Mathematics

Elementary School Math

The elementary math program supports students in developing rich conceptual understandings within the standard strands of operations and algebraic thinking, numbers and operations in base ten, numbers and operations with fractions, measurement, and data, and geometry. The following practices are integrated into math lessons:

• Making sense and persevering through problem solving
• Demonstration of quantitative and abstract reasoning
• Construction of viable arguments and feedback on the reasoning of others
• Modeling with mathematics, using tools strategically, and attending to precision
• Looking for and making use of patterns and structure

Classroom Math Instruction

For classroom instruction, we use Envisions Mathematics as our instructional tool.  Envisions is grounded in problem-based and visual learning that enable students to gain a deeper understanding of math concepts. Each lesson includes a few components: 

• Problem Based Learning
  • Solve and Share 
• Practice and Problem Solving
  • Visual Learning 
  • Guided and Independent Practice 
• Assess
• Differentiate (Small Group/Centers) 

Within this lesson framework, students start the lesson by attempting a new problem type independently while the teacher circulates to identify potential errors or areas to build sophistication in thinking. A discussion follows to drive towards a mathematical big idea. After students name that understanding, they use it to complete practice problems. The teacher can use the practice problems and/or quick checks to assess student understanding, and then uses that information to plan for the final section of the lesson. At the end of the lesson the teacher provides targeted instruction based on student data from the lesson and/or previous topic assessments to address gaps in understanding from current grade level standards or to enrich student understanding to dig more deeply into the grade level standards.  

Math Enrichment

Johnsen and Sheffield (2013) explain in mathematics, the role of all students, but especially those in need of enrichment should be to:

• “think, reason, make sense, and go deeper;
• talk to a partner and generate new ideas;
• repeat and rephrase what others have said and explain why they agree or disagree
• make generalizations and justify conclusions;
• add on new ideas, new methods of solution, new questions, and original problems and related solutions;
• record solutions, reasoning, and questions; 
• pose new mathematical questions of interest to investigate; and 
• create innovative mathematical problems and solutions”

With those thoughts in mind, as a district we recommend teachers provide students in need of math enrichment with opportunities to participate in and possibly lead collaborative and group work, opportunities to share thinking and reasoning skills during classroom discourse. We also suggest using open-ended questions and real-world mathematical puzzles or questions which require students to utilize all of the mathematical reasoning skills that they are building. We recommend finding opportunities for students to dig more deeply into the mathematics that they are learning. We do not recommend teaching the next grade level content as this has not been shown to support students in building positive mathematical identities and mindsets, as it gives the impression that math is a race to get through. We do not want students to complete math faster. We want them to develop deeper and richer understandings of the mathematics that they are engaging in.

Ability grouping is not a recommended district practice for meeting the needs of our advanced students.  If we intend to support all students, including our advanced learners, in building the necessary mathematical passion, creativity, and perseverance, to develop into mathematical innovators, ability grouping is not the answer. Instead, providing students with opportunities to work in mixed and flexible groups attending to learning in the ways described above would enrich and accelerate  all student learning. 

Accelerated Math

At Shenendehowa, we do not recommend whole grade acceleration before fourth grade as in Grades 1 - 3, students are beginning to develop the logic and reasoning skills that will be required for the rest of their mathematical career. In addition, they are beginning to develop their own mathematical identity, which can often be impacted negatively by accelerating a student too early in their schooling, setting them up for less mathematical opportunities in the future.  We do offer opportunities for accelerated math to students starting in 4th or 5th grade (they will be identified for this opportunity in the prior spring).  If your child is currently in Accelerated math, and has a successful year, they will remain in Accelerated Math. Accelerated math is different from enrichment, and involves students moving ahead a FULL year of mathematics (4th graders take 5th grade math, 5th graders take 6th grade math).  This is a significant change in program and reserved for those students who have reasoning abilities far exceeding their peers.  There is a required summer bridge program to “fill-in” the learning that students might miss by skipping a year of mathematics.  

Profile of an Accelerated Math Student

• Consistently achieves 90% or above on in class math assessments.  
• Scoring in the 90th percentile or above on STAR Math testing.  
• Achieves a Level 4 on NYS testing.  

In addition,

• Reasons abstractly and thinks symbolically. 
• Enjoys problem solving and solving problems with alternative solutions.  
• Grasps mathematical concepts and strategies quickly.  
• Perseveres through challenges.  
• Extends mathematical thinking to new situations.

For more information on accelerated math pathways.  

Math AIS

Students are identified for Academic Intervention Services (AIS) using many data points as noted in the District MTSS plan. The purpose of AIS in mathematics is to “accelerate” student learning by targeting prior standards to scaffold success with the new ones. To that end, AIS teachers do not provide instruction that is identical to the grade level instruction. Instead, they collect data on students to identify those who have gaps in their understanding and instruct students in those prerequisite skills so that they are able to access and succeed with the grade level learning. Students who are struggling with grade level learning, but have the prerequisite knowledge, will receive targeted instruction in small groups within the classroom and would not receive AIS.  

In the 24-25 school year, as a district we began using a new resource to support our Math AIS Instruction, which is Bridges Math Intervention. This tool  addresses critical numeracy and computation skills and is infused with models that promote student thinking and engagement, generally starting with perceptual manipulatives, moving to two-dimensional representations (frames, grids, graphic organizers, sketches, and the like), and finally to mental images. We have reviewed our grade level curriculum to ensure that in AIS the skills being targeted are centered around the prerequisite knowledge required to be successful in the classroom. Due to this, Math AIS will be flexible, as a student may be struggling with the skills they need to be successful with one skill area, but later in the year they may demonstrate mastery of the skills related to the next. Those times are time for celebration and students may return to the classroom as the instruction in AIS groups may not align to their needs.  

Data points reviewed for Math AIS:

• STAR Math 
• District Cumulative Common Math Assessments 
• Bridges Placement Exams 

Middle School Math

• Program of Studies 
• MS Math Progressions

• Program of Studies
• HS Math Progressions 

NYS Assessment

All students in grades 3 through 8 are required to take the NYS assessment in mathematics to identify students who are not meeting the state standards and provide those students with the help they need to be on grade level. These are typically given in April and May.

NYS Regents Exams are given in Integrated Algebra, Geometry, and Algebra Two/Trigonometry. For a Regents diploma, students must achieve a 65 on any math Regents exam.