Mathematics

Math Program

MATH

The math program is researchand standards based. Math program is being implemented ingrades K-2. The pre and post assessments indicate which children are beginning,developing or secure in a particular math concept or skill. The rubrics usedassist teachers in refocusing instruction to meet the needs of individualstudents. Presently, there aren’t any standardized assessment tools for gradesK-2 other than the pre and post assessment and checklists for the Everyday MathProgram. Teacher’s assessments are informal, observational and anecdotal. Wehave assessed all the “at risk” students to gather additional data. Thisassessment and the Everyday Math Assessments and the MCLASS K-2 Assessment areused to identify students that need intervention as well as enrichment as well.This in depth math assessment is a good indicator of early numeracyproficiency.

In studying student work in math related to problemsolving and the ways in which children develop number sense, we looked atbeginning, developing and secure students including special education studentsand English language learners. We will continue to use FASTT Math, a technologyintervention program, that uses research based validated methods to helpstudents develop fluency with basic math facts. The teachers are able to adjusttheir teaching based on these assessments for the whole group, small group aswell as individual instruction that targets the specific needs of students.Formal and informal daily visits to classrooms show that the teachers areknowledgeable in implementing Everyday Math. The students are actively engagedin purposeful mathematical activities and conversations. The mini-lessons aretailored to meet the specific needs of the children in the classroom. We willcontinue to use the EXEMPLARS to help students to further develop problemsolving strategies and critical thinking skills in mathematics.

Since there are different math concepts that are taughton each grade level, we look for trends and gaps in instruction on each gradelevel. We analyzed the end of unitassessments in Everyday Math to determine which concepts/skills need to betargeted for individual students and to look at instructional trends on eachgrade level to identify patterns or gaps in instructional practices that neededfurther development. Developing number sense is an area that we needed todeepen and as a result, we are supplementing the Every Day Math program with“Contexts for Learning.”

We will continue to implement the 60 minute math blockdaily. P.S. 112 isimplementing the Everyday Math Program in kindergarten, first and secondgrades. Everyday Math, a programthat originated from the University of Chicago, is a nationally recognizedmathematics program that emphasizes problem solving, the use of manipulatives,and real world problems. Writing about math is being implemented inkindergarten, first and second grades. The goals of the program are to ensure that students use manipulativesto develop and understanding of math concepts. By developing experiences using concrete materials, studentsare easily able to make the transition to advanced mathematicalconcepts. The program exposesstudents to multiple ways of solving mathematical problems. Context forLearning is being implemented to enhance our math program.

Key vocabulary is introduced, learned and reinforced. Students are flexibly grouped toaddress individual needs. Studentsinteract and engage in a variety of cooperative learning activities that fostercritical thinking skills. Everydaythere is a “problem of the day” for the students to solve. The “problem of the day” is a mini warmup exercise that is designed to stimulate critical thinking skills.

Every student in grades K-2, including special education andELL’s, will have an understanding of mathematics through the experimentation ofideas in the context of real world situations. Students are and will be mainstreamed in all appropriateinstructional areas. Themathematics program is aligned with the NYS and NYC Learning and PerformanceStandards. The mathematics programis both developmental and comprehensive in scope and sequence withinstructional goals to teach, practice, assess, remediate or extend skillstaught. Monthly pacing calendarsare used to ensure continuity of instruction. The use of math journals will be used to promotemeta-cognition.

Literature books thatdeal with mathematical concepts will be used to increase math vocabulary andcreate awareness in students as to how mathematics is integrated intocurriculum areas and into real life. Students will complete book reports and will keep a record of all booksread. Students will experiencewriting in mathematics by creating their own word problems and recordinganswers. Students will developstrategies to explain and communicate to others the solutions to their problemsin oral and written forms.

Student progress is regularly assessed using pre-andpost-tests at the end of each unit of instruction, math journals, authenticperformance and the MCLASS K-2 math assessment. Instruction is refocused basedon student needs. Studentsidentified as “at risk” receive immediate interventions in the skillscategories in which they display deficiencies. The Principal, Assistant Principal and the Math Coach meetwith teachers to address the results of assessments so as to plan instructionthat addresses student needs. Inaddition, teachers are continually aligning the program with performancestandards to monitor student achievement.

MATHINTERVENTION

It should be notedthat P.S. 112 is an early childhood school and there is no formal or uniformassessment citywide for mathematics in early childhood that would assist us inkeeping with the same criteria set forth by the State for AIS.

The following are themath interventions provided to “at risk” students:

· increasedinstructional time in math is provided by the classroom teacher

· increasedstudent teacher interactions through reduced class size in grades K-2.

· smallgroup instruction by the classroom teacher is provided to meet student needs/differentiatedinstruction.

· ExtendedDay provides math instruction to students identified as “at risk” in math.

The school has a part time MathCoach. She works with novice as well as experienced teachers to effectivelyimplement the Everyday Math Program and to provide them with focused andintensive professional development based on the identified needs of thestudents as well as the teacher.

60 MINUTE DAILYMATH BLOCK

P.S. 112 hasimplemented a daily 60 minute math block using the math workshop model. The workshop model includes a” problemof the day”, homework review, mental math, a developmental math lesson, teachermini-lesson, small group instruction and a reflective activity where studentsshare their findings.. There is a monthly pacing calendar.

The developmentalmath lessons are planned weekly. All instruction includes three days of skills based instruction on aspecific area of mathematics. Concepts are developed from the concrete to the abstract andmanipulatives are used to illustrate abstract concepts. Key vocabulary is introduced, learnedand reinforced. Flexible groupingof students is used to support individual strengths and weaknesses; cooperativegrouping is used when appropriate. Assessment is ongoing and is both written and oral. Students maintain math journals and areexpected to explain their answers both orally and in writing.

Two days are devotedto problem exploration experiences that include real world problems and thereinforcement and enhancement of concepts taught during the week.

The structure of the60- minute math lesson is as follows:

Problem of the Day-(5 minutes) is a mini math “warm up” exercise to stimulate mathematicalthinking. A problem from EverydayMath requires that the children use vocabulary and problem solving strategiesand analysis through either individual or collaborative efforts.

Mental Math-(5minutes) is an oral or written response to a math concept, skill or strategythat involves up to ten answers. It is used to review previously introduced concepts as well as tomotivate and interest students in material that has not yet been presented.

Homework Review-(5 minutes) spiraled homeworkassignments reflect the key concepts studied during the day as well as previousdays. A review of the homeworkleads into the current day’s lesson. Trouble spots are identified and addressed.

Mini-Lesson- (5 minutes)The teacher demonstrates theconcept that the children will be applying in small groups. a motivator orintroduction engages children in a topic through a word problem or real lifereference.(Mini Lesson-Teacher Directed)

.Developmental Lesson - (25 minutes) has a clearobjective, e.g. how many ways can you count to 100? The developmental lesson is taught in three stages:

· Theobjective is met using a variety of instructional methodologies and tools. Through the use of individual andflexible group instruction, students learn to apply the skills. An oral orwritten exercise is completed that allows the teacher to assess the extent towhich each child has learned the lesson. This also provides an opportunity to modify the instruction, re-teach,review and integrate the technology application.

· Sharing-Studentsgather as a group to discuss the strategies they used and to share theirjournal entries.

ACCOUNTABLE CONVERSATIONS

Children are expected to be able todiscuss their work and the strategies they used to solve problems inmathematics in small groups and in pairs as well as in a whole group.

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Presently, there aren’t any standardized assessment tools for gradesK-2 other than the pre and post assessment and checklists for the Everyday MathProgram. Teacher’s assessments are informal, observational and anecdotal. Wehave assessed all the “at risk” students to gather additional data. Thisassessment and the Everyday Math Assessments and the MCLASS K-2 Assessment areused to identify students that need intervention as well as enrichment as well.This in depth math assessment is a good indicator of early numeracyproficiency. In studying student work in math related to problemsolving and the ways in which children develop number sense, we looked atbeginning, developing and secure students including special education studentsand English language learners. We will continue to use FASTT Math, a technologyintervention program, that uses research based validated methods to helpstudents develop fluency with basic math facts. The teachers are able to adjusttheir teaching based on these assessments for the whole group, small group aswell as individual instruction that targets the specific needs of students.Formal and informal daily visits to classrooms show that the teachers areknowledgeable in implementing Everyday Math. The students are actively engagedin purposeful mathematical activities and conversations. The mini-lessons aretailored to meet the specific needs of the children in the classroom. We willcontinue to use the EXEMPLARS to help students to further develop problemsolving strategies and critical thinking skills in mathematics. Since there are different math concepts that are taughton each grade level, we look for trends and gaps in instruction on each gradelevel. We analyzed the end of unitassessments in Everyday Math to determine which concepts/skills need to betargeted for individual students and to look at instructional trends on eachgrade level to identify patterns or gaps in instructional practices that neededfurther development. Developing number sense is an area that we needed todeepen and as a result, we are supplementing the Every Day Math program with“Contexts for Learning.” We will continue to implement the 60 minute math blockdaily. P.S. 112 isimplementing the Everyday Math Program in kindergarten, first and secondgrades. Everyday Math, a programthat originated from the University of Chicago, is a nationally recognizedmathematics program that emphasizes problem solving, the use of manipulatives,and real world problems. Writing about math is being implemented inkindergarten, first and second grades. The goals of the program are to ensure that students use manipulativesto develop and understanding of math concepts. By developing experiences using concrete materials, studentsare easily able to make the transition to advanced mathematicalconcepts. The program exposesstudents to multiple ways of solving mathematical problems. Context forLearning is being implemented to enhance our math program. Key vocabulary is introduced, learned and reinforced. Students are flexibly grouped toaddress individual needs. Studentsinteract and engage in a variety of cooperative learning activities that fostercritical thinking skills. Everydaythere is a “problem of the day” for the students to solve. The “problem of the day” is a mini warmup exercise that is designed to stimulate critical thinking skills. Every student in grades K-2, including special education andELL’s, will have an understanding of mathematics through the experimentation ofideas in the context of real world situations. Students are and will be mainstreamed in all appropriateinstructional areas. Themathematics program is aligned with the NYS and NYC Learning and PerformanceStandards. The mathematics programis both developmental and comprehensive in scope and sequence withinstructional goals to teach, practice, assess, remediate or extend skillstaught. Monthly pacing calendarsare used to ensure continuity of instruction. The use of math journals will be used to promotemeta-cognition. Literature books thatdeal with mathematical concepts will be used to increase math vocabulary andcreate awareness in students as to how mathematics is integrated intocurriculum areas and into real life. Students will complete book reports and will keep a record of all booksread. Students will experiencewriting in mathematics by creating their own word problems and recordinganswers. Students will developstrategies to explain and communicate to others the solutions to their problemsin oral and written forms. Student progress is regularly assessed using pre-andpost-tests at the end of each unit of instruction, math journals, authenticperformance and the MCLASS K-2 math assessment. Instruction is refocused basedon student needs. Studentsidentified as “at risk” receive immediate interventions in the skillscategories in which they display deficiencies. The Principal, Assistant Principal and the Math Coach meetwith teachers to address the results of assessments so as to plan instructionthat addresses student needs. Inaddition, teachers are continually aligning the program with performancestandards to monitor student achievement. *MATHINTERVENTION* It should be notedthat P.S. 112 is an early childhood school and there is no formal or uniformassessment citywide for mathematics in early childhood that would assist us inkeeping with the same criteria set forth by the State for AIS. The following are themath interventions provided to “at risk” students: · increasedinstructional time in math is provided by the classroom teacher · increasedstudent teacher interactions through reduced class size in grades K-2. · smallgroup instruction by the classroom teacher is provided to meet student needs/differentiatedinstruction. · ExtendedDay provides math instruction to students identified as “at risk” in math. The school has a part time MathCoach. She works with novice as well as experienced teachers to effectivelyimplement the Everyday Math Program and to provide them with focused andintensive professional development based on the identified needs of thestudents as well as the teacher. *60 MINUTE DAILYMATH BLOCK* P.S. 112 hasimplemented a daily 60 minute math block using the math workshop model. The workshop model includes a” problemof the day”, homework review, mental math, a developmental math lesson, teachermini-lesson, small group instruction and a reflective activity where studentsshare their findings.. There is a monthly pacing calendar. The developmentalmath lessons are planned weekly. All instruction includes three days of skills based instruction on aspecific area of mathematics. Concepts are developed from the concrete to the abstract andmanipulatives are used to illustrate abstract concepts. Key vocabulary is introduced, learnedand reinforced. Flexible groupingof students is used to support individual strengths and weaknesses; cooperativegrouping is used when appropriate. Assessment is ongoing and is both written and oral. Students maintain math journals and areexpected to explain their answers both orally and in writing. Two days are devotedto problem exploration experiences that include real world problems and thereinforcement and enhancement of concepts taught during the week. The structure of the60- minute math lesson is as follows: Problem of the Day-(5 minutes) is a mini math “warm up” exercise to stimulate mathematicalthinking. A problem from EverydayMath requires that the children use vocabulary and problem solving strategiesand analysis through either individual or collaborative efforts. Mental Math-(5minutes) is an oral or written response to a math concept, skill or strategythat involves up to ten answers. It is used to review previously introduced concepts as well as tomotivate and interest students in material that has not yet been presented. Homework Review-(5 minutes) spiraled homeworkassignments reflect the key concepts studied during the day as well as previousdays. A review of the homeworkleads into the current day’s lesson. Trouble spots are identified and addressed. Mini-Lesson- (5 minutes)The teacher demonstrates theconcept that the children will be applying in small groups. a motivator orintroduction engages children in a topic through a word problem or real lifereference.(Mini Lesson-Teacher Directed) .Developmental Lesson - (25 minutes) has a clearobjective, e.g. how many ways can you count to 100? The developmental lesson is taught in three stages: · Theobjective is met using a variety of instructional methodologies and tools. Through the use of individual andflexible group instruction, students learn to apply the skills. An oral orwritten exercise is completed that allows the teacher to assess the extent towhich each child has learned the lesson. This also provides an opportunity to modify the instruction, re-teach,review and integrate the technology application. · Sharing-Studentsgather as a group to discuss the strategies they used and to share theirjournal entries. *ACCOUNTABLE CONVERSATIONS* Children are expected to be able todiscuss their work and the strategies they used to solve problems inmathematics in small groups and in pairs as well as in a whole group.

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