Henrico County Public Schools New Mathematics Teachers General Math Session How to make your horse thirsty and other stuff you might want to know August 19, :30 p.m. – 4:30 p.m. Glen Allen High School

Introductions Get into groups of 3-4. Find 3 things your group has in common with each other. Introduce another person in your group (name, school, teaching experience) and a common item.

Objectives To familiarize you with curriculum expectations. To introduce you to the materials, places, people and processes that can help you do your best. To teach you how to get what you want.

How well do you know HCPS? 12 Middle Schools and 9 High Schools 2 Non-Traditional Programs All high schools and one middle school have “centers” 4 areas of focus in the district: Academic Progress Closing Gaps (Academic & Behavioral) Relationships Safety & Security Math Focus: Good Teaching! Instructional Planner 21 st Century Skills/Process Standards 3 R’s: Rigor, Relevance, and Relationships Engagement Questioning

Virtual Tour – HCPS Math Website HCPS Math Website: Here is the info!

HCPS Secondary Math Courses One stop shopping for all your course needs! Course websites New website updates! We’ll explore more later Curriculum Guides Pacing Vertical Articulation VDOE Enhanced Scope and Sequence Lessons SOL and Curriculum Framework Teacher Notes and Elaboration Benchmark Blueprint Breakdown of winter benchmark test

Each SOL course contains… Pacing guides SOL tracker Link to VDOE SOL Link to VDOE mathematics website

2009 Mathematics Standards of Learning  Rigor has been increased  Repetition has been decreased  Retention and application of content from previous years required  Vertical alignment has been improved  Again, the textbooks are a resource and should not be relied upon for instruction.

Planning VDOE Website: Curriculum Framework SOL Test Blueprints Keep in mind, SOLs are the MINIMUM standard. Our textbooks are outdated and do not reflect the new rigor! They should not be your first resource!

Pay attention to details!

Unpacking the Standards

SOL Tracker SOL are broken down into a teacher checklist Shaded rows are SOL bullets Non-shaded rows are broken down SOL paragraphs

Activity: Unpacking the Standards Unpack Algebra 1 Standard A.9 Scavenger Hunt! What information do I need? Where is it located? How do I get there?

If you teach to the SOL test…

Instructional Planner New to ! All teachers have to submit 1 Instructional Planner each nine weeks You can collaborate with colleagues Content/Topic may be determined by school based upon data

Put the following Instructional Design components in the appropriate order. (P) Unpacking the Standards (L) Identify Instructional Goals (A) Write Performance Objectives (N) Develop Summative Assessments (N) Develop Instructional Strategies (E) Develop Instructional Materials (R) Design/Conduct Formative Assessments (Q) Reflect and Revise

Solution! (P) Unpacking the Standards (L) Identify Instructional Goals (A) Write Performance Objectives (N) Develop Summative Assessments (N) Develop Instructional Strategies (E) Develop Instructional Materials (R) Design/Conduct Formative Assessments (Q) Reflect and Revise

Instructional Planner Resources Instructional Planner Video Part 1 Instructional Planner Video Part 2 Instructional Planner Resources Overview IP Components IP FAQ’s IP Checklist IP Timeline IP Blank Template Submitted Instructional Planners Submitted Instructional Planners Revised Blooms Teacher Planner Kit Revised Blooms Teacher Planner Kit Exemplars HCPS Leadership Blog: PD Resources blogs.henrico.k12.va.us/leadershipblogs.henrico.k12.va.us/leadership

View the training template

Instructional Focus To address the increased rigor of the SOL, Henrico County’s instructional focus will be the centered around the NCTM Process Standards. 1. Problem Solving 2. Reasoning 3. Representations 4. Communication 5. Connections The observational focus will be rigor and engagement.

Process Standards/Goals for Students

What if cupcakes are the discipline?

Effective Questioning Is 15 a prime number? Students can answer with a simple Yes or No. What does the student’s response inform the teacher about the pupil’s knowledge about prime numbers? Why is 7 an example of a prime number? Not a one-word answer. This requires a student to recall prior knowledge to explain and justify their reasoning.

HCPS Teacher Resource Page A lot of links to important documents! ExamView test banks 2. Online textbooks 3. Software files (TTM, ExploreLearning, Reflex, etc.) 4. CASIO Graphing calculator instructions 5. NTA PowerPoint and files

STEM Teacher Recruitment and Retention Incentive Awards Hold an active five-year Virginia teaching license (Collegiate Professional or Postgraduate Professional License) with an endorsement in Middle Education 6-8: Mathematics; Mathematics: Algebra I; Mathematics; and be assigned to a teaching position in a corresponding subject area. Teachers Reassigned from a Fully Accredited School to a Hard-to-Staff School or School Not Fully Accredited Regardless of teaching experience, be a teacher who is reassigned from a fully accredited school in a Virginia school division to a hard-to-staff school or a school that is not fully accredited in the school year. Teachers New to the Profession or Teachers With Up to Three Years’ Teaching Experience [Applicants must have less than three years’ teaching experience.] Be a teacher new to the profession (no teaching experience) or a teacher with up to three years of teaching experience (less than three years’ teaching experience); Successful teachers selected to participate in the pilot program under this criteria will be eligible to receive a $5,000 initial incentive award after the completion of the first, second, or third year of teaching with a satisfactory performance evaluation and a signed contract in the same school division for the following school year. MEMO # Science, Technology, Engineering, and Mathematics (STEM) Teacher Recruitment and Retention Incentive AwardsScience, Technology, Engineering, and Mathematics (STEM) Teacher Recruitment and Retention Incentive Awards

Speaking of calculators… Make sure that the calculator is a TOOL used for instruction! It has become a crutch for many students and teachers. Be accountable for them and have a system for storing and collecting them.

Observations/Evaluations Teacher Evaluation Process – focus on process skills Walkthrough “Snapshot” observations Teacher requested observations Students must show growth in 2 areas: Content – SOL multiple choice Skills/Tasks – Communication focus Teacher Evaluation Process

Instruction: Why focus on tasks? Classroom instruction is generally organized and orchestrated around mathematical tasks The tasks with which students engage determines what they learn about mathematics and how they learn it “There is no decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics”. Lappan & Briars, 1995

The Die Hard with a Vengeance version of teaching Polya's four-step problem solving process Problem Based Learning

Was this a worthwhile task? Does the problem challenge students to use higher-level critical thinking skills? Are there multiple ways to solve this problem? Is it accessible to all students? What process standards were utilized?

Instruction: Two tasks. Martha’s Carpeting Task Martha was re-carpeting her bedroom which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase? Fencing Task Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen in which to keep the rabbits. 1. If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? 2. How long would each of the sides of the pen be if they had only 16 feet of fencing? 3. How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

Instruction: Tasks - Comparison Similarities Both require prior knowledge of area Area problems Differences Way in which the area formula is used The need to generalize The amount of thinking and reasoning required The number of ways the problem can be solved The range of ways to enter the problem

Task Characteristics High cognitive demand Significant content (i.e., they have the potential to leave behind important residue) Require justification or explanation Make connections between two or more representations Open-ended Allow entry to students with a range of skills and abilities Multiple ways to show competence

Instruction: Tasks Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking. Stein, Smith, Henningsen, & Silver, 2000 The level and kind of thinking in which students engage determines what they will learn. Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997 If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks. Stein & Lane, 1996

People who can help you! YOU Mentor or Buddy Dept Chair Assistant Principal SpecialistColleaguesITRTCoaches

You can lead a horse to water, but you can’t make him drink In the past, an acceptable philosophy for educators was:

If you lead a horse to water and he doesn’t want to drink, it’s your job to make him thirsty. The present philosophy for educators goes something like this:

Questions? Please contact me about anything! Skip Tyler

Examine the HCPS Curriculum Guides 42 Examine the HCPS online courses Examine the HCPS teacher resource page.

Breakout options Changing Instruction Video – Dan Meyer (slide 44) What Can You Do With This (WCYDWT) Video (slide 45) Wordle Activity – wordle.net – copy/paste standards to create a graphic (slides 36-42) Examine curriculum guide, websites, teacher resource page (slide 43) Four scenarios (slides 47-51) NCTM process standards & Blooms Taxonomy (slides 52-60) Vertical articulation (slide 61) Breaking down the standards wordle (slides 62-70) Teacher Evaluation – complete a skills problem and grade on a rubric Other options?

Changing Instruction Dan Meyer – Math class needs a makeover Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. At TEDxNYED, Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.

WCYDWT Video (What Can You Do With This) The best motivator of all is connecting math to the real world.

A critical point …a teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a task for, and some means of, independent thinking.” Polya, 1973/1945

Four Scenarios!!! Read the scenario presented Think through and jot down answers Share ideas/Ask Questions

Scenario #1 You want to experiment with a new teaching method and would like to incorporate manipulatives into your lessons, but you are unsure if it will go over well with your students. What can you do? What are some possible solutions? Who can assist you with this situation?

Scenario #2 As a new mathematics teacher, you are assigned a mentor/buddy and are somewhat nervous about your teaching assignment. You are surprised to learn that your mentor, though very nice, does not teach your content. You also learn that the only other teacher who teaches your content is an old grouch who does nothing but complain. What can you do? What are some possible solutions? Who can assist you with this situation?

Scenario #3 You and your collaborative partner are not seeing eye-to- eye on classroom management and instruction. The kids are beginning to notice that the two of you are not working as a team. What can you do? What are some possible solutions? Who can assist you with this situation?

Scenario #4 Several students are bored with your lesson on solving two-step equations. They start to ask the age old question, “Why do we have to learn this?” What can you do? What are some possible solutions? Who can assist you with this situation?

NCTM Process Standards Communication Use the language of mathematics to express mathematical ideas precisely. Writing about mathematics. Discussing mathematical ideas. You have eleven fruits in your basket, some are one kind of fruit, and the rest are another kind. How many of each could you have?

NCTM Process Standards Connections Between different mathematical areas Between mathematics and science Between mathematics and other subject areas (such as history, literature, and art) Between mathematics and the real world Example Mr. Goodlock drives to and from Hermitage almost every day. Along the way the posted speed limits range from 30 mph to 65 mph. Mr. Goodlock has logged his daily commute.

NCTM Process Standards Connections These are the posted speed limits and the odometer reading at the beginning of each drive segment Mr. Goodlock encounters: Odometer Reading Posted MPH Parking Lot Calculate the amount of time Mr. Goodlock spends in each speed zone. Make a graph showing your results. Mr. Goodlock usually drives at the posted speed limit. If we assume a trip with no traffic and we ignore time spent at stop signs and traffic lights -- what is the total driving time for Mr. Goodlock's trip?

NCTM Process Standards Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Translation: include one and two-step story problems typically found in textbooks. A school auditorium can seat 648 people in 18 equal rows. How many seats are there in each row? Process: requires solution processes other than computational procedures. Application: computation is generally the solution process used to solve application problems. How many soda cans would it take to fill the school gym?

NCTM Process Standards Reasoning Look at the set shown below. {15, 23, 39, 42} Which number is prime? Reasoning Look at the set shown below. {2a, 3a, 4a, 5a} If a is a prime number, how many members of the set are also prime? Reasoning & Proof Recognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof

NCTM Process Standards Mathematical Representations Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena Sam went to a store and spent half of his money. Then he gave one-fifth of what he had left to his sister. Of the amount he had left, he lost half of it. When Sam got home, he had $0.50. How much money did he have before entering the store?

Bloom’s Taxonomy

1. 76, 79, 75, 77, 74 For the data listed, the value 76.2 represents the A. Median B. Mode C. Range D. Mean What is the mathematics assessed in the item on the right? Which cognitive level does the question address?

Bloom’s Taxonomy 1. The difference in cost between a large bag of chips and a small bag of chips was $.90. Alicia bought 5 large bags and 3 small bags of chips for her party and spent $ What was the cost of a small bag of chips? F $5.74 G $2.49 H $2.15 What is the mathematics assessed in the item on the right? Which cognitive level does the question address?

Examine the 5-8 Vertical Articulation 61 Identify the similarities and differences between the grade levels What are the key verbs? Was there anything that surprised you? Breaking Down the 6-8 Standards List the 5 most important concepts you see in Grades 6 and 7 Can you draw a representation of the topics?

Number and Number Sense & Computation and Estimation 62 Grade 6

Number and Number Sense & Computation and Estimation 63 Grade 7

Number and Number Sense & Computation and Estimation 64 Grade 8

Measurement and Geometry 65 Grade 6

Measurement and Geometry 66 Grade 7

Measurement and Geometry 67 Grade 8

Probability, Statistics, Patterns, Functions, and Algebra 68 Grade 6

Probability, Statistics, Patterns, Functions, and Algebra 69 Grade 7

Probability, Statistics, Patterns, Functions, and Algebra 70 Grade 8