1. Questionnaire of MPCK

The questionnaire of perceptions of mathematics pedagogical content knowledge (MPCK) is designed by the author according to the related literatures of mathematics teaching knowledge. The questionnaire is four-point Likert scale. The coding and linguistic variables are 1 = strongly disagree 2 = disagr ee , 3 = agree and 4 = strongly agree. In this study, the questionnaire consists of six dimensions. These dimensions are mathematics content knowledge (MCK), students' cognition knowledge (SCK), mathematics instruction knowledge (MIK), mathematics instruction practice (MIP), mathematics assessment knowledge (MAK) and teacher professional responsibility (TPR). The validity has been confirmed based factor analysis and experts . The Cronbach reliability , which is one of internal consistency indices, with respect to each dimension is between 0. 81 and 0.90. It means that the validity and reliability are acceptable.

The re are totally 259 primary school teachers in Taiwan participating in the study. Of these teachers, there are 73 male teachers and 186 female teachers. The sample distribution is shown in Table 1. It indicates most teachers are located at 6-15 and 16-25 in-service years.

4. Results and Discussions

4.1. Statistics Description and Number of Clusters

Mean and standard deviation of each dimension are depicted in Table 2. It reveals that the lowest mean score is students' cognition knowledge (SCK) but its standard deviation is quite high. On the contrary, the highest mean score is teacher professional responsibility (TPR) but its standard deviation is the lowest. General speaking, the perceptions as to all dimension of MPCK almost locates at "3 = agree".

The average scores of dimensions for each teachers are the raw data for fuzzy clustering. On the process of fuzzy clustering, partition entropy and partition coefficient are used to decide number of C clusters. As shown in Table 3, from C=2 to C=8, the largest partition coefficient (0.889458) and the smallest partition entropy (0.133875) occur when it is C=6. Therefore, it means the subject could be properly classified into six clusters.

Since optimal number of clusters is six which are from cluster I to cluster VI, the sample size and percent are shown in Table 4. Cluster III has the largest sample size (84 and 32.43%) and cluster I has the smallest sample size (20 and 7.7 2%) .

4.2. Description and Characteristics of Clusters

Based on the results of fuzzy clustering, the cluster centers for each dimension of MPCK are shown in Table 5. Figure 3 displays the line chart of these cluster centers.

According to Table 5, Cluster I have the lowest dimensional scores and the cluster VI has the highest dimensional scores. In Figure 3, the lines across dimensions of MPCK are almost parallel. Hence, it means the dimensional scores almost increase as they are from cluster I to cluster VI. As to the dimensions of mathematics assessment knowledge (MAK) and teacher professional responsibility (TPR), there exist little differences. It reveals that cluster IV has higher MAK and TPR than cluster V. Cluster II also has higher TPR than cluster III.

In comparison with Table 4 and Table 5, one is concluded that cluster III owns the largest sample size among clusters and its scores of cluster center are almost lower than 3. Therefore, quite a few of teachers perceive that their own mathematics pedagogical content knowledge (MPCK) is not very well.

It is prospective to compare the means of all dimensions among clusters. As shown in Table 6, it clearly displays that there are significant difference on means of all dimensions among clusters.

Further investigation on the cross analysis for cluster and years of in-service is shown in Table 7. The Chi-square test is , . It indicates there exits significantly difference as to frequency distribution. Teachers who are under 15 years of in-service tend to belong to cluster I, II and III. On the contrary, teachers who are 16 years of in-service and over tend to belong to cluster IV and VI. Therefore, one is concluded that teachers who have more years of in-service will have higher scores on all MPCK dimensions. Experienced teachers would have higher perceptions of MPCK.

Acknowledgements

This research was supported by Ministry of Science and Technology of Taiwan, R. O. C. under grant MOST 103-2511-S-142 -024 -MY3.

References

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2. Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics enough to teach third grade, and how can we decide? American Educator, 14-22, 43-46.

3. Bezdek, J. C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithm. NY: Plenum.

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18. Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge. Teaching and T eacher E ducation, 21(5), 509-523.

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20. Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.

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22. Siller, H. S., Kuntze, S., Lerman, S., & Vogl, C. (2011). Modelling as a big idea in mathematics with significance for classroom instruction-How do pre-service teachers see it. In Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 990-999).

23. Thompson, A. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics (pp. 127-146). New York, NY: England: Macmillan Publishing Co, Inc.

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Clustering Analysis on Teachers' Perceptions of Mathematics Pedagogical Content Knowledge

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The purpose of this study is to cluster the perceptions of mathematics pedagogical content knowledge (MPCK) for teachers. The subject is 259 primary school teachers in Taiwan. This study constructs dimensions of MPCK according to the review and conclusions of literature.

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Math Manipulatives & Reading Resources - Didax Educational Resources

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For over 40 years, we've specialized in helping educators to address individual learning styles and diverse student needs. Through the use of math manipulatives and resources for language arts, we strive to make teachers more successful.

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Click an issue image to see its table of contents.

Spring 2015
Table of Contents

COMMENTS FROM THE EDITOR
Angela T. Barlow, Middle Tennessee State University Murfreesboro, Tennessee

1

MATH TEACHERS' CIRCLES AS A FORM OF PROFESSIONAL DEVELOPMENT: AN IN-DEPTH LOOK AT ONE MODEL
Diana White, University of Colorado Denver

3

NORMS FOR TEACHERS' DISCUSSIONS OF STUDENTS' MATHEMATICS IN PROFESSIONAL DEVELOPMENT SETTINGS
Cyndi Edgington, North Carolina State University
Paola Sztajn, North Carolina State University
P. Holt Wilson, The University of North Carolina at Greensboro
Marrielle Myers, Kennesaw State University
Jared Webb, The University of North Carolina at Greensboro

12

THE ESSENCE OF FORMATIVE ASSESSMENT IN PRACTICE: CLASSROOM EXAMPLES
Marjorie Petit, Marge Petit Consulting, MPC
Mary Bouck, Michigan State University

19

ENVISIONING THE ROLE OF THE MATHEMATICS TEACHER
Charles Munter, University of Pittsburgh

29

THE PERSPECTIVES OF TEACHER LEADERS ON MATHEMATICS, LEARNING, AND TEACHING: SUPPORTING REFORM-ORIENTED INSTRUCTION
Michelle T. Chamberlin, University of Wyoming
Melissa L. Troudt, University of Northern Colorado
Reshmi Nair, Hood College
Alisa Breitstein, University of Northern Colorado

41

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Click an issue image to see its table of contents. Spring 2015Table of Contents COMMENTS FROM THE EDITOR Angela T. Barlow, Middle Tennessee State University Murfreesboro, Tennessee 1 MATH TEACHERS' CIRCLES AS A FORM OF PROFESSIONAL DEVELOPMENT: AN IN-DEPTH LOOK AT ONE MODEL Diana White, University of Colorado Denver 3 NORMS FOR TEACHERS' DISCUSSIONS OF STUDENTS' MATHEMATICS IN PROFESSIONAL DEVELOPMENT SETTINGS Cyndi Edgington, North Carolina State UniversityPaola Sztajn, North Carolina State UniversityP.

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EDU530 Moving Through the Curriuculum .docx

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The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.

The progressions can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics. They would be useful in teacher preparation and professional development, organizing curriculum, and writing textbooks. Progressions documents also provide a transmission mechanism between mathematics education research and standards.

For more information on the project, please visit the project website.

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Progressions Documents for the Common Core State Standards for Mathematics

# data[].attributes.attachment_link.description
The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels, informed both by research on children's cognitive development and by the logical structure of mathematics.

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Online Tool in the form of a game. Allows students to interact with each other. You can set the skills that each student works on.

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Amazing pets, epic battles and math practice. Prodigy, the no-cost math game where kids can earn prizes, go on quests and play with friends all while learning math.

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Posted:

While many math educators may be able to order fractions from largest to smallest in their sleep, teaching that skill to students and recognizing effective teaching strategies in instructional materials is more complicated. An adult might have an efficient and effective method of determining the largest fraction within a group-a method that works every time they do it themselves-but this knowledge alone is not enough to help students learn the skill of ordering fractions.

In addition to being able to do the skill, a teacher needs to be able to quickly determine if alternative methods will always give the correct answer. Teachers also need to be able to accommodate students who might order fractions using different methods that are also correct and equally as efficient, while at the same time offering support to learners in the conceptual building stages of ordering fractions when efficiency is not the only consideration. This conceptual building may involve specific representations of fractions for specific purposes. Some students might think about a fraction as a shape; others might think about a fraction as a point on a number line. Teachers should understand when each representation is preferable, and understand that thinking of fractions on a number line boosts students' connection between fractions and other types of numbers.

In addition, teachers should support the use of different representations and, when appropriate, steer students toward using a certain representation in order to make connections that will be helpful in future study of mathematics. This additional knowledge that is necessary to teach mathematics-beyond what is needed to do mathematics-has been dubbed by Deborah Ball, mathematics education researcher at University of Michigan, as "Mathematical Knowledge for Teaching" or MKT.

In our project working with teachers to adapt their instructional materials for fractions, the group built our MKT collaboratively by examining tasks from both a student and teacher perspective. One aspect of MKT that we worked on throughout the project is the ability to choose a task that helps students learn a particular strategy for solving. Consider the three sets of fractions below:

Set A: 1/4, 1/20, 1/19, 1/2, 1/10

Set B: 4/13, 3/11, 6/20, 1/3, 2/5

Set C: 5/6, 3/8, 2/3, 3/7, 1/12

Which of these sets of fractions would be best for helping students learn to develop several different strategies for comparing fractions?

While each of the sets gives students an opportunity to compare fractions, there are specific strategies that students might use for each. By thinking together as a group about different fraction comparison strategies such as using common numerators, using common denominators, and using benchmark fractions, we were able to determine what an ideal set of numbers for comparing fractions might look like, based on the techniques that the teacher wanted to encourage in their students.

For example, Set A above can be compared using only the strategy of common numerators, since these fractions are all unit fractions. Set B uses fractions that are all less than ½, missing a prime opportunity for benchmarking as a comparative strategy. Also, Set B does not give an opportunity to use common numerators or common denominators as a strategy without finding equivalent fractions. Set C gives an opportunity to compare with common numerators (⅜ and 3/7) as well as an opportunity to use ½ as a benchmark since some fractions are greater and some are less than ½ .

By collaboratively ordering fractions, looking at student work and student strategies to order fractions, and considering various different tasks that ask students to order fractions, our group was able to increase our collective MKT on this topic. Before our work together, when asked which of the three sets of fractions would best help students learn to develop several different strategies for comparing fractions, 30% of teachers in the project answered the question correctly by choosing Set C. When asked at the end of our work together, 73% of teachers correctly chose Set C. This increase shows how providing teachers with training to boost their MKT can help them learn to identify higher quality tasks and design lessons that support students in developing a deeper understanding of mathematical skills and concepts.

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Mathematical Knowledge for Teaching - Achieve the Core Aligned Materials

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While many math educators may be able to order fractions from largest to smallest in their sleep, teaching that skill to students and recognizing effective teaching strategies in instructional materials is more complicated. An adult might have an efficient and effective method of determining the largest fraction within a group-a method that works every time ...

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Chapter 132 Proposed Mathematics Standards 10-2019

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Developing Mathematical Content Knowledge for TeachingElementary School Mathematics

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Developing Mathematical Content Knowledge for TeachingElementary School Mathematics

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Home

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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Mathematics coaching has been shown to be one of the most effective ways to increase teacher effectiveness and student learning. The book Coaching in Mathematics Education, from NCSM's new Essential Action Series, will serve as a guiding reference for coaches, teachers, administrators, and others as mathematics coaching programs become more prevalent throughout schools worldwide.

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Principles to Actions - National Council of Teachers of Mathematics

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Specific teaching practices and principles that are essential for a high-quality mathematics education for all students.

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Taking Action - National Council of Teachers of Mathematics