A Look at the Math Standards—Unfiltered

As I prepare for the classroom, I’ve asked trusted colleagues what math resources I should be looking over. Almost without exception, they direct me to the Progressions Documents for the Common Core State Standards. If you are unfamiliar with these, they are narratives that describe the progression of topics across grades. They help explain why the standards are sequenced the way they are and offer pedagogical strategies and solutions to challenging areas of mathematics.

Helpfully, working with the Kahn Academy, Common Core author Dr. Bill McCallum has shared a series of videos describing specific progressions. Dr. McCallum walks viewers through the standards with reference to research, examples of math problems associated with domains and clusters, and anecdotes about authoring the standards themselves. You can view the videos through the links below.

Common Core Introduction

CCSS Fractions Part I

CCSS Fractions Part II

CCSS Place Value

CCSS Multiply and Dividing Negative Numbers

CCSS Algebra Grade 8

CCSS Decimals

CCSS Statistics in Middle School

CCSS Negative Numbers

CCSS Exponents

CCSS Ratios and Proportions

CCSS Geometry

CCSS Expressions and Equations (Grades 5 trough 7)

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Presentation Before the Reno Lodge 13 – Free & Accepted Masons of Nevada

Reno Lodge 13 – Free & Accepted Masons of Nevada gathered for their monthly meeting which including a presentation on the Common Core State Standards. Dr. Amy Weber-Salgo and I reviewed the difference between standards, assessment and curriculum before reviewing the instructional shifts and the evidence that informed the creation of the Common Core. Moreover, Amy and I shared resources, developed by classroom teachers in Northern Nevada, that have been used to reach the expectations of the CCSS.

June 10th Presentation PowerPoint

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Ideas for the First Week of Math Instruction

“A great question for any teacher… is where to begin.” I remember David Coleman, one of the lead authors of the Common Core State Standards, saying this at a speech before educators in 2012. I find myself asking this same question as I prepare to teach math next academic year—especially those first few critical days of school in which I am trying to establish routines and procedures while simultaneously introducing content. Through serendipitous luck, or just smart enough to hang out with some really strong teachers**, I learned about Jo Boaler and her website www.youcubed.org.

Dr. Boaler helpfully outlines tasks for the first five days of math instruction that address the Common Core, the mathematical practices, growth mindset, persistence, and are highly differentiated because they are “low floor and high ceiling.” Each comes with the requisite materials (free), demonstration videos, and annotations so you know that what you are implementing is grounded in evidence. The table below describes what the first five days can look like.

Day 1 Inquiry task, the four 4’s. Number operations MP1: Make sense of problems and persevere in solving them. MP6: Attend to Precision.
Day 2 Looking at numbers to “see” factors and multiples Factors, multiples, prime numbers, number relationships, algebraic expressions and equations MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning
Day 3 Paper folding task Area, fractions, triangles, squares, and estimation MP3: Construct viable arguments and critique the reasoning of others and MP4 Model with mathematics
Day 4 World’s most famous triangle Patterns in number, triangular numbers, addition, powers MP1: Make sense of problems and persevere in solving them. MP7: Look for and make use of strcutre. MP8: Look for and express regularity in repeated reasoning
Day 5 Seeing Shapes Algebraic thinking, generalization, forming an algebraic expression, algebraic equivalence MP1: Make sense of problems and persevere in solving them MP2: Reason abstractly and quantitatively MP7: Look for and make use of structure

Dr. Boaler is a proponent of the Common Core and she outlines why through the video linked here. Moreover, she explains how practitioners can create a classroom where students have a “learning orientation towards math” and away from a “performance subject.” The video is worth a watch especially if you are struggling with ideas about how to make math more engaging for students.

**Thank you to Katie Penney and Janelle Turnier for introducing me to Jo Boaler and her website YouCubed.

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Back to the Classroom to Teach 4th Grade

For the last four years, I have been introducing myself as a Teacher On Special Assignment working for Washoe’s Curriculum & Instruction Department. That changes in a few weeks when the new academic year begins and I officially become one of the 4th grade teachers at Huffaker Elementary. It’s a move I am quite excited about but simultaneously, I will miss being able to direct most of my energy to the Core Task Project.

In 2011, my colleagues Torrey Palmer, Cathy Schmidt and I started the Core Task Project (CTP) as a means of accessing the K-6 ELA Common Core State Standards and answering the question, what does it mean to do Common Core. In 2011, there were no shortage of answers from national consultants encouraging teachers to deconstruct the standards, to states creating crosswalks and translation guides, to publishers doing alignment studies affirming the use of their programs. Interestingly, this council was hard to reconcile with what we were learning from the authors of the Common Core and its work and validation team members. Consequently, we brought 18 teachers together to help co-construct an answer to our question.

What was interesting about the work is that it put teachers at the center of our district’s Common Core implementation. Everything was effectively field-tested by practicing teachers and if a pedagogical move or instructional resource failed in a classroom, it was no longer used and promoted. Conversely, if it was successful, we would share these in future sessions of the Core Task Project and teachers would pass these on in staff meetings, grade level PLCs, or trainings they created. Moreover, because we were only using free resources, anyone could opt into the CTP, making the successful outcomes scalable.

Keeping teachers at the center of any district reform is challenging—doing it with Common Core is especially difficult. We have become deeply paternalistic in education; that is, we invite consultants to districts to tell teachers what to do or we send people to conferences with the expectation that they will become expert on something—and then tell teachers what to do. The CTP flipped the script and brought the conferences and research to teachers directly. In short, the CTP cut out the middleman. Instead of hearing from a conference attendee or consultant, we learned as a community and became the experts. We would watch video on YouTube and Vimeo (e.g. Dr. P. David Pearson, Dr. Dan Willingham, Dr. Freddy Hiebert, Dr. Louisa Moats, Dr. Tim Shanahan, and dozens of others), find resources well-matched to the learning, and then breath life into the aforementioned through Social Emotional Learning, engagement strategies, and evidence-based instructional moves. This was all taken through the Plan-Do-Study-Act cycle and classroom teachers were able to match academic theory with practice.

The basic construct of CTP, that states and districts would share the evidence that informed the Common Core in an “unfiltered” way, use vetted, scalable and free resources, and trust the expertise of teachers would seem to be quite intuitive. Instead, what I have discovered from educators throughout the country who have used the materials at www.coretaskproject.com and www.63000resources.com and have emailed with questions, is that this orientation to the work is the exception not the rule. Too often, interpretations of the Common Core are passed down to the classroom and teachers are expected to navigate myriad different (and sometimes contradictory) efforts. This should not be the case but with money returning to the system after a long recession, I suspect that districts will be inclined to return to the habit of sending people to conferences and hiring consultants rather than sharing information directly with those working with children on a day-to-day basis.

The Core Task Project is by no means over. This site will remain a place where training resources, annotated video, vetted materials, and teacher narratives are posted. Likewise, www.63000resources.com will continue to be maintained and resources added. In fact, classroom teachers are currently finding and creating items for the site and these will be posted throughout the summer. Moreover, I have created a new space for my classroom where you can view how I am taking the principles of the CTP into www.roomd4.com.

The last four years have been an extraordinary professional and personal experience. It is not often that your mom calls and says, “I just heard you on NPR!” I am thankful to the hundreds of educators who took part in the CTP and who reminded us that when teachers are equipped with great information, exceptional things happen in classrooms.

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Session 7 of Core Task implementation Project (The End)

The last session of the Core Task implementation Project concluded with a focus on writing and the instructional move, “Painted Essay.” The strategy, which fits well with Session 3 of CTiP and the In Common resources, gives practitioners a way to guide students through informative and argumentative writing. The session also included a chance to reflect on the instructional move “Questions, Reason, Example” and to review on an incredible year of learning. Some of that learning was captured through the following video filmed by Thomas Lay.

This year 200 educators attended the monthly CTiP meetings from 21 different schools. Their experiences helped inform the K-6 ELA implementation efforts and resulted in hundreds of students working with complex text, academic vocabulary, text-dependent questions, evidenced-based writing and content-rich nonfiction.

Session 7 PowerPoint

Painted Essay Directions and Examples

Teacher Reflection Form

Kahoot Link for CTiP Quiz (a little blended learning)

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My Running Diary of an Anita Archer Presentation—Part 2 (Writing)

Beginning at minute 5:52, Dr. Anita Archer frames her presentation on Providing Explicit Instruction on Writing Arguments by outlining her “principles.” They include 1) breaking down complex skills into obtainable skills; 2) providing explicit instruction that involves modeling and guided practice; 3) providing immediate, quality feedback; providing judicious practice; and carefully considering motivation. With respect to breaking down complex skills, Dr. Archer suggests first having students write the body of an argumentative essay before writing the introduction (minute 12:57). With the introduction written, students would go back to the body and then write a conclusion. Dr. Archer does qualify that this “breaking” down technique is more likely to be used with Tier 3 student then Tier 2 students; and more often with Tier 2 students then Tier 1. In other words, you may not have to or want to do this with all students.

At minute 18:45, Dr. Archer outlines the research supporting the use of feedback to promote good writing. She continues with an example in which students take only a small part of a rubric to engage in peer editing. In turn, all student are able to gain access to quality feedback instead of always waiting to hear something from a teacher. The key is “highly focused” peer feedback. The slide, linked here, outlines some of that research.

Dr. Archer addresses the issue of motivation at minute 30:02. It is Dr. Archer’s assertion that compared to reading, solving math equations, and speaking in class, writing is the most difficult to get kids motivated for. She continues that to get students motivated they need to a have a perceived probability of success, an interest in the topic, and “narrow” choice.

Minutes 35:00 through 44:50 focus on the use of rubrics. Dr. Archer draws from checklists and Trait Scoring during this time. Oddly, she suggests that student’s do “close readings” of rubrics, which hardly consistent with what close reading is.

Dr. Archer continues with several strategies to use with decontextualized prompts.

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Running Diary of an Anita Archer Presentation—Part 1

Anita Archer will be in Washoe County on May 15th to speak to our adminstrators and supervisors and then on May 16th to work with classroom teachers and instructional coaches. Many of us, however, will be unable to attend these events. The good news is that Dr. Archer is one of those rare educational consultants willing to have herself filmed and have her content posted to the Internet. Consequently, you can opt into Dr. Archer’s presentations, free of charge, including this one filmed by Utah State University.

The first part of the presentation focuses on handwriting. Archer makes a compelling case for why automaticity and fluency with forming letters and words leads to better writing. She stops short, however, of endorsing cursive instruction and sticks to the outcomes within the Common Core Reading and Language Standards. At minute 13:00, Archer outlines the research supporting the cognitive benefits of students being able to print their upper and lower case letters and at minute 23:13, Dr. Archer forwards two strategies for students who are disfluent writers. That is, she shares research that supports having student write frequently and having children practice “repeated writings.”

At minute 25:14, Dr. Archer transitions to spelling and shares the reciprocal nature between spelling and reading. At minute 30:55 she criticizes several common approaches to spelling practice including crosswords, word searches, writing words in sentences, and looking up words in dictionaries. What she suggests does work includes dictation, peer tutoring, and copy-cover-write-check. Dr. Archer puts theory into action by showing a lesson demonstration with 2nd graders (35:00). Following the demonstration, Dr. Archer lists the routine she used with the students—pictured below.

Archer Spelling Routine

Dr. Archer transitions to sentences at minute 45:02. Archer promotes the following instructional approaches to increase proficiency with this skill. This includes sentence expansion (minute 46:16), meaningful sentences (48:45) and sentence combing at 54:45.

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