Book Club Meeting Dates: May 10, May 24 and June 9 Time and location: TBA I have created this blog as a way for us to share our reflections about the book: Visible Learning For Mathematics. Just as our students benefit from the rich conversation about math, it is through our conversations that we benefit from deeper learning and connect the way we view Math to the best way our students learn. If you are like me, I like to try new things in the classroom. That is great. because new things can benefit our students. When things are new, we can expect that the unexpected will continue to keep us growing in our profession as educators and students growing as learners. Why this book? ...When considering the book to offer for this book-club, this book became the obvious choice. I was gravitating towards Jo Boaler's book Mathematical Mindsets https://www.youcubed.org/ until I saw Steve Ventura's talk at Lompoc High School. In his talk, he told us about the meta studies that John Hattie did with research based strategies, measuring and ranking their effect sizes. Note: Appendix A. Effect Sizes, page 235. We are given the list of effects with their ranking for a variety of influences. This is a book that offers research based strategies that are ranked in order of effect size. I believe that all teachers want students to have the benefit of greater growth. I think that teachers will want to start using influences near the top of the rankings hoping that we will be able to see the results. Does it make any sense to do something with a lower ranking if I can help my students get there quicker by using a strategy with a higher ranking influence? Please do not see this as anything negative about the Jo Boaler book. On the contrary, (it is on the summer reading list). If you believe that mindset is an issue for your students then her book would be a good place to start the process of sustainable improvement. The whole idea of Growth Mindset needs to be ingrained into our culture and all subjects, not just in Math. I guess that is why I don't just connect the concept of Growth Mindset with Math. Carol Dweck's book and resources http://mindsetonline.com/whatisit/about/changed my life and will always be #1 on my book list. I often hear students tell themselves "I can't do it". Both of these authors show us that we can. If you look at the data you may conclude that Mathematics is at a crossroads in our country. Do you think that this could be something we can fix? If you are familiar with the Mathematical Practices you may conclude that some students might just need to see it a different way. If used as a resource to help us shift our daily instruction, Visible Learning For Mathematics https://us.corwin.com/en-us/nam/visible-learning-for-mathmatics-grades-k-12/book255006#contents gives us evidence based research that encourages us to make those informed decisions. I encourage your thoughts. happy reading! Summer reading list: http://robertkaplinsky.com/6-non-education-books-educators-read/ Must view Ted Talk: https://www.ted.com/talks/carol_dweck_the_power_of_believing_that_you_can_improve?language=km?utm_source=tedcomshare&utm_medium=referral&utm_campaign=tedspread Questions for thought: What are some of our challenges in teaching Math? How do we incorporate the concept of Growth Mindset into our daily routines? Preface: The preface begins by explaining what should be obvious for most of us, "people who understand mathematics have a higher quality of life." This statement is followed up with a variety of supports from many worthy sources. If a student has a talent in Math, that talent should be nurtured. I believe that teachers have a responsibility to hlep our students to be the best version of themselves whenever possible. In order to do this, it is necessary to enthusiastically teach all subjects, especially Math, as rigorously as we can. Teachers can use the Barometer of Influence pp. 21-22 to help them plan lessons https://resources.corwin.com/vl-mathematics that offer "more growth-for-the-lesson". Chapter 1. Making Learning Visible in Mathematics I have trouble visualizing things. I can't seem to organize much in my mind, I always need to write it down, look at a calendar, pull up a web-site or something similar. I suspect many students have the same requirements. Teachers need to realize that there are many students who are visual learners while we are creating rigorous lessons. Rigor is defined as a balance among conceptual understanding, procedural skills and fluency, and application with equal intensity. (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010). So how can we build lessons that help students to visualize rigor? The book encourages us to think of the nature of learning in the categories of surface, deep, and transfer. I suggest that we think of where our students fall under each of these categories when we plan our lessons in order to better support student learning. Surface Learning: Initiation to new ideas. Deep Learning: consolidating understanding of mathematical concepts and procedures and making connections Transfer Learning: students take the reins of their own learning and are able to apply their thinking to new contexts and situations. Questions for thought: How can we increase the "rigor" in our Math lessons? How can we begin to write our Math lessons to address the three categories of learning? How can we support our visual learners? Chapter 2: Making Learning Visible Starts with Teacher Clarity Teachers know that learning intentions need to be communicated in student friendly language. I remember my first year of teaching, I was told to put the learning objective on the board and refer to it throughout the lesson. This is because students need to be able to clearly explain what they should be able to do by the end of each lesson so that they can make important real-world connections. The book suggests that we present these "learning intentions" as "I can" statements. For example, I used to write: Students will be able to... on the board but now teachers should write: I can...Visible Learning for Mathematics suggests doing this with the help from an "I can..." statement (page 60). This, combined with the suggested traffic light system in which students place their names on red, (I don't know this yet), yellow light (I'm almost there), or the green light, (I can help someone else tomorrow) The Chapter finally offers teachers two rubrics for students. The Self-Reflection Rubric for Group Collaborative Assessments give students the opportunity to reflect on how well they did in group assignments and what they need to do to improve, Figure 2.5. Then we are given a well written Rubric for Rich Mathematical Task. Questions for thought: How can we transform our classrooms through the use of "I Can" statements? How can we improve student collaboration? What does a "rich Mathematical Task" look like? Resources: 5 Practices for Orchestrating Productive Mathematics Discussions [NCTM] Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching Chapter 3: Mathematical Tasks and Talk that Guides Learning "Giving students appropriate tasks at the right time in their learning cycle is crucial to move students from surface to deep and transfer learning." (pg 73) Exercises verses Problems, there is a real difference how they should be used within the learning cycle. Spaced practice or a few exercises on a concept each day over several days has an effect size of .71. Fluency exercises that are sometimes made into "timed tests" can do more harm to mathematical understandings, motivation and a students view on mathematics. Slow and steady is the best recommendation for fluency assignments. Students need deliberate practice, guided by the teacher, not repetitive skill-and-drill tasks. Could this be why students struggle to learn Math facts? Difficulty is not the same as Complexity (figure 3.1) page 77 More complex: Strategic Thinking (draw on students' ability to think strategically; Expertise (push students to stretch and extend learning) Less Complex: Fluency (builds automaticity) ; Stamina (supports perseverance) Difficulty is the amount of effort one must put in while complexity is the level of thinking, the number of steps, or the abstractness of the task. Complexity can be supported by having students work in groups and justify their thinking. This encourages collaboration, group communication and planning and meta-cognition strategies. More videos and blogs about Complexity: http://www.heinemann.com/ChildrensMath/ Four levels of cognitive demand (figure 3.2) pgs. 81-82 is a helpful tool for teachers to use when they are planning instruction making sure to balance instructional time and mathematical tasks appropriately. Examples of tasks at each of the four levels of cognitive demand are available in figure 3.3 on page 84. Lower level demands: Memorization & procedures without connections Higher level demands: Procedures with connections & doing Mathematics The discussion of making learning visible through mathematical talk begins with teacher questioning. Posing purposeful questions encourage students to explain, elaborate and clarify thinking to build understanding, revel students' current understanding of a concept and make the learning of mathematics more visual and accessible. Questions can help teachers check for student misconceptions or partial understanding and to help build and deepen students' understanding. Funneling questions can guide students down the teacher's path to find the answer. And focusing questions allow students to do the cognitive works of learning by helping to push their thinking forward. (figure 3.4) pg 92 Prompts are questions or statements used to remind students to leverage what they already know in order to think further. (Types of Prompts for Mathematics) Figure 3.5 page 95. Cues are more direct than prompts because they shift the student's attention to the relevant information required to move forward. (Types of Cues for Mathematics) Figure 3.6 pg. 96 Reflection and discussion questions pg. 97 Chapter 4 Surface Mathematics Learning Made Visible Have you ever started teaching a concept with a project or activity that gives purpose to the learning objective? This is the introduction to Chapter 4. I drive by the "new Costco" that is being built in Santa Maria almost every day. They are still preparing the soil getting ready to pour the foundation. How can we put up walls if we don't prepare the soil? If we don't pour a good foundation? So why do we wonder why our students have trouble with the objectives of our lessons if we don't give them a purpose for the learning. Surface learning is most effective when using approaches that foster initial acquisition of conceptual understanding followed by procedural skills. The mathematical practices need to be taught directly and frequently through teacher modeling. With practice, students will begin to incorporate these habits into their daily work. It is suggested that teachers teach with the mathematical practices, lesson plan with the mathematical practices in mind, refer often to them, create a bulletin board or poster for each practice and have students reflect on the practices that they have learned. They can reflect on the practices on exit tickets or during Math Talks. Ways to incorporate Surface Learning include a variety of Mathematical talk and Metacognition activities including: Number talks, a brief daily routine that helps students develop computational fluency by sharing their thinking processes: http://players.brightcove.net/268012963001/default_default/index.html?videoId=5117848323001 Guided questions are helpful to students as they make sense of what is going on and guiding them to draw their own conclusions. Worked examples are math problems that have been fully completed to show each step of a mathematician's arrival at a solution. Direct Instruction is when the teacher decides the learning intentions, makes them clear and visible to students, do some demonstrations, checks for understanding and follows all this up with recaps and closure. Strategic use of vocabulary instruction offers an effect size of .67! Formal mathematical language leading to developing a mindset for thinking mathematically must be taught for depth and transfer. Three types of words or three tiers were discussed in chapter 1, Tier 1=everyday words, Tier 2= general academic words and Tier 3 domain specific words used in a given content area. Sentence frames that can build metacongnitive thinking can be found in figure 4.7 pg 121 and is available for download.http://resources.corwin.com/sites/default/files/Figure_4.7.pdf Word walls can be a useful tool in the teaching of academic vocabulary providing visual references for students but should consistently be referred to throughout a unit of study in order to be effective. Graphic Organizers such as the Frayer model can also be a useful tool in the study of vocabulary. Stategic Use of Manipulatives for Surface Learning The use of manipulatives bridges students' learning as they move from surface to deep learning. http://nlvm.usu.edu/en/nav/vlibrary.html So what kind of Math homework should I assign is a regular question I get these days. I see lots of Drops in the Bucket being assigned and I used to use it as a daily warm-up. The book suggests a 2-4-2 strategy for mathematics homework designed to build distributed practice into the homework process. Daily homework includes 2 problems on the new skill, 4 cumulative review problems and 2 problems that support reasoning and justification by requiring students to show and explain their work. Effect Size for Spaced practice = .71 (pg 129) Feedback is best when it is provided "just-in-time, just-for-me" when and where it can do the most good. Feedback about the process, not just the task, moves students to deeper learning. Strategic Use of Mnemonics It is important to remember that mnemonics should not be used as a replacement for an understanding of Mathematical concepts. However they can be used to assist learners to recall substantial amounts of information. Reflection and Discussion Questions: How can we encourage mathematical discourse in the classroom? How can we facilitate the strategic use of manipulative s in our classrooms to support surface learning. What ways can we incorporate the mathematical practices in our Math lessons to best support student outcomes? Chapter 5: Deep Mathematics Learning Made Visible The focus of Deep Learning is recognizing relationships among ideas and is particularly linked to mathematical practices 3, 7 and 8. Deep learning can be developed through rich tasks and accountable talk. Common Core MP 3: Construct viable arguments and critique the reasoning of others. This practice requires that students engage in deeper dialogue. Discourse reaches beyond discussion and includes ways of representing, thinking, agreeing and disagreeing. Students involved in academic discourse are able to ask questions that help to clarify an argument or justify their reasoning with evidence. Common Core MP 7: Look for and make use of structure.. This practice requires that students recognize patterns and it is beneficial for teachers to facilitate discourse Common Core MP 8: Look for and express regularity in repeated reasoning. What strategies from Chapter 5 do you see happening in this teacher's lesson? Mathematical Talk that Guides Deep Learning. The effect size for classroom discussion is 0.82. Accountable talk begins with the teacher who is consistently modeling the conversation moves and using appropriate prompts and questions to facilitate the conversation. Figure 5.6 on page 145 gives us a useful chart offering examples of accountable talk moves. Reduced teacher talk increases the opportunities for students to do more thinking and increase learning. Teachers can support additional opportunities for student discourse by incorporating accountable talk into their lessons. Accountable talk means that the conversation remains on topic, that the information presented is accurate and that the thinking is deep. In order for a teacher to better support students in accountable talk, teachers will benefit from the use of language frames, which are scaffolds that prompt the type of talk we want from students. Re-voicing, when a teacher restates a student comment or embeds the thinking in a question. And restating, when rephrase or repeat what a peer has said. Norms of Class Discussion The norms of class discussion should be explicitly taught at the beginning of the school year and consistently reinforced and maintained when necessary. Norms are the agreements of a group about how the members will work together. Four basic dimensions of norms are: trust, belonging, sharing and respect. Rules and procedures should reinforce the norms and should be developmentally appropriate. With an effect size of .82, it is recommended that 50% of classroom time be devoted to classroom discussion with teachers taking care that the tasks be complex enough, there is time in which students can agree and disagree with each other, there is sufficient language support such as sentence frames and teacher modeling, and that both individual and group accountability is provided making learning visible for students and teachers. Grouping students based on ability Grouping students strategically does not mean having students choose their own groups, grouping by ability or tracking students. The most effective grouping strategy is one that is flexible and balanced. Appropriate group size is three to five. Collaborative learning can be supported by providing groups with contribution checklists or ways students can contribute. Sample checklist is included in Figure 5.10 on page 160. Allowing students to move (effect size .53), peer tutoring (effect size .55) can also increase student learning. Individual Accountability If all students are to be accountable for group work, there are some strategies that can help to support student accountability. Writing rules such as if anyone writes, everyone writes, conversation round-table (Figure 5.11) where each group member has a section reserved for their own ideas, and individual questions for each students to answer before the group work. This can ensure that each student has ideas to share in the group. Accountable Talk within Whole Class Discourse In effort to support whole class discourse, teachers should consider the physical layout of the classroom and think creatively about ways to use the environment. Other methods are inside-outside circles where students stand or sit in an inner and outer circle. Members of each circle take turns discussing for a set period of time then switch. Strategy selection allows students to gather in areas of the classroom based on their chosen strategy for solving a problem, then discuss with the larger group the benefits of each method. Strategic Use of Manipulates for Deep Learning Research suggests that the instructional sequence of moving from physical representations through visual representations to symbolic representations leads to gains in math learning and understanding. Discussion Questions: How can accountable talk improve the mathematical discourse in your class? What rich tasks are most appropriate for supporting deep learning? Chapter 6: Making Mathematics Learning Visible though Transfer Learning The Nature of Transfer Learning Transfer Learning is about the ways students construct knowledge and reality for themselves as a result of surface and deep knowing and understanding. Transfer learning is when students take the lead of their own learning to their lives and are able to use the tools they have learned to help them solve new problems on their own. Near transfer occurs when a new situation is paired with a context students have experienced. In far transfer, students are able to make connections between remote situations. The Paths for Transfer:Hugging and Bridging Methods for Low-Road and High Road Transfer (Figure 6.1) pg. 180. Selecting Mathematical Tasks That Promote Transfer Learning Tasks that best promote transfer learning encourage connections. These will likely be higher complexity tasks with higher difficulty. Such tasks may not have a clear entry point or might have multiple entry points and multiple steps and they may have on one correct solution. Students should be able to use evidence to justify their thinking. These tasks could be inter-disciplinary and may take more than one lesson to solve. Teachers could assign an appropriate performance task or 3 Act Math lesson that is appropriate to the standard being taught. Learning becomes more meaningful when learners see what they're learning as being meaningful in their own lives. It is beneficial to students to try to consider the similarities and differences between the new and a recently completed problem. Effect size for compare and contrast new with old problems (1.23). Meta cognition Promotes Transfer Learning Meta cognition is the ability to think about our own thinking and meta cognitive strategies have an effect size of .69. Palincsar (2013) describes metacognitive awareness as consisting of three parts: 1. Knowing about out learning selves 2. An understanding of what the task demands and necessary strategies to complete it 3. The means to monitor learning and self-regulate Students need guidance in how to become more meta cognitively aware. Students need to learn how to self-question. Self-questioning is a meta cognitive strategy that allows us to track our understanding and catch ourselves when we are off target. Teachers can encourage meta cognition by administering pre-lesson and post-lesson questions. Pre-lesson questions are available on page 186 (figure 6.2). Other helpful tools are to develop a checklist of questions that encourage meta cognition and reinforce learning which can be used as writing prompts for journal entries. Self-Reflection allows learners to develop expertise and avoid repeating the same errors when solving similar problems. It helps students to understand where they were and where they are now page 188 (Figure 6.3). Chapter 7: Assessment, Feedback, Meeting The Needs of All Learners Formative evaluation is the process of gathering assessment evidence to inform instruction. The process has several key elements: Clarifying, sharing, and understanding learning intentions and criteria for success Effective classroom discussions, activities, and learning tasks that elicit evidence of learning Providing feedback that moves learning forward Activating learners as instructional resources for one another Activating learners as the owners of their own learning Feedback for teacher: Adjusting Instruction, daily formative evaluation is a chief way for teachers to make instructional decisions Feedback for student: Adjusting Learning, Feedback is designed to close the gap between students' current level of understanding or performance and the expected level of performance. Teachers need to know: Students's current level of performance, students' expected level of performance, and actions they can take to close the gap. Effective feedback needs to be timely, specific, understandable, and actionable and needs to direct attention to what;s next. Effect size for Feedback 0.75 Feedback Strategies pg. 204 (figure 7.3) There are four types of feedback. Feedback about the task, feedback about the process, self-regulatory feedback and feedback about self. Summative evaluation is when we use broader assessments with the purpose of determining what students know and are able to do at a given point in time. Meeting Individual Needs through Differentiation Differentiated instruction is the use of a variety of instructional approaches to modify content, process and or products in response to the learning readiness. A classroom that is structured for differentation has both a wide range of learning resources and a flexible classroom environment. Teachers can differentiate instruction by making adjustments in three areas, content, process and product. Adjusting Instruction to Differentiate: Our goal is to be sure that each learner is making progress mastering the grade level standards at an appropriate degree of challenge, the zone of proximal development. Intervention: Recommendations for Response to Intervention: pp. 216-223 Homework Effect Size: 0.29 Response to intervention Effect Size: 1.07 Matching Learning Styles with Instruction 0.17 and Test Prep .27 Conclusion Having access to Effect Sizes is an advantage so when we plan our instruction, we can choose strategies that have a greater possibility to be effective for our students. Summer reading list: http://robertkaplinsky.com/6-non-education-books-educators-read/ Must view Ted Talk: https://www.ted.com/talks/carol_dweck_the_power_of_believing_that_you_can_improve?language=km?utm_source=tedcomshare&utm_medium=referral&utm_campaign=tedspread Building a Culture of Success
BLOG POST PROMPT Based on the descriptions in Gruenert ch. 4, what type of school culture exists among all teachers at your school? Provide examples and make connections to the explanations in the text. (Be sure to authentically reflect on your school as a whole, and not a subculture.) Choose an instrument from the Gruenert text to use in order to gather data on school culture, and have at least three to five individuals at your school provide feedback using the instrument. (The more data, the better; the more diverse the individuals, the more authenitc the data is!) Building a Culture of Success The focus of this Blog Post Reflection is to identify the school culture that exists at our school site. In general, a successful school culture has to do with vision, unity and empowerment. The principal’s job is to build a vision for the school that encourages unity among the staff and gives the staff the freedom and encouragement necessary to empower them and together build a culture of success. While students come and go, the staff should continue to move the school in a positive direction by means of the established culture year after year. In order to determine that type of culture our school has I used the School Culture Typology Consensus worksheet developed by Gruenert and Valentine (2006). I surveyed our staff at our last staff meeting. I followed the survey with the Culture Typology Reflection Sheet giving the staff the chance to synthesize and to personalize the data collected. Column E, Column D, and Column F received the most points. After viewing the results and reading the comments, I have come to the conclusion that our school is currently demonstrating School Culture Type 2: Comfortable-Collaborative. I believe that this is in part because we have new leadership who brings in a new vision for our staff. In addition, our new leadership has shifted our method of instruction to the blended learning model in order to maintain the school’s viability. While the teachers are settling into our new roles at the school, there is still much for the staff to learn, including implementation of CIP practices. Our next challenge is one of crunching the numbers and creating some real goals for both our teachers and our students. Teachers in a comfortable-collaborative school culture don’t ask essential questions about their work and how to improve; they limit their conversations to sharing advices and tricks of the trade. (Gruenert, Whitaker, 2015). While we still have a way to go, our culture is much improved when compared to previous years. The motto of a comfortable-collaborative school could be, “We are all fighting the same battle, so we need to get along.” (Gruenert, Whitaker, 2015). This is a brief summary of the Culture Typology Reflection Sheets that were returned with the Surveys by the staff. All staff members agreed that we need more time to work on best practices and we need more opportunities to observe other teachers and schools. Also, we need collaborative long term and short term goal-setting. On a positive note, staff members commented that the staff share high academic expectations from our student body. We are also able to work together as a team, problem solve together and share professional development opportunities and experiences. We already have a positive school culture conductive to professional effectiveness, positive morale dedicated to student learning and success. What kind of Culture Do We Want? We want a collaborative culture at our school. In fact, I believe we are close to achieving this goal. For example, of the 5 surveys I distributed at Wednesday’s staff meeting, I was able to get 100% returned by Friday. I would attribute this to the dedication and willingness of the staff to create a culture of collaboration. While getting along is certainly an important step, we realize that our work is far from over and that there is more to accomplish. In order to move our school forward, we have to shift the mindset of our staff to more of a collaborative culture as described by (Gruenert, Whitaker, 2015). It is through the process of creating goals, both academic and professional, that we can move this school to the kind of culture we want, a culture of collaboration.
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