Hello colleagues, It's great hearing from ELA coaches Jane, Rachel, and Meesha this week, and they'll be with us through Sunday 4/12/15, so don't hesitate to ask your questions of them. Thank you, ladies!
Beginning next Monday April13, 2015, we will be hosting our next week-long discussion "A Deep Dive: What’s behind the New Professional Development Materials for Mathematics CCR Standards?" Our discussion leaders will be national coaches Kaye Forgione and Fabio Milner.
Similar to this week's focus on ELA, the purpose for next week's discussion is to support administrators, professional development staff and all those who are implementing the math standards to:
- Learn how the activities embedded within the four professional development units lead to “light bulb” moments. For example, realizing the importance of text complexity or how to craft quality writing prompts.
- Discover how to organize or amend the delivery of the the professional development units or ideas to fit the particulars of a local context.
Please join the conversation to pose your questions and share your experiences thus far with implementing the math standards in your practice. We are fortunate to have access to these national experts and a forum where we can support one another as we move forward in this important work.
The math professional development units are available at the links below.
CCR Standards: The Instructional Advances in Mathematics, Units 1–4 http://lincs.ed.gov/professional-development/resource-collections/profile-778
Looking forward to diving deeply into math next week!
Cheers, Susan Finn Miller
Moderator, CCR Community of Practice
Many educators in the field that I work with see the new standards, or any increase in rigor or change in general, as a bad moon rising, because it could make it more difficult to credential the folks who are down on the corner. But I think change is a constant, so we need to keep rollin' on the river. Maybe I'm just a fortunate son, being that I've spent most of my career working at the state level in Virginia and now with a rapidly growing publisher that is solely focused on solving problems for adult education teachers and learners. The question I'd like to help with is, "How do we help educators get excited about what's coming up around the bend?"
I hope it's okay to share this teaser here. Essential Education has put together a great new FREE guidebook for educators called the College and Career Readiness Roadmap. We'll be giving it away at the COABE conference in Denver next week. If anyone wants a digital copy or a hard copy mailed to them, you can email me at firstname.lastname@example.org (be sure to let me know the name of your organization and the state you work in). The FREE 117 page resource helps teachers by identifying "key shifts" to new focuses and practices of CCR aligned instruction. If it's okay to share this here, I will follow up with an excerpt that highlights the three key shifts that we see taking place in mathematics. I personally received tremendous fanfare and gratitude when Essential Education gave out 800 copies of our 2014 GED Test Curriculum Blueprint at COABE in New Orleans in 2013 (and many more at local conferences ever since). Similarly, I believe that our new CCR Roadmap will boost the spirits of adult ed instructors who put in daily hard work in the classroom, but only as long as they can see the light. As I'm lookin out my back door, I realize that resources like the ones being shared here make me really proud, Mary (I mean, Susan).
Thanks, everyone, for all you do for adult learners.Jason Guard, MPA
Adult Education and Blended Learning Specialist at Essential Education
email@example.com Twitter: @jkguard
Even if I have to run through the jungle I'll be sure to visit your booth for my free copy of this resource.
Thanks for jumping on board my little 'cartoon before the movie' effort at levity, Dianna.
I will dial it back now and let the serious discussion unfold, since humor may not compute for many of the mathematicians on here. I was an English major, so it helps me, personally, to have a little fun during big changes, and Credence Clearwater Revival (CCR) were a fun band. Requests for copies are coming in via email as well as promises to visit at COABE. I'm glad to see that eyes are on this discussion thread. As promised, here are the 'three key shifts' excerpt from the mathematics section of our CCR Roadmap and also found in descriptions of the Common Core State Standards. Nonetheless, I think it's very relevant to this thread's topic, and hopefully will help with the task of making PD around the CCR Standards more approachable and accessible to trainers and instructors in the field. Keep in mind that these are very general introductory remarks that are built upon throughout the CCR Roadmap to help guide instructional strategies.
The three key shifts in mathematics instruction focus on understanding mathematical principles.
Students should understand mathematical thinking and apply mathematical ideas, not merely memorize
•• The first shift is focus. The CCR standards encourage math instruction that is narrower and
deeper. Time is always in short supply in adult ed classrooms. Focus on teaching the most
important math topics fully and well. Get at the foundational reasons behind these math
topics. Teach “why,” not just “how.” The CCR standards for math define priority topics to narrow
the focus of math instruction and build foundational math understanding.
•• The second shift is coherence. This means building new math on previous learning. Make
the connections between what you’re teaching and the foundational math. Higher level
standards build on the lower-level ones, so that a student is developing one idea over time
instead of constantly facing a new and unrelated math topic in the next lesson.
•• The third shift is rigor. The CCR standards for math ask students to understand key concepts,
master procedures, and apply math to real-world contexts. Understanding the conceptual
underpinnings of math and applying math to build strong knowledge.
Thanks, Jason, for the comments. And for the reference to one of the bands from my youth!
Many of us mathematicians do appreciate humor, and welcome it at any time.
The excerpt from the CCR Roadmap are very timely for this discussion forum, with the added spice of the Standards for Mathematical Practice that make a fourth (albeit officially unnumbered) key shift. And would suggest to add to Rigor the definition of the word, "scrupulous or inflexible accuracy or adherence:the logical rigor of mathematics." Students and teachers alike should never forget to check for correctness, accuracy and precision.
I just watched this video about Common Core based math instruction from one of the designers of the CCSS. It's probably made the rounds on LINCS already, but the disparity between teaching "answer getting" and actually understanding the mathematics really resonated with me. I think building relevance and real world application are ways to achieve this kind of deeper learning, but it really comes down to the intent of the teacher with their instruction. What are they setting out to accomplish? What problem are they trying to solve? The same goes for publisher products, which I believe sets Essential Education apart (but I digress).
It's a 17 minute video, but you can just watch the first 5mins to get the basic idea.
Hello everyone, You guessed correctly, Jason, that we've discussed the issue of answer getting and the Phil Daro math video you cited, which is well worth watching in its entirety. You can check out the discussion thread, which also highlighted several other resources related to "tuning mistakes into learning opportunities" here https://community.lincs.ed.gov/discussion/turning-mistakes-learning-opportunities
Cheers, Susan Finn Miller
Moderator, CCR CoP
I LOVE the CCR references - in fact, I hadn't even made the connection between the abbreviations' similarities! Your post was extremely creative and I applaud your efforts! I will definitely stop by and say hello at COABE! Illinois is one of 12 states selected by OCTAE to participate in the CCR/SIA alignment project, and I am honored to be on the state team. We have a great deal of work ahead of us, but I am excited at the opportunity we have to continue the work we have been doing to bring content-based educational reform to our adult ed programs and students. This really is an exciting time to be in adult ed!
You definitely made us smile, Jason! Looks like a helpful resource, too.
Moderator, CCR CoP
The delivery of the College and Career Readiness Standards for Adult Education has created quite a bit of anxiety and tension in the adult education world. This is very understandable because they point to significant changes necessary for a full and faithful implementation.
Thus arises the question of why are these standards and changes needed. The short answer is that whatever we were doing for the last however many years was not working well, because it left major gaps in many adult learners' preparation for successful transitions into college and careers. This by itself justifies the need for change. It does not address, however, the question of why we should change in the direction of the CCR Standards.
There are several reasons that make such change very desirable. More uniformity in expectations helps adults who receive their training or learning in one area of the state or the country to have similar training or learning as that expected in another area into which they might move. Mobility is becoming more prevalent and, arguably, makes this advantage more important today than in the past. However, in my humble view, it is because of the key shifts the CCR Mathematics Standards define so clearly that moving in their direction becomes highly desirable. The clear definitions of Focus, Coherence, and Rigor they include, together with the stress on Standards for Mathematical Practice, are enough to create curricula and programs that have a better chance of leading more adult learners to more success in more educational and employment endeavors.
The frequently maligned Standards for Mathematical Practice are really habits of mind that refer to higher-order thinking skills empowering individuals able to use them to present better arguments, to understand and criticize the logical flaws of statements and arguments presented by the media, politicians, friends, and others, to become better problem-solvers, to make good conjectures and generalizations, to express themselves more clearly and accurately. And note that I am not talking about mathematics, but rather in any arena. I think this constitutes a powerful argument in favor of the CCR Standards.
Professional Development Materials on CCR Math Standards
These training materials replicate four key activities designed to help participants learn what it means to implement the CCR Standards for Mathematics in adult education. The activities were created for adult educators who participated in three CCR Standards Implementation Institutes offered in 2014. The materials can be found here: http://lincs.ed.gov/programs/ccr/math
Participants receive and develop a practical, transferable understanding of the fundamental advances in instruction embedded in the CCR Standards, which are crucial to preparing adult students to meet the real-world demands of college and careers. At the heart of the instructional advances is a careful examination of the critical content and processes that fuel mastery in mathematics, including focusing on core concepts and skills, coherent progressions from level to level and pursuing conceptual understanding, procedural skill and fluency, and application with equal intensity.
- Unit 1, Focusing on the Major Work of the Levels, addresses the most critical concepts and skills that students must master to be prepared for college and careers.
- Unit 2, Thinking Across Levels to Connect Learning, concentrates on the concept of coherence and the central role it plays in the CCR Standards.
- Unit 3, Engaging the Three Components of Rigor, investigates what it means to create a rigorous mathematics curriculum.
- Unit 4, Connecting Standards for Mathematical Practice to Content, provides techniques to enrich instruction by integrating the eight Standards for Mathematical Practice with content-specific standards.
Each ready-to-use unit includes a facilitator’s guide, an annotated PowerPoint presentation, and participant materials.
This unit is designed to allow participants to investigate in depth Key Advance 1—focus—within the five adult education levels (A, B, C, D, and E) of the CCR Standards. Participants learn to identify topics that are and are not major topics for the various levels. During the hands-on activity for this unit, participants first read descriptions that summarize the major work of each CCR adult education level. These descriptions define the most critical concepts and skills for preparing students for college and careers.
Then participants review a set of lesson topics listed by level to determine which of the topics are likely to address the major work of that level. During this activity, small- and whole-group discussions are crucial to building clear and common understanding among participants of what constitutes the major work of each level.
The CCR Standards are by necessity more focused than K-12 standards because adult education programs do not have the "luxury" of 12-13 years during which to help adult learners to master the content. Thus arises the value of understanding Focus as an essential design component of the CCR Standards, and that is why it is one of the Key Advances in College and Career Readiness Standards. A deliberately focused set of standards that attends to content areas and specific topics that are core to applications and future studies, will position more adult learners better for success in both arenas of careers and higher education.
This unit is designed to allow participants to apply what they have learned from Unit 1, during which they explored the importance of focusing on the major work within a level. In this unit, participants think about linking key mathematical concepts across levels.
The activity provides participants an opportunity to closely read several CCR Standards for Mathematics and then think deeply about how the content progresses across the levels and reflects coherence through their sequencing.
Participants investigate three key progressions present in the CCR Standards: the first dedicated to building fluency with operations, the second dedicated to expressions and equations, and the third focused on real-life applications. Standards within each of the three progressions are provided to participants on like-colored cards. Participants are first asked to identify which progression (i.e., fluency with operations, expressions and equations, and real-life applications) aligns with each of the three color-coded sets of cards. Then they organize the cards within each color group by level, from Level A through Level E. By carefully building the learning trajectory within and across levels, participants learn how the CCR Standards support students’ new understandings based on previously learned concepts and skills.
The importance of coherence in the curriculum cannot be stressed enough; without it the curriculum may become unappealing, confusing, disconnected. Its lack would likely dissuade many learners from making a bigger effort and, ultimately, from learning.
Thanks to Fabio for posting such helpful descriptors for the Math PD materials--and most particularly for Unit 1 on Major Work of the Level/Focus and Thinking Across Levels to Connect Learning/Coherence. I will be jumping into the discussion today to address any questions or comments that might arise, particularly with respect to the Unit 1 and Unit 2 materials. Tomorrow and Friday, we plan to focus on the remaining math professional development units.
Professional development on the College and Career Readiness Standards is so very important, and we hope that these online professional development materials prove to be helpful to all of you. Have any of you used all or parts of the materials? If so, how did it go? Do some of you see ways in which the materials will be useful with your teachers? Do you have ideas on how you might employ them?
This unit will allow participants to investigate the three components of rigor. It will teach participants how to recognize each component of rigor from the language of the standards, and how to make important connections among these components in instruction.
Participants will search selected CCR Standards for clues concerning which of the components of rigor seem to be expected. For example, at various levels, specific content standards use the word “fluently,” which means “quickly and accurately.” These refer to procedural skill and fluency. If a standard requires that students know a definition or use a memorized procedure, then again the targeted standard is procedural skill and not conceptual understanding.
However, if a standard requires explanations, analogies, comparisons, contrasts, or interpretations, it is aimed at assessing conceptual understanding.
Several standards refer explicitly to real-world problems, but there are also examples of purely mathematical applications. For example, after learning to rewrite polynomial expressions by combining like terms (a procedural skill), a student may be asked to apply that skill to finding the factors of a quadratic expression by splitting the linear term into two like terms and then finding the common factor for each pair. Application, as a component of rigor in the CCR Standards, is more than simply solving a verbal problem. In this sense, applications might be contextual (real-world), or purely mathematical.
The goal for participants is to discern the full meaning of each standard. Understanding the demands of a standard will allow them to confirm that the requirements of the standard have been met.
Some common misconceptions about rigor also will be addressed. They include the belief that:
- “Rigor” means the required mathematical technique must be complex, as opposed to requiring complex thinking;
- “Real-world” means “everyday,” as opposed to “connected to problems presented in contexts that might, or might not, be academic”; and
- “Rigorous” means “difficult.”
During the activity, small- and large-group discussions will help participants gain a clear and shared understanding of the three components of rigor and what it means to engage each of the three components with equal intensity.
Thanks, Jason, for posting the link to the video done by Phil Daro. I just watched it, and the points Phil makes are very applicable for adult educators and adult learners alike. As teachers of mathematics, it should be our goal to help students acquire math knowledge, not just get the right answers. So Phil is making some good points with respect to rigor, which is the key advance we are focusing on today. Phil emphasizes the point that simply teaching students procedures to solve problems is not sufficient. He points out how important it is for students to have a conceptual understanding of the mathematics they are learning so they can apply it later to problems in a meaningful way. Phil sees answers, both wrong and right, as key to generating math knowledge---and emphasizes that in the math classroom answers should not be the end product but rather part of the process. While answer getting is important for all learners, it should not be our instructional focus. Rather, teachers should help students learn the mathematics which they, in turn, can then apply to solve a problem.
The last unit in our online training package addresses the CCR's Standards for Mathematical Practice. The unit is designed to help teachers understand the Standards for Mathematical Practice and how they can be effectively connected to mathematics content in the lessons they use with adult learners. Below is a summary of the unit:
Unit 4: Connecting Standards for Mathematical Practice to Content
To begin, participants will independently conduct a close read of the Standards for Mathematical Practice and highlight keywords and phrases. This will allow participants who are not familiar with the Standards for Mathematical Practice to get a better grasp of what they are. It also will provide participants who are familiar with the Standards for Mathematical Practice an opportunity to reacquaint themselves with their substance.
The first part of this unit (Matching the Standards for Mathematical Practice to Content Standards) asks participants to read and analyze the requirements of a Level B CCR Standard, and imagine a lesson that might target that standard. Then, participants will determine which Standards for Mathematical Practice would be central to that lesson and which might be used in a supporting role. Participants also will be asked to identify which Standards for Mathematical Practice are not relevant to the imagined lesson or the standard it targets. All three observations are important in understanding how to connect the Standards for Mathematical Practice to mathematical content.
Part Two of this unit (Enriching a Mathematics Lesson) will ask participants to read and analyze a sample lesson and look for opportunities for students to engage the specific Standards for Mathematical Practice. Participants will look for those Standards for Mathematical Practice that are central to the lesson, those Standards for Mathematical Practice that support the Standards for Mathematical Practice central to the lesson, and those that are not relevant to the lesson.