Henrico County Public Schools New Mathematics Teachers General Math Session How to make your horse thirsty and other stuff you might want to know

Henrico County Public SchoolsNew Mathematics TeachersGeneral Math Session

How to make your horse thirsty and other stuff you might want to knowAugust 21, 20121:30 p.m. 4:30 p.m.Hermitage High SchoolWelcome!IntroductionsName, School, Teaching ExperienceWhat brought you to HCPS?What made you decide to teach math?ObjectivesTo familiarize you with curriculum expectationsTo introduce you to the materials, places, people and processes that can help you do your bestTo teach you how to get what you wantTodays ScheduleIts pretty simpleGeneral InformationBreakCollaborative Teaching/DifferentiationBreakout SessionsMiddle SchoolHigh School

PlanningVDOE Website: http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/review.shtml Curriculum Framework SOL Test BlueprintsKeep in mind, SOLs are the MINIMUM standard.6If 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 Learning82009 Mathematics Standards of Learning9Rigor has been increasedRepetition has been decreasedRetention and application of content from previous years requiredVertical alignment has been improved

Vertical Articulation Documents10

Click here for documentsVertical Articulation of Content11ConsistencyConnectionsRelevance

Why is it important knowledge to have?All these lead to deeper understanding and long-term retention of contentPay attention to details!

http://teachers.henrico.k12.va.us/math/Teacher/Downloads/NTA/DANCING_BEAR_MOONWALKING_BEAR_CYCLIST_AWARE.wmv HCPS Curriculum GuidesAll of the previous items have been consolidated into ONE document!HCPS Website: http://blogs.henrico.k12.va.us/math/

HCPS Curriculum GuidesPacingVertical ArticulationBig IdeasVDOE Enhanced Scope and Sequence LessonsSOL and Curriculum FrameworkTeacher Notes and Elaboration

Instructional FocusTo address the increased rigor of the SOL, Henrico Countys instructional focus will be the centered around the NCTM Process Standards.Problem SolvingReasoningRepresentationsCommunicationConnections

The observational focus will be rigor and engagement.Summer InstitutesNeed 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 Learninghttp://teachers.henrico.k12.va.us/math/Teacher/downloads/nta/die_hard_jugs.mov.wmv 16Was 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 PageA lot of links to important documents! http://teachers.henrico.k12.va.us/math/teacher.html

ExamView test banksOnline textbooksCarnegie Learning filesGraphing calculator instructions

Speaking of calculatorsMake 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/EvaluationsNew Teacher Evaluation Process August 28th at HSHSSnapshot observationsTeacher requested observationsFormal Evaluation Process

People who can help you!You can lead a horse to water, but you cant make him drink

In the past, an acceptable philosophy for educators was:If you lead a horse to water and he doesnt want to drink, its your job to make him thirsty.

The present philosophy for educators goes something like this:InstructionMake lessons activeLimit lecture the least effective teaching methodModel the skills that you want your students to exhibitDevelop concepts rather than answersVary your teaching strategiesChallenge the students - rigor

Have fun learning!Encourage students to participateSet the stage for student success

Getting Started & Surviving the first month!NCTM tips for teachers - http://www.nctm.org/resources/content.aspx?id=9584Develop a support systemIn your departmentIn your schoolIn your county*In your family*

Manage Your Time WiselyPlanningDevelop a scheduleThe first year in any job is the hardest Plan effective lessonsMake objectives clear to the studentsRoutine and structure are good, but dont fall into a rut. Try to vary activities from time to time. Be prepared for the unexpected. It will happen. Daily.

26Classroom ManagementPositive first impressionsGreet and welcome your students as they enter the roomHave a plan for the classShare your enthusiasmHelp students to be successfulUse positive reinforcement to motivate students - give out awards for both good academics and for good effortHave structure and proceduresWith these in place discipline followsYou dont want students creating classroom rules on the flyFewer rules are betterBe fair (fair does not mean equal)

Dont send mixed messages. Be consistent!27Assessing InstructionAssessmentMore than tests and quizzesAssessment for Learning ActivEngage!Spell out what topics will be on the test. This will especially help those with poor study skills.ExamView banksGradesInterims, Quarters, SemesterseClass grading programTechnologyGraphing and Scientific Calculators

28Interims - 4.5 weeks - benchmarkQuarters - 9 weeks and used in determining semester gradesSemesters - 18 weeks and used in determining final gradesWhy give grades less than 50%?Total Points vs CategoriesA critical pointa 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, 1973/194529WCYDWT Video(What Can You Do With This)The best motivator of all is connecting math to the real world.

Changing InstructionDan 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.http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html

Questions?Please contact me about anything!Skip Tylerestyler@henrico.k12.va.us652-3753Break

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

Collaborative Teaching/Differentiated LearningMs. Ashley Reyher Collaborative Math Classrooms: Co-teaching Tips and StrategiesCollaborative Math flipchart

Breakout sessionsHigh school stays here 139 Skip TylerMiddle school goes to room 160 Jamie Perkins

Lets Wordle the standards!Course 1 Standards38Grade 6

Course 2 Standards39Grade 7

Course 3 Standards40Grade 8

Algebra 1 Standards41

Geometry Standards42

Algebra 2 Standards43

Examine the HCPS Curriculum Guides44http://blogs.henrico.k12.va.us/mathThese are still drafts and may have minor edits.Examine the HCPS online courses and teacher resource page.http://teachers.henrico.k12.va.us/math/teacher.html

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 substanceto your lesson.

Set realistic expectations foryour students

Additional Slides for ReferenceFour Scenarios!!!Read the scenario presentedThink through and jot down answersShare ideas/Ask Questions51Scenario #1You 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 #2As 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 #3You 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 #4Several 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 tasksThe tasks with which students engage determines what they learn about mathematics and how they learn itThere 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, 199556Rich Mathematical Tasks: The Cornerstone of Rigorous InstructionInstruction: Two tasks.Marthas Carpeting TaskMartha 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 TaskMs. Browns class will raise rabbits fortheir spring science fair. They have 24feet of fencing with which to build arectangular rabbit pen in which to keepthe rabbits.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?How long would each of the sides of the pen be if they had only 16 feet of fencing? 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. 57Rich Mathematical Tasks:Fencing TaskBuild pens with physical materials (linear and area pieces)Draw pens on grid paper (grid paper)Make a table of the dimensions of possible pensMake a graph that shows the relationship between one linear dimension and the area (graph paper or graphing calculator)Set up an algebraic equation and solveInstruction: Tasks - ComparisonSimilaritiesBoth require prior knowledge of areaArea problemsDifferencesWay in which the area formula is used The need to generalizeThe amount of thinking and reasoning required The number of ways the problem can be solvedThe range of ways to enter the problem58Way in which area formula is used -Marthas Carpeting can be solved by knowing and using the area formula but this formula alone is not sufficient to solve the Fencing Task- Marthas carpeting does not lead to a generalization but the Fencing Task doesThe amount of thinking and reasoning required - Marthas Carpeting requires limit thinking and reasoning while the Fencing Task cant be solved without itFencing task might be considered a more equitable task -- for several reasonsBuild pens with physical materials (linear and area pieces)Draw pens on grid paper (grid paper)Make a table of the dimensions of possible pensMake a graph that shows the relationship between one linear dimension and the area (graph paper or graphing calculator)Set up an algebraic equation and solveInstruction: TasksNot 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, 199659Task CharacteristicsHigh cognitive demand Significant content (i.e., they have the potential to leave behind important residue)Require justification or explanationMake connections between two or more representationsOpen-endedAllow entry to students with a range of skills and abilitiesMultiple ways to show competence60These last two characteristics can help make a task EQUITABLE -- That is, level the playing field so that students with a wide range of abilities can ENTER a TASK.Tying it All TogetherImproved 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.

6161CommunicationConnectionsProblem SolvingReasoning and ProofRepresentationNCTM Process Standards62NCTM Process StandardsCommunicationUse 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?63NCTM Process StandardsConnectionsBetween different mathematical areasBetween mathematics and scienceBetween mathematics and other subject areas (such as history, literature, and art)Between mathematics and the real worldExampleMr. 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. 64NCTM Process StandardsConnectionsThese are the posted speed limits and the odometer reading at the beginning of each drive segment Mr. Goodlock encounters:Odometer ReadingPosted MPH0602.7557.84511.83518.26524.33027.3Parking LotCalculate 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?65NCTM Process StandardsProblem SolvingBuild new mathematical knowledge through problem solvingSolve 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?66New Door Problem - Rearrange the 7 letters in New Door to form one word

Process - At an air show, 8 skydivers were released from a plane. Each skydiver was connected to each of the other skydivers with a separate piece of ribbon. How many pieces of ribbon were used in the skydiving act?NCTM Process StandardsReasoningLook at the set shown below. {15, 23, 39, 42}Which number is prime? ReasoningLook 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 & ProofRecognize 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 67From 2004 Grade 8 SOL testNCTM Process StandardsMathematical RepresentationsCreate 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?

68Sam 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?

Blooms Taxonomy

69Blooms Taxonomy76, 79, 75, 77, 74 For the data listed, the value 76.2 represents the

A. Median B. Mode C. Range D. MeanWhat is the mathematics assessed in the item on the right?

Which cognitive level does the question address? 70Grade 6 2006 SOL test, AnalysisAns. DBlooms TaxonomyThe difference in cost between a largebag of chips and a small bag of chipswas $.90. Alicia bought 5 large bags and3 small bags of chips for her party andspent $17.22. What was the cost of asmall bag of chips?F $5.74G $2.49H $2.15J $1.59What is the mathematics assessed in the item on the right?

Which cognitive level does the question address?712006 SOL Algebra 1 test, systemsAns. JEffective QuestioningIs 15 a prime number?Students can answer with a simple Yes or No.What does the students response inform the teacher about the pupils 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.72It provides an opportunity to make an assessment without necessarily asking supplementary questions. The question, Is 15 a prime number? requires follow-up questions to get a full response on which to make an assessment.

The question Why is 7 an example of a prime number? is an example of the general question Why is x an example of y? This is one type of question that is effective in providing assessment opportunities.Examine the 5-8 Vertical Articulation73Identify the similarities and differences between the grade levelsWhat are the key verbs?Was there anything that surprised you?Breaking Down the 6-8 StandardsList the 5 most important concepts you see in Grades 6 and 7Can you draw a representation of the topics?Number and Number Sense & Computation and Estimation74Grade 6

Number and Number Sense & Computation and Estimation75Grade 7

Number and Number Sense & Computation and Estimation76Grade 8

Measurement and Geometry77Grade 6

Measurement and Geometry78Grade 7

Measurement and Geometry79Grade 8

Probability, Statistics, Patterns, Functions, and Algebra80Grade 6

Probability, Statistics, Patterns, Functions, and Algebra81Grade 7

Probability, Statistics, Patterns, Functions, and Algebra82Grade 8