Research shows that the work of a strong teacher is the most important school factor in student learning. But when it comes to teaching, there\u2019s always something new to learn. Professional development sessions, such as in-service training, can help teachers keep up with the latest research on teaching and find ways to use it in their classrooms.<\/p>\n
To help elementary math teachers,\u00a0Paola Sztajn<\/a>, associate dean for research and innovation for NC State\u2019s College of Education, and P. Holt Wilson<\/a>, associate professor of mathematics education at UNC Greensboro, have teamed up to edit a book on professional development.<\/p>\n Learning Trajectories for Teachers: Designing Effective Professional Development for Math Instruction<\/a><\/em>\u00a0uses experiences from four successful programs to show how to help teachers master strategies for teaching elementary math and use them with students. We asked Sztajn and Wilson to explain the challenges and rewards of this work \u2013 without using numbers.<\/p>\n The Sztajn\/Wilson<\/strong>: Learning trajectories are frameworks that organize what we know about how learning can unfold. They are empirically developed maps describing how the learning of a particular mathematical concept progresses to become more sophisticated through instruction.<\/p>\n For example, a child learning to count starts by rote TA<\/strong>: Sztajn\/Wilson<\/strong>: Of course learning always brings that \u201caha moment,\u201d and for any teacher, these moments are what keep us going! In our work with teachers around learning trajectories, we always start by looking at students\u2019 mathematical behaviors. Teachers, most of the time, have seen these behaviors in their classrooms. But once we start naming the behaviors and placing them in a trajectory that maps learning, it all comes together in that \u201caha moment.\u201d Naming and recognizing these behaviors allow teachers to talk to each other about something that previously they perhaps were not sure was happening in all classrooms, with lots of students. Recognizing which of these behaviors represent more sophisticated mathematical ideas also helps teachers recognize what students know and appreciate their progress in learning a mathematical concept before mastering it.<\/p>\n TA<\/strong>: Sztajn\/Wilson<\/strong>: Our book is unique in the sense that, for each of the projects we include, instructional designers discuss what really happens in their professional development, and, just as importantly, how they got to that particular design. So we talk about the designers\u2019 learning over time in programs they implemented and continued.<\/p>\n As a field, we know a lot about how to design TA<\/strong>: Sztajn\/Wilson<\/strong>: Everyone! This needs to be a systemwide approach that has a consistent message all the way from the district leaders, to principals, to instructional leaders and then to teachers.<\/p>\n Several school systems now have great mathematics teacher leaders and coaches who can carry out professional development with teachers. These leaders are usually well aware of the research going on and of what represents high-quality mathematics instruction. These professionals play an important role in the school building, educating principals about what they should look for and, at the same time, working with teachers to improve instruction. They also connect to researchers and professional development designers, working with them to bring new knowledge and evidence-based instructional strategies into the schools. When this is happening in all buildings, then district-level leadership needs to maintain a consistent message about what counts in mathematics teaching and learning. Oftentimes, there are disconnected messages within the district and within schools about what high-quality instruction is \u2013 and that is a problem.<\/p>\n For example, it\u2019s contradictory to say that communicating TA<\/strong>: Sztajn\/Wilson<\/strong>: Respecting teachers and their professional knowledge is one important message. Professional development has to offer actionable, useful ideas that matter to teachers in classrooms. When working with trajectories, it is important to attend to how teachers are making sense of the trajectories and what helps the teachers in their teaching. Also, a major issue for all projects is how instruction can position all students as competent to support each and every child in their mathematics learning. We learned that trajectories, when implemented with explicit goals of overcoming deficit perspectives on learning, can help teachers support the learning of all their students.<\/p>\n This post was\u00a0originally published<\/a>\u00a0in NC State News.<\/em><\/p>\n","protected":false,"raw":"Research shows that the work of a strong teacher is the most important school factor in student learning. But when it comes to teaching, there\u2019s always something new to learn. Professional development sessions, such as in-service training, can help teachers keep up with the latest research on teaching and find ways to use it in their classrooms.\r\n\r\nTo help elementary math teachers,\u00a0Paola Sztajn<\/a>, associate dean for research and innovation for NC State\u2019s College of Education, and P. Holt Wilson<\/a>, associate professor of mathematics education at UNC Greensboro, have teamed up to edit a book on professional development.\r\n\r\nLearning Trajectories for Teachers: Designing Effective Professional Development for Math Instruction<\/a><\/em>\u00a0uses experiences from four successful programs to show how to help teachers master strategies for teaching elementary math and use them with students. We asked Sztajn and Wilson to explain the challenges and rewards of this work \u2013 without using numbers.\r\n\r\nThe\r\nAbstract (TA)<\/strong>: Can you explain the concept behind\r\nlearning trajectories and give an example of how they work?\r\n\r\nSztajn\/Wilson<\/strong>: Learning trajectories are frameworks that organize what we know about how learning can unfold. They are empirically developed maps describing how the learning of a particular mathematical concept progresses to become more sophisticated through instruction.\r\n\r\nFor example, a child learning to count starts by rote\r\nreciting the number names, then develops one-to-one correspondence, and then\r\ndevelops the concept of cardinality, which is the understanding that when\r\ncounting a collection of objects, the number name associated with the last\r\ncounted object represents the totality of the collection and not the name of\r\nthat particular object. The child can then start producing quantities and also\r\nstart counting backwards. Later, the child can count starting at any number and\r\nskip count. Such progression of thinking requires instruction and should also\r\nguide instruction.\r\n\r\nTA<\/strong>:\r\nWhen you do in-service training on teaching mathematics, is there an \u201caha\r\nmoment\u201d when teachers see how learning trajectories can help them reach\r\nstudents?\r\n\r\nSztajn\/Wilson<\/strong>: Of course learning always brings that \u201caha moment,\u201d and for any teacher, these moments are what keep us going! In our work with teachers around learning trajectories, we always start by looking at students\u2019 mathematical behaviors. Teachers, most of the time, have seen these behaviors in their classrooms. But once we start naming the behaviors and placing them in a trajectory that maps learning, it all comes together in that \u201caha moment.\u201d Naming and recognizing these behaviors allow teachers to talk to each other about something that previously they perhaps were not sure was happening in all classrooms, with lots of students. Recognizing which of these behaviors represent more sophisticated mathematical ideas also helps teachers recognize what students know and appreciate their progress in learning a mathematical concept before mastering it.\r\n\r\nTA<\/strong>:\r\nYour book focuses on the importance of sharing effective approaches to\r\nprofessional development about teaching math. What gets in the way of doing\r\nthis?\r\n\r\nSztajn\/Wilson<\/strong>: Our book is unique in the sense that, for each of the projects we include, instructional designers discuss what really happens in their professional development, and, just as importantly, how they got to that particular design. So we talk about the designers\u2019 learning over time in programs they implemented and continued.\r\n\r\nAs a field, we know a lot about how to design\r\nprofessional development for teacher learning. Scaling up and sustaining these\r\nmodels of professional development are the challenges. Instructional\r\nimprovement takes time as well as deliberate and continuous effort over many\r\nyears within a supportive school environment \u2013 right there are some of the\r\nmajor barriers. Most school systems cannot afford to invest in teacher learning\r\nand in allowing learning to be an integral component of the teaching profession\r\nover time. We have not found a systemic way to include consistent time for\r\nteacher learning in our schools. Teachers spend a significant part of their\r\ntime in the classroom with their students or attending to other demands within\r\nthe school building.\r\n\r\nTA<\/strong>:\r\nWho should take the lead in improving professional development in teaching\r\nmath? Principals? Instructional designers? District leaders?\r\n\r\nSztajn\/Wilson<\/strong>: Everyone! This needs to be a systemwide approach that has a consistent message all the way from the district leaders, to principals, to instructional leaders and then to teachers.\r\n\r\nSeveral school systems now have great mathematics teacher leaders and coaches who can carry out professional development with teachers. These leaders are usually well aware of the research going on and of what represents high-quality mathematics instruction. These professionals play an important role in the school building, educating principals about what they should look for and, at the same time, working with teachers to improve instruction. They also connect to researchers and professional development designers, working with them to bring new knowledge and evidence-based instructional strategies into the schools. When this is happening in all buildings, then district-level leadership needs to maintain a consistent message about what counts in mathematics teaching and learning. Oftentimes, there are disconnected messages within the district and within schools about what high-quality instruction is \u2013 and that is a problem.\r\n\r\nFor example, it\u2019s contradictory to say that communicating\r\nmathematical ideas is important and, at the same time, expect students in\r\nclassrooms to be always quietly working on their individual worksheets. When\r\nthe system lacks a coherent vision for high-quality mathematics instruction,\r\ntogether with a coherent message all the way through, it\u2019s really hard to\r\nimprove teaching through professional development. That\u2019s why improving\r\nprofessional development and teaching is everyone\u2019s job, from researchers to\r\nleaders at all levels of the educational system to teachers themselves.\r\n\r\nTA<\/strong>:\r\nWhat lessons can we take from the four groups in your book that have been\r\nfocusing on improving professional development with learning trajectories?\r\n\r\nSztajn\/Wilson<\/strong>: Respecting teachers and their professional knowledge is one important message. Professional development has to offer actionable, useful ideas that matter to teachers in classrooms. When working with trajectories, it is important to attend to how teachers are making sense of the trajectories and what helps the teachers in their teaching. Also, a major issue for all projects is how instruction can position all students as competent to support each and every child in their mathematics learning. We learned that trajectories, when implemented with explicit goals of overcoming deficit perspectives on learning, can help teachers support the learning of all their students.\r\n\r\nThis post was\u00a0originally published<\/a>\u00a0in NC State News.<\/em>"},"excerpt":{"rendered":" Paola Sztajn, Ph.D., associate dean for research and innovation for the NC State College of Education, has co-edited a book on professional development that focuses on the use of learning trajectories in elementary math instruction. She explains why everybody should be taking the lead in improving professional development in teaching math.<\/p>\n","protected":false},"author":243,"featured_media":25139,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"source":"","ncst_custom_author":"","ncst_show_custom_author":false,"ncst_dynamicHeaderBlockName":"","ncst_dynamicHeaderData":"","ncst_content_audit_freq":"","ncst_content_audit_date":"","ncst_content_audit_display":false,"ncst_backToTopFlag":"","footnotes":"","_links_to":"","_links_to_target":""},"categories":[185,205,203],"tags":[791,409,217,890,267,237],"_ncst_magazine_issue":[],"class_list":["post-25355","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news","category-our-people","category-research-and-impact","tag-faculty-books","tag-math-education","tag-news","tag-paola-sztajn","tag-professional-development","tag-stem"],"displayCategory":null,"acf":{"ncst_posts_meta_modified_date":null},"_links":{"self":[{"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/posts\/25355","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/users\/243"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/comments?post=25355"}],"version-history":[{"count":2,"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/posts\/25355\/revisions"}],"predecessor-version":[{"id":25358,"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/posts\/25355\/revisions\/25358"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/media\/25139"}],"wp:attachment":[{"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/media?parent=25355"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/categories?post=25355"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/tags?post=25355"},{"taxonomy":"_ncst_magazine_issue","embeddable":true,"href":"https:\/\/ced.ncsu.edu\/news\/wp-json\/wp\/v2\/_ncst_magazine_issue?post=25355"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nAbstract (TA)<\/strong>: Can you explain the concept behind
\nlearning trajectories and give an example of how they work?<\/p>\n
\nreciting the number names, then develops one-to-one correspondence, and then
\ndevelops the concept of cardinality, which is the understanding that when
\ncounting a collection of objects, the number name associated with the last
\ncounted object represents the totality of the collection and not the name of
\nthat particular object. The child can then start producing quantities and also
\nstart counting backwards. Later, the child can count starting at any number and
\nskip count. Such progression of thinking requires instruction and should also
\nguide instruction.<\/p>\n
\nWhen you do in-service training on teaching mathematics, is there an \u201caha
\nmoment\u201d when teachers see how learning trajectories can help them reach
\nstudents?<\/p>\n
\nYour book focuses on the importance of sharing effective approaches to
\nprofessional development about teaching math. What gets in the way of doing
\nthis?<\/p>\n
\nprofessional development for teacher learning. Scaling up and sustaining these
\nmodels of professional development are the challenges. Instructional
\nimprovement takes time as well as deliberate and continuous effort over many
\nyears within a supportive school environment \u2013 right there are some of the
\nmajor barriers. Most school systems cannot afford to invest in teacher learning
\nand in allowing learning to be an integral component of the teaching profession
\nover time. We have not found a systemic way to include consistent time for
\nteacher learning in our schools. Teachers spend a significant part of their
\ntime in the classroom with their students or attending to other demands within
\nthe school building.<\/p>\n
\nWho should take the lead in improving professional development in teaching
\nmath? Principals? Instructional designers? District leaders?<\/p>\n
\nmathematical ideas is important and, at the same time, expect students in
\nclassrooms to be always quietly working on their individual worksheets. When
\nthe system lacks a coherent vision for high-quality mathematics instruction,
\ntogether with a coherent message all the way through, it\u2019s really hard to
\nimprove teaching through professional development. That\u2019s why improving
\nprofessional development and teaching is everyone\u2019s job, from researchers to
\nleaders at all levels of the educational system to teachers themselves.<\/p>\n
\nWhat lessons can we take from the four groups in your book that have been
\nfocusing on improving professional development with learning trajectories?<\/p>\n