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 21, :30 p.m. – 4:30 p.m. Hermitage High School

Welcome! Introductions Name, School, Teaching Experience What brought you to HCPS? What made you decide to teach math?

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

Today’s Schedule It’s pretty simple… 1. General Information 2. Break 3. Collaborative Teaching/Differentiation 4. Breakout Sessions Middle School High School

Planning VDOE Website: Curriculum Framework SOL Test Blueprints Keep in mind, SOLs are the MINIMUM standard.

If you teach to the SOL test…

The Standards of Learning provide a good framework. However, teaching is more than just learning an SOL! Standards of Learning

2009 Mathematics Standards of Learning 9  Rigor has been increased  Repetition has been decreased  Retention and application of content from previous years required  Vertical alignment has been improved

Vertical Articulation Documents 10 Click here for documents

Vertical Articulation of Content 11 Consistency Connections Relevance Why is it important knowledge to have? All these lead to deeper understanding and long-term retention of content

Pay attention to details!

HCPS Curriculum Guides All of the previous items have been consolidated into ONE document! HCPS Website: HCPS Curriculum Guides Pacing Vertical Articulation Big Ideas VDOE Enhanced Scope and Sequence Lessons SOL and Curriculum Framework Teacher Notes and Elaboration

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.

Summer Institutes Need a refresher? Visit the HCPS math website!

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?

HCPS Teacher Resource Page A lot of links to important documents! ExamView test banks 2. Online textbooks 3. Carnegie Learning files 4. Graphing calculator instructions

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 New Teacher Evaluation Process – August 28 th at HSHS “Snapshot” observations Teacher requested observations Formal Evaluation Process

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:

Instruction Make lessons active Limit lecture – the least effective teaching method Model the skills that you want your students to exhibit Develop concepts rather than answers Vary your teaching strategies Challenge the students - rigor Have fun learning! Encourage students to participate Set the stage for student success

Getting Started & Surviving the first month! NCTM – tips for teachers Develop a support system In your department In your school In your county *In your family*

Manage Your Time Wisely Planning Develop a schedule The first year in any job is the hardest Plan effective lessons Make objectives clear to the students Routine and structure are good, but don’t fall into a rut. Try to vary activities from time to time. Be prepared for the unexpected. It will happen. Daily.

Classroom Management Positive first impressions Greet and welcome your students as they enter the room Have a plan for the class Share your enthusiasm Help students to be successful Use positive reinforcement to motivate students - give out awards for both good academics and for good effort Have structure and procedures With these in place discipline follows You don’t want students creating classroom rules on the fly Fewer rules are better Be fair (fair does not mean equal) Don’t send mixed messages. Be consistent!

Assessing Instruction Assessment More than tests and quizzes Assessment for Learning – ActivEngage! Spell out what topics will be on the test. This will especially help those with poor study skills. ExamView banks Grades Interims, Quarters, Semesters eClass grading program Technology Graphing and Scientific Calculators

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

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

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.

Questions? Please contact me about anything! Skip Tyler

Break

Differentiate in the classroom. Realize that students have different skills sets.

Collaborative Teaching/Differentiated Learning Ms. Ashley Reyher Collaborative Math Classrooms: Co-teaching Tips and Strategies Collaborative Math flipchart

Breakout sessions High school stays here – 139 – Skip Tyler Middle school goes to room 160 – Jamie Perkins

Let’s Wordle the standards!

Course 1 Standards 38 Grade 6

Course 2 Standards 39 Grade 7

Course 3 Standards 40 Grade 8

Algebra 1 Standards 41

Geometry Standards 42

Algebra 2 Standards 43

Examine the HCPS Curriculum Guides 44 These are still drafts and may have minor edits. Examine the HCPS online courses and teacher resource page.

Parting words of wisdom…

Try to anticipate how a student might misuse equipment

Encourage your students to pay attention and make detailed observations.

Make sure there is substance to your lesson.

Set realistic expectations for your students

Additional Slides for Reference

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?

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

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

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

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

Tying it All Together Improved vertical alignment of content with increased cognitive demand. Key conceptual models can be extended across grade levels. Refer to the Curriculum Framework. Pay attention to the changes in the verbs. 61

Communication Connections Problem Solving Reasoning and Proof Representation 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?

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.

Examine the 5-8 Vertical Articulation 73 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 74 Grade 6

Number and Number Sense & Computation and Estimation 75 Grade 7

Number and Number Sense & Computation and Estimation 76 Grade 8

Measurement and Geometry 77 Grade 6

Measurement and Geometry 78 Grade 7

Measurement and Geometry 79 Grade 8

Probability, Statistics, Patterns, Functions, and Algebra 80 Grade 6

Probability, Statistics, Patterns, Functions, and Algebra 81 Grade 7

Probability, Statistics, Patterns, Functions, and Algebra 82 Grade 8