If you don’t know the answer, leave it blank.

If you don’t know the answer, leave it blank.
Please find and fill out your FAL pre-assessment. If you don’t know the answer, leave it blank. 2:15-2:30 James gives directions.

Let’s get started…

Sir Ken Robinson: Teachers as Gardeners
2:30-2:34 Turtle - What’s the takeaway here? A teacher cannot create learning, any more than a gardener can create a plant. Teachers can only provide the conditions in which learning can take place.

Why FAL? Georgia Department of Education
Twitter Hashtag: #GACISMath Why FAL? Georgia Department of Education Curriculum and Instruction Mathematics Team Brooke Kline, Lead Program Specialist James Pratt, Secondary Mathematics Specialist Turtle Toms, Elementary Mathematics Specialist Brooke- 2:34-2:36 Welcome, intro, why are we here? We want you to leave being able to answer the essential questions, “Why Should Our Teachers be Using Formative Assessment Lessons?”

Basic facts come before deep learning.
True or False? Basic facts come before deep learning. Rigorous education means teacher lecture. Covering a topic means it has been taught. Brooke- 2:36- 2:40 Let’s start by taking a look at a few statements about education and learning. As we look at the next 4 slides, discuss with your neighbors whether you believe these statements to be true or false.

Acceleration creates a more rigorous class.
True or False? Teaching to student interests entails a compromise of teacher standards. Acceleration creates a more rigorous class. Brooke- 2:36- 2:40

A quiet classroom signifies good learning.
True or False? A quiet classroom signifies good learning. Traditional schooling prepares students for life. Brooke- 2:36- 2:40

True or False? Formative assessment is a special kind of test, or series of tests that teachers learn to use to find out what their students know. Formative assessment is a program that districts adopt and teachers add to what they already do. Any practice that gathers information for the purpose of improving programs or improving teaching is a part of formative assessment. Brooke- 2:36- 2:40

Keep your pre-assessment near, and use it for note-taking, if you wish.
Brooke- 2:40- just a reminder.

2011-2012- Cohort 1: Six districts piloted FALs
Cohort 2: 52 districts training in FALs 60 FALs currently aligned to CCGPS (MS & HS) Some frameworks now have FALs embedded James: 2:40- 2:42 Who is using FALs in Georgia? Who is providing the training? Info about Vicki, Ann Shannon & cohort one Info about Vicki/RESAs & cohort two

The use of FAL by districts is growing. Why?
Formative Assessment Lessons (FAL) are currently in use in several districts. The use of FAL by districts is growing. Why? Turtle: Let’s listen to what an involved participant in Cohort one has to say. Any volunteers?

Turtle- 2:43-2:47 Who has an elevator speech they’d be willing to share about FALs? 2 minutes, tops.

Turtle: 2:47-2:48 So, let’s think about what we know about brain research, and what Sir Ken Robinson had to say about teachers as gardeners. How can we create conditions under which student understanding is optimized, and teachers can provide optimal conditions for growth? Here’s what the research says about our brains. Interesting, and obvious once you think about it. Problem solving developed as a survival mechanism.

Convince a bored 15 year old that math is vital to her survival.
2:49 Turtle - We certainly know what doesn’t work when it comes to effective mathematics teaching and learning… Because what doesn’t work hasn’t worked for decades. We’ve been guilty of much of the following for years, with lip service paid to actually changing practice to reflect current research.

Bad Math? Imitative Turtle - Monkey see, monkey do. Teacher shows you, you practice. This is the layout of many traditional lessons. Makes for surface recall at best, with no understanding of why this process works, so no transferability to novel situations or variations on a theme. Leads to inflexible application.

Bad Math? Passive/receptive
Turtle - Spoon feeding- Teacher breaks everything down into steps/processes/tricks so students can do the math without necessarily understanding how it works. Invert and multiply anyone? Learning a traditional algorithm means learning not only how to execute it with several examples, but also being able to explain its mathematical significance and prove that its various steps produce a correct answer. Understanding algorithms is also central to developing computational fluency. Being able to compute fluently includes making smart choices about which tools to use and when. The subtraction algorithm works for determining change amounts- Let’s say you have a tab of 3.98, and you have a 5 dollar bill to pay with. How much change will you get back? You can stack it up, and borrow, which is exactly what rote learners do, or you can think, $3.98 is two cents away from $4.00, so $1.02. Easy peasy. Now if I have to talk about this, all the better, because I’m learning how others might solve the same problem.

Minimal student explanations, comparisons
Bad Math? Minimal student explanations, comparisons Turtle - Teachers do all the work, explaining beautifully, while students sit passively during the lecture, with no guarantee of understanding. As a matter of fact, often the only measure of understanding is a multiple choice test at the end of a series of lessons on a topic. Gee, I hope its my lucky day! Let’s remember, learning is not a passive activity. Students learn about mathematical topics best through solving meaningful, contextual problems, and through collaborative mathematical discussions.

Turtle - Brains work better when they are actively engaged
Turtle - Brains work better when they are actively engaged. Aren’t we in the business of growing brains? If you hear a bit of info- 3 days later you’ll remember 10% If you are engaged visually and emotionally during learning- what you recall jumps to 65%

? Turtle - Do we really want to put all of our eggs in the wrong basket?

What am I supposed to do? Turtle - Let’s look at some moves that must be made- a research-based techniques for mathematics learning and teaching. Much more engaging for teachers and students!

Passive Active Turtle - FALs create the conditions for a shift from passive to active learning.

Transmission Challenging
Turtle - And from a transmission view of teaching to a challenging view of learning. Transmission- I do, we do, you do. Challenging- Opening with a problematic mathematical situation which creates cognitive distress and reveals misconceptions, followed by students and teachers making sense of the math together, and ending with a plenary discussion which pulls the mathematical ideas together and coherently articulates them. Add an ungraded pre and post test and you’ve got a FAL. You’ve also got one of the most effective teaching methods known, which has been used to great effect internationally.

Post-Assessment Pre-Assessment Collaborative Task Misconceptions
Understandings Pre-Assessment Feedback Discussion Explanations Collaborative Task Improvement Deeper Understanding Post-Assessment Brooke- So- what is the structure of a FAL? This is the FAL structure. Part one is the pre assessment. In a way, you’ve already experienced part one. You took a pre-assessment about FALs. In the normal FAL setting, as teachers, we would take your pre-assessments, look them over, and have our fingers on the pulse of your understanding and misunderstanding. In a perfect world, you would have taken this assessment yesterday, ed your responses, and we would have stayed up all night compiling the data. Due to our setting today, and the fact that we didn’t know in advance who might decide to show up, we are engaging in bad practice, and blindly forging ahead. The next part of the FAL is the collaborative task. During this learning task, instruction occurs in a way that may seem unfamiliar. Students are immersed in a problematic mathematical situation, and must collaboratively make sense of it, instead of the teacher explaining how to do the math. This part of the task is rich with discussion, feedback, and explanation on the part of students and teachers. Finally, the students take a post assessment. The post assessment is the same one that they took at the beginning. Now students have a much better understanding of the math, and teachers have a much better understanding of the students. Learning moves forward on a solid footing. What I’ve doing here is framing the FAL. You, as students, now know the structure of what you are about to experience. In other words, you have an idea of the big picture. Teachers do this with students before every FAL. Let’s continue with a real mathematics FAL now, so you can see how it feels to FAL…

Let’s do a little math… James

James- This is your preassessment
James- This is your preassessment. A teacher would use the pre-assessment to determine misconceptions students might have about probability. Here are your directions- Read through each statement and make sure you understand it. Try to answer each question as carefully as you can. Show all your work so that we can understand your reasoning. You shouldn’t worry too much if you don’t understand or can’t do everything, because in the next lesson you will engage in a similar task which should help. By the end of the next lesson, you should be able to answer questions such as these confidently. That is the goal of this lesson. (again, I’m framing the FAL for the students) Work on this independently. Once you are done, we will work on a probability task in collaborative groups. We are starting the timer now.

Five Minutes

Four Minutes

Three Minutes

Two Minutes

One Minute

TIMES UP!!

Understandings Pre-Assessment Feedback Discussion Explanations Collaborative Task Improvement Deeper Understanding Post-Assessment Turtle - You’ve just done the pre-assessment. This would occur after some learning has already taken place about probability. The teacher gives the pre-assessment in order to find out what you know, what you don’t know, and where misconceptions might lie.

Turtle- Remember, in the FAL setting, we would have looked at the pre-assessment, which is not graded, by the way (an interesting point, and worth an entire session on its own), and would have prepared feedback questions for use during this task based on their observations of student responses. Student difficulties would be summarized in a series of questions. Due to the constraints of this venue, we will be using pre-prepared feedback questions when you work on the task. These are the suggested questions provided with this FAL. Why no scoring- in a nutshell: research shows this will be counterproductive, as it will encourage students to compare their scores, and will distract their attention from what they can do to improve their mathematics. We want students to realize that the outcome or goal of school is getting smarter, not getting grades.

Put your meta-goggles on…
Turtle- Meta-goggles. When we ask you to put on your meta-goggles, we want you to think about what you are thinking and experiencing while engaged in the problem-solving task. These are two elements, effective questioning and cooperative small groups, associated with growth in student understanding and engagement. We want you to think about whether or not FALs encourage and allow for teacher inclusion of these elements while you engage in the problem solving task. Effective questioning? Cooperative small groups?

James- Your task is to decide if the statement is true
James- Your task is to decide if the statement is true. Once you have made a decision you will need to be able to convince me, so work together to convince each other.

5 minutes

4 minutes

3 minutes

2 minutes

1 minute left.

30 seconds

Is everyone ready?

James- Let’s connect some dots- What did you decide
James- Let’s connect some dots- What did you decide? Do you agree or disagree? Can you explain your answer? Can you think of a simple experiment that could simulate the statement? This task highlights the simple misconception that students often think the results of random selection are dependent on numbers rather than ratios.

Understandings Pre-Assessment Feedback Discussion Explanations Collaborative Task Improvement Deeper Understanding Post-Assessment Turtle- You’ve just completed the introductory part of the collaborative task . You are encouraging discussion and allowing students the luxury of thinking without pressure. Pressure inhibits mathematics. Faster isn’t necessarily smarter. Sharing of explanations and discussion of explanations allows for multiple solution paths, clarification of erroneous thinking, emotional engagement, visual demonstrations, flexible application of previous understanding.

Turtle- New set of lenses in our goggles. This time, let’s look for these as we engage in the next portion of the FAL. Building on prior knowledge? Exposing and discussing misconceptions?

James- Bring your timer, James. Use a manual timer for this- 5 minutes

Understandings Pre-Assessment Feedback Discussion Explanations Collaborative Task Improvement Deeper Understanding Post-Assessment Turtle - The section of the FAL you just experienced is a continuation of the task. During this collaborative activity, students are expected to make sense of the math, be able to explain their reasoning, and defend their thinking. We are also beginning to solidify some mathematical truths, and determine efficient processes. (all within the context of the mathematical task at hand). And, again, suggested questions to provoke cognitive dissonance are provided in the FAL.

Turtle- New lenses- watch and think about this. Methods vs. answer-getting? Connections? Collaboration?

UK teacher and students discuss this FAL

Understandings Pre-Assessment Feedback Discussion Explanations Collaborative Task Improvement Deeper Understanding Post-Assessment Turtle- So now you’ve gone through most of a FAL, in a very cursory fashion. You’ve done the pre-assessment, you’ve participated in a whole class discussion and a collaborative task designed to unearth and create cognitive dissonance around misconceptions. You’ve seen a bit of a plenary discussion where student understanding is consolidated. Now, as a student, you would retake your pre-assessment. This would complete the cycle, and allow you to see what you’ve learned, how you’ve gotten smarter. As a teacher, this informs you of the same: student growth. So, let’s do a post assessment- but instead of the one associated with this FAL, we are going to revisit our T/F about education and learning.

Brooke- let’s revisit our T/F questions
Brooke- let’s revisit our T/F questions. Let’s talk about each statement, and discuss some possible misconceptions.

Basic facts come before deep learning.
True or False? Basic facts come before deep learning. Rigorous education means teacher lecture. Covering a topic means it has been taught. Basic facts come before deep learning . This one translates roughly as, “Students must do the boring stuff before they can do the interesting stuff.” Or, “Students must memorize before they can be allowed to think.” In truth, students are most likely to achieve long-term mastery of basic facts in the context of engaging, student-directed learning. There are 42 notes in “Twinkle, Twinkle, Little Star,” and most readers will be able to recite them from memory, in order. Assuming eight possibilities for each note, that’s quite a feat. Perhaps more remarkable is the fact that ten years from now, everyone will still be able to recall the 42 notes without any study. The music provides a mental framework for remembering and the notes form a meaningful whole. Suppose people studied the notes without the music – as disconnected bits of information. Some people would remember more than others, but no one would recall the notes for long. The key to long term mastery is a context in which facts become part of a web of meaning that the brain constructs. Rigorous education means a teacher talking . Young people must figure things out on their own. In the same way a parent can’t make children see things from their perspective, a teacher can’t make a student see a connection between, say, multiplication and algebraic thinking. In order to do so, the student’s brain must literally rewire itself to create new pathways between its neurons. If the student’s brain creates knowledge, it follows that the more learners can control the learning, the more connections they can make. Teachers have knowledge to impart, but durable learning is more likely when students talk, create, and integrate knowledge into meaningful projects. The art of a teacher is to construct ways for students to discover. Covering it means teaching it . Teachers are often seduced by the idea that if they talk about a concept in class, they have taught it. At best, students get tentative ideas that will be quickly forgotten if not reinforced by a student-centered activity.

Teaching to student interests means a compromise of teacher standards.
True or False? Teaching to student interests means a compromise of teacher standards. Acceleration creates a more rigorous class. Teaching to student interests means dumbing it down. Every student brings preconceptions to the classroom. That’s another way of saying that the synapses and neurons of every student’s brain are in a particular configuration. For learning to occur, the student’s brain must build on what is already there, and the best learning occurs when teachers and students can share control in a way that meets the teacher’s objectives while matching the students’ frame of reference. Teachers who make their classes relevant to student interests are not “dumbing it down” or compromising their standards; they are conforming to a biological reality. If we could somehow see inside a student’s brain, its circuitry would correspond to its knowledge. Since new learning always builds on what is already in the brain, teachers must relate classroom teaching to what students already know. Teachers who fail to do so, whether due to ignorance or in pursuit of a false idea of rigor, are running afoul of that biological reality. Acceleration increases rigor . Some schools accelerate their strong students so that they can cover more material. Successful programs are more likely to ask such students to delve deeper into important topics. Deep knowledge lays a stronger foundation for later learning.

A quiet classroom means good learning.
True or False? A quiet classroom means good learning. Traditional schooling prepares students for life . A quiet classroom means good learning . Students sitting quietly may simply be zoned out -- if not immediately, then within 15 minutes. A loud classroom, with proper parameters for discussion in place, includes the voices of many students who are actively engaged. Traditional schooling prepares students for life. The best learning takes place in a context in which the learner needs the knowledge in order to do something useful or interesting. Learning is more likely to stick if students are able to apply what they have learned in new contexts. A culminating project is often superior to a final exam, or a standardized test, because it requires an additional reorganizing of information in the mind of the student as he or she creates something new. Studying for a test merely rehashes what has already been learned. In the words of a student, “I’ve constantly got all the things I’ve learned on projects in the back of my head. If I’m memorizing for a test, I forget it a week later.” Listening to teachers and studying for tests has little to do with life in the world of work. People in the work world create, manage, evaluate, communicate, and collaborate.

True or False? Formative assessment is a special kind of test, or series of tests that teachers learn to use to find out what their students know. Formative assessment is a program that districts adopt and teachers add to what they already do. Any practice that gathers information for the purpose of improving programs or improving teaching is a part of formative assessment. Bullet 1- Formative assessment is not a test item, a test, or a series of tests. Formative assessment is an intentional learning process teachers engage in with their students to gather information during the learning process to improve achievement Formative assessment is a learning partnership that involves teachers and their students taking stock of where they are in relation to their learning goals. Bullet 2- Formative assessment is not a prepackaged program or set of techniques that teachers adopt and enact. Formative assessment is a philosophy of teaching and learning in which the purpose of assessing is to inform learning, not merely to audit it. The formative assessment process is a fundamental reframing of the work teachers and students do day to day and minute by minute in the classroom. Bullet 3- To be considered part of the formative assessment process, information gathered must be used to inform the learning of current students. Although the quality of teaching rises as a result of formative assessment, the intended outcome must be to raise the learning and achievement of the students currently in the classroom on the concepts, processes, and skills that formed the basis for the assessment.

Brooke- so, would you like to retake your assessment now
Brooke- so, would you like to retake your assessment now? Any changes you’d make to your original answers? Have you grown in your understanding of formative assessment?

Ask yourself, ask your colleagues…
James- Anything? Anyone? How do you support this change?

James- Choose up to 3 participants to share questions, and or observations.

Feel like this? We’ve got resources to help you go from pushing to…

Feel like this! Taking in the scenery from a whole new perspective.
For starters, there’s a session on FALs this Friday, facilitated by Vicki Mixon, our trainer, and Melissa Stewart, a cohort one convert. Attend, enjoy, learn. Also, we will post this session on GSO, so that you may access these slides, and the resources listed on the last slides of this presentation. So, to sum up this portion of our presentation:

“ It ain’t what people don’t know that hurts them.
It’s what they do know that ain’t so.” Will Rogers This concludes the FAL segment of this presentation. Now Brooke Kline, Lead Mathematics Specialist, will share updates about the Georgia Mathematics Program. Prepare to be riveted.

A Review of Georgia’s Mathematics Program
Our other objective for today’s session is to provide you with a extremely condensed version of the message we delivered this summer to teachers at the GCTM academies which were held at 8 at locations across the state. This is a message we are from the authors of the common core. We want you to be aware of this message that was delivered and we are also asking for your help in delivering this message to all teachers across the state as we realize not all teachers were able to attend the summer academies. We will continue to piece in this message in our unit-by-unit webinars, but we also understand that we are not reaching all teachers via the webinar…so your help will be greatly appreciated. Vital shifts in Content Delivery…A couple of things that are important to point out In mathematics, content is content, and certainly in CCGPS some of that content may have shifted from one grade level to another For example, MAD was a high school topic in GPS, but is now addressed in 6th grade in CCGPS Clearly it has not changed mathematically, but the way that we deliver it to our students has changed… And that was one of the main points of focus in our summer presentations…how we can address the shifts in content delivery… I would also like to point out or bring to your attention a more personal view that I have been able to develop over the last couple of years from my work with CCSS… As a new teacher many years ago, I was very content focused…probably solely focused on content As I matured as a teacher, I began to realize that all of this content I was solely focused on, was not doing my students a lot of good if they could not apply it or transfer it to novel situations…or situations that had real world implications. What I realized is that my students needed to be able to “think”… (that is what I called it)… In other words, the content did not do them much good if not learned in the context of the practice standards And this is what I feel is at the heart of the common core standards…Use the content to practice with the Standards for Mathematical Practice Now, I understand the importance of students success on assessments, but I really feel the key to success on any assessment is the development of the practice standards Will they be successful if they have memorized the formula to the area of a trapezoid…possibly. Will they be successful if they have to make sense and persevere, attend to precision, reason abstractly and quantitatively, construct viable arguments, critique the reasoning of others, model with mathematics, use appropriate tools strategically, look for and make sense of structure, and look for and express regularity in repeated reasoning…I think so…that’s the one I am backing Because if my students have not memorized the formula for the area of trapezoid, I feel very confident they will be able to figure it out if they have developed the ability to think required by the practice standards. A Review of Georgia’s Mathematics Program 2012 GACIS Conference September 26, 2012 CCGPS: Vital Shifts in Content Delivery Brooke Kline Lead Program Specialist for Mathematics

8th grade – solving simple systems of equations
One thing you may have noticed about the mathematics CCGPS, is that the word “fluency” or the expectations of fluency are prevalent. Fluencies are frequent and often explicit in K-6, and although not mentioned in 7-12, fluencies are expected in all grade levels Quick examples – 7th grade expected fluency in solving simple linear equations 8th grade – solving simple systems of equations HS – algebraic manipulation & seeing mathematics as a tool to model real-world situations So, I would like for you to take a look at this activity on the slide dealing with multiples of 9…(explain activity ) Now I want you to answer this question – What does fluency mean to you? In your folder, you will find an index card. Please take that out and write down your definition of fluency. And I also want you to write down whether you feel this activity is getting at fluency…and explain why you feel it is or is not. Going to give you a minute to do so. (After a minute) Fold your index card and put it aside for right now. 9/17/2018

Focus Coherence Fluency Deep Understanding Applications Balanced Approach
If you were able to join us this past spring in our GPB sessions which dealt with the content standards and the shifts in content, you will remember that we introduced you to six lenses (F, C, F, DU, A, & BA) which were articulated by the authors of the CCSS in order to provide a framework to address the necessary changes in instruction demanded by the CC. The first two encompassing the major design principles of CCSS …but since then, the authors realized that this list was a little cumbersome and chose to compress …

Focus Coherence Fluency Deep Understanding Applications Balanced Approach
…Fluency, Deep Understanding, Applications, and Balanced Approach. When talking about one of these 4, we often referenced the other 3 in it’s definition or explanation. For instance when we talked about fluency in our GPB session, we stated, “fluency, which is not just about being quick and rattling off an algorithm, but it is about teachers and students having a deep understanding which allows both to be flexible in their thinking (balanced approach), and to decide which methods and strategies would be most efficient and appropriate (Application)”

Focus Coherence Rigor So the authors have compressed those four lenses (F, DU, A, & BA) into the one lens of rigor. Therefore, we now have three lenses which provide a framework through which to address the necessary changes in instruction demanded by the Common Core.

Focus Focus: Remember the mathematics big picture and focus on areas where there is a lot of return for the time invested. The first lens being focus (state the general definition) In the summer sessions we asked teachers to define focus and discuss in small groups what it means to them. We then provided “Focus Reminders”…these were the messages from the authors of the core or other experts…and we again asked for teachers to discuss and share their thoughts in regards to these reminders. In your packet/folder, you will find a document titled “Vital shifts in Content Delivery- key points”. Included in this document are the focus reminders that we are not going to discuss today, but were presented and discussed with the teachers this summer We ask that you take the time to read over these key points in the near future so you are familiar with these focus reminders.

In the spirit of focus, we also shared some support materials available to us from the authors of the CC which can be found on the achievethecore website. They have outlined the clusters at each grade level and from my understanding, are still currently working on high school course cluster delineation. Not all of the content in a given grade is emphasized equally in the standards. Some clusters require greater emphasis, or focus, than the others based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. In addition, an intense focus on the most critical material at each grade allows depth in learning, which is carried out through the Standards for Mathematical Practice. This table identifies the Major Clusters, Additional Clusters, and Supporting Clusters for this grade. So, my first thought is are these three categories creating power standards? Major clusters are not to be confused with power standards which often create an exclusive curriculum in which other standards are often neglected, or not taught at all, and this can leave gaps in student skill and understanding creating negative consequences on learning progressions. Good way to think of it…major clusters are like the posts on a fence Posts are very important to that fence, but we still need the rails of the fence for it to be considered a fence, otherwise it would just be a bunch of posts in the ground that are not connected! The additional and supporting clusters can not be ignored as they are the rails of the fence…they connect the major clusters. In summary, to say that some things have greater emphasis is not to say that anything in the standards can safely be neglected in instruction. 9/17/2018

The next lens is that of coherence (state the general definition)
In the summer GCTM session, we did the same with coherence as we did with focus in that we asked teachers to define, share and discuss their thoughts in regards to coherence. On the key points document, you will also find the “Coherence Reminders”, which we are not going to discuss today, but were presented and discussed with the teachers this summer. We again ask that you take the time to read over these key points in the near future so you are familiar with these coherence reminders. Coherence Coherence: Think across grades and link to major topics within grades

Standards for Mathematical Practice
During on discussion about coherence and the coherence reminders, we asked the teachers to the think about the critical learning progression of fractions We had them take out their standards and construct this progression from K-12…to think about and see the coherence of this progression that is so critical and crucial for students as they progress to Algebra I think you already know how I feel about these practices from my opening… This set of practices engenders an attitude that creates a mathematical character that accompanies a student from K-rest of life…a way to think about mathematics… They assist in developing a mathematical mindset…it is an approach to problem solving It is how our students develop their mathematical characters which can be used for the rest of their life (even when they think they are not engaging in math…but actually are!) Let’s refer back to what you just you just experienced in the FAL Did you apply some of these practices as you worked your way through the FAL? Do you apply these practices in many of the things you do each day in non-mathy situations? My guess is that you use them quite often in your daily professional and personal life. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others Reasoning and explaining 4. Model with mathematics. 5. Use appropriate tools strategically. Make sense of problems and persevere in solving them. 6. Attend to precision. Modeling and using tools 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Seeing structure and generalizing (McCallum, 2011)

Rigor The next lens is that of rigor (state the general definition) Remembering that this consists of fluency, deep understanding, application, and a balance approach. In the summer GCTM session, we did the same with rigor as we did with focus & coherence in that we asked teachers to define, share and discuss their thoughts in regards to rigor. On the key points document, you will also find the “Rigor Reminders”, which we are not going to discuss today, but were presented and discussed with the teachers this summer. We again ask that you take the time to read over these key points in the near future so you are familiar with these rigor reminders. Rigor: Require solid conceptual understanding, fluency, and application

Has your definition of fluency changed?
Let’s revisit fluency through these three lenses …Take out your note card Has your definition of fluency changed? Is this fluency when you look through the three lenses? Is there coherence, is there focus, and is there rigor? If your definition needs changing, how would you change it? Turn to your elbow partner and discuss We could probably talk about this all day…many opinions, many factors…what has happened prior…hard to tell just from this activity Therefore, we won’t tell you whether this meets a definition of fluency…the answer is completely dependent upon the context, just like mathematics…certainly gives you something to think about! 9/17/2018

What Now? Say YES to: Say NO to: Teaching CCGPS
So…What Now? The plates of teachers are extremely full! The authors of the Core are suggesting things for us to say yes to or to add on to that plate, therefore we have to create balance by removing things from the plate, so we have created a list of things to say no to to keep things in balance. Please read this list of yeses and nos. These are the suggestions we have provided to the teachers in order to keep their plate balanced. Do they make sense to you? Do you have questions? (1st bullet) This means know and teach CCGPS. Don’t go back and try to make what you used to do fit these new standards. There was a 90% alignment, but it is not a perfect match, we can’t rely on crosswalks. (2nd bullet) Planning like Goldilocks- Strands are generally too big, standards are too small and fragmented, and units which address clusters of related standards are just the right size. It’s not about which standard you are teaching today, rather, what standards are students mastering in this unit. (3rd bullet) We have traditionally been focused on answer getting in the US. Unfortunately, a right answer is not necessarily a reliable indicator of mathematical understanding. Correct responses are essential, but as a part of the process, not the product. (Daro) A student can give a right answer, but have huge misunderstandings about mathematics. Wrong answers, and particularly, their accompanying explanations, should serve as canaries in the mathematical mine. They indicate where misunderstandings lie, possibly held by many students. (4th bullet) Consistent use of terminology and understanding of that terminology across the grades, makes life easier for everyone…students, teachers, and parents! Doing so ensures less to learn along the way, and nothing to undo as students progress through the standards. What Now? Say YES to: Say NO to: Teaching CCGPS Planning like Goldilocks Embracing ‘answer getting’ as simply part of the process Consistent terminology Retrofitting/Crosswalks Teaching standard by standard Focusing on only getting the correct answer Inconsistent terminology

What Now? Say YES to: Say NO to:
(5th bullet) Mnemonics and tricks add additional curriculum. Detailed example of +/- canceling and x^2/x^2 canceling…why would we be surprised when they give an answer of 0, as many students do (50% of test takers). It would be difficult for me to remove “cancel” from my vocabulary…not really suggesting that. But we are suggesting that this process is taught with deep understanding so students realize the difference…the second example of “canceling” is actually simplification by using the inverse property of multiplication. A proportion is an equation…why confuse our middle schoolers by suggesting a new process – why not stick with the properties of operations to solve these equations and not introduce cross-multiplication which becomes a meaningless algorithm for students. We use the same properties in 3rd grade and in pre-calculus – if the students’ learn to use the properties with deep understanding, they become a very powerful tool for them as they provide them with mathematical flexibility. (Also talk about the butterfly method…meaningless algorithm) (6th bullet) We teach FOIL for multiplication of binomials, then confuse students when this doesn’t transfer to multiplication of larger polynomials. (7th bullet) In 2nd grade, line up numbers on the right to add/subt – but in 4th, line up decimals to compare? True understanding of place value greatly exceeds these superficial ideas. (8th bullet) It is not always necessary to firmly establish the mathematics, prior to providing problem solving situation making sense of the mathematics through problem situations is frequently neglected, when in fact the problem can actually assist students in learning the relevant mathematics. In mathematics, we often give the mathematics and demonstrate how you do it, and then explain why it is needed, and then give them a problem that will use that type of mathematics but it is important to reverse this process, (again, think about the FAL today) give them the problem and let them bring to the table what they know, let them find the mathematics…allow the productive struggle Great way to diagnose what students are bringing to the unit, demonstrates the variety among students in what they are bringing, and enables us to productively sketch our plan…you might be surprised that you may not have to sketch out as much as you thought…and may open your mind to seeing different approaches to a problem. Say YES to: Say NO to: Solving an equation with understanding - the power of the properties The strength of the distributive property Deep understanding of place value Deep understanding and the most important ideas in CCGPS which need our attention Canceling, proportions and cross-multiplying, the butterfly method FOIL – things that only work in certain circumstances Lining up the whole numbers on the right/lining up decimal points ‘Covering’ topics and the over-reliance on pacing guides

Call to Action Keep learning about Formative Assessment Lessons.
Visit grade level wikis: 2012 Summer Mathematics Academy – CCGPS Vital Shifts in Content Delivery Presentation & Finger on the pulse of teacher thinking/questions/resources Join CCGPS Mathematics Curriculum Supervisors wiki and District Supervisor Roster: Submit contact information to View current grade level webinars and archived recordings of introductory webinars and video broadcasts: Here is your call to Action…things we are asking you to do… (paraphrase slide)

Thank You! Brooke Kline Lead Program Specialist bkline@doe.k12.ga.us
Also…follow us on twitter at GaDOEMath…we are tweeting Thank you for your time and attention and please do not hesitate to contact us. James Pratt Program Specialist (6-12) Turtle Toms Program Specialist (K-5) Follow us on Twitter @GaDOEMath

FAL Resources McREL: What We Know About Mathematics Teaching and Learning Mathematics Assessment Project: Inside Mathematics:

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