Middle School Math

All MCS students in grades 6-8 will be assessed three times per year using the iReady Diagnostic.  The pacing guide includes estimated time frames for when the assessments will occur, but the exact date will be set district-wide at the start of each school year.

iReady diagnostic data should be used to help determine school-wide, classroom, and individual student needs.  Intervention and enrichment should take place based upon all data sources.

Formative assessments should be used to inform teachers of student understanding and guide instruction.  The purpose of formative assessments is to provide feedback to the teacher, not to judge students’ performance, thus formative assessments should not be included in student grade calculations.  

Each unit within the 6-8 curriculum guides suggests a time for formative assessments to be given (usually two-thirds of the way through the unit).  Those unit formative assessments may be in the form of a rich math task, a traditional assessment, or the textbook’s math probe.  The exact nature of each formative assessment has been left to teacher discretion, but all teachers are highly encouraged to assess student understanding for gaps and misconceptions before completing the unit.

Teachers should use the anecdotal and/or quantitative data from the formative assessments to determine if students are showing an understanding of the content and skills in the unit before moving on to finish the unit.  Multiple days have been included in the units for assessing student understanding and re-teaching/re-engaging students, if the assessment shows gaps or misconceptions in their understanding.

The WVGSA Test Authoring Tool is a great way to gather information about student understanding.  Claire Southerly provided the linked notes on Test Authoring.

Teachers should use available data sources, including but not limited to, iReady diagnostics, classroom summative and formative assessments, class assignments, and the online personalized pathway to determine students’ need for targeted and intensive instruction.  Documentation of tiered interventions should be reported in Panorama.  Suggestions for tiered interventions are included in each unit. 

Students in grades 6-8 will receive personalized math instruction based on their specific needs through the ALEKS online program. 

Monongalia County Schools recommends students engage in their personalized math pathway for a minimum of 45 minutes per week, but individual school administrators will set the expectations for their buildings.  Teachers are encouraged to utilize ALEKS for 45 consecutive minutes, rather than breaking the time into smaller time periods.

Students should be encouraged to utilize paper and pencil (for example a spiral notebook or journal) when working through their personalized pathway in ALEKS.  Doing so may reinforce skills, discourage students from attempting to work out solutions mentally, and encourage students to display their thinking and justify their solutions.  Additionally, use of a notebook or journal can give teachers an opportunity to better assist students in identifying their mistakes or misconceptions.

The iReady personalized pathway and teacher lessons for mathematics are available for teachers to use as additional supplemental activities.

In order to be considered for advanced placement (taking a course one year or more above current grade level), students in grades 6-8 must first show mastery of grade level standards to be skipped.  Examples of data used to determine mastery can be found on the MCS Middle School Pathways document, effective February 2023.

Classroom teachers have the option to provide students enrolled in on-grade-level mathematics with enrichment through the county-created accelerated pathway found in ALEKS.  Completion of the accelerated pathway will not guarantee advancement, but may provide students with the opportunity to gain skills needed to show mastery on district identified skills mastery assessments.

Middle school students will be assigned ALEKS pathways based on their course enrollment.  In some cases, additional pathways may be appropriate for students.  The linked document indicates the pathways approved for Monongalia County middle school students, as well as the criteria for enrollment. 

The National Council of Teachers of Mathematics (NCTM) has outlined 8 teaching practices to ensure effective, high quality, student centered instruction.  Monongalia County Schools believes these eight practices should be at the foundation of math classroom instruction.

1. Establish mathematics goals to focus learning.

2. Implement tasks that promote reasoning and problem solving.

3. Use and connect mathematical representations.

4. Facilitate meaningful mathematical discourse.

5. Pose purposeful questions.

6. Build procedural fluency from conceptual understanding.

7. Support productive struggle in learning mathematics.

8. Elicit and use evidence of student thinking.

Providing students with opportunities to productively struggle in mathematics cultivates students' abilities to grapple with challenging problems while encouraging critical thinking and perseverance. By prioritizing active learning and problem-solving skills, this approach fosters a deeper understanding of mathematical concepts and enhances students' confidence in their mathematical abilities, emphasizing reasoning over rote memorization.

A key feature of the productive struggle is that it should be productive.  Teachers should facilitate activities by providing adequate time for students to engage in critical thinking (but not so long that it creates frustration), asking students scaffolded leading questions that require students to do the work (not stepping in to do the work for them), encouraging mistakes, and identifying misconceptions.

During a productive struggle, students should be encouraged to elaborate on what they know, talk to their group members, explain their reasoning, and justify their strategies.  Teachers can utilize questioning and learner engagement techniques (see following sections) to help move the students forward during a productive struggle.

The Math Assessment Project identifies five principles for effective questioning that can be used to guide teachers in using questioning to facilitate rigorous classroom discussions.  A more thorough description of each principle can be found in the Appendix.

1. Plan questions ahead of time that encourage thinking and reasoning (Suggested resources: Bloom’s Question Starters, Questions to Develop Mathematical Thinking)

2. Ask questions in ways that include all students (see the following section on Student Engagement Strategies)

3. Give students time to think

4. Avoid judging students’ responses

5. Follow up students’ responses in ways that encourage deeper thinking

Margaret Smith & Mary Kay Stein’s research on facilitating math discussions is commonly referenced by math practitioners (including our latest textbook adoption).  Smith & Stein have identified Five Practices for Orchestrating Productive Mathematics Discussions.  A brief summary of each practice can be found in the Appendix.

1. Anticipating likely student responses

2. Monitoring students’ actual responses while they work together

3. Selecting particular students to present their work during whole-class discussions

4. Sequencing the student responses that will be displayed in a specific order

5. Connecting student responses to one another and to the key mathematical ideas

Student engagement should include opportunities for students to think and discuss mathematics.  As a result, effective questioning in the mathematics classroom should be done in such a way as to include all students (all students should have the opportunity to think and discuss the question).  Use of classroom strategies such as Visible Thinking Routines, Cooperative Learning Structures, and Learner Engagement Techniques create a classroom culture where all voices are heard. 

Monongalia County Schools is continually updating a list of strategies that can be used to provide opportunities for students to think and talk. 

Getting students to talk may not be difficult, but getting students to talk about mathematics can be challenging!  Regular use of math routines as warm ups or exit tickets can be used to encourage thinking and talking using mathematical language.  Monongalia County Schools has compiled a list of websites that include short open-ended math activities which can be used during warm up and exit routines (bottom section of the webpage).

Teachers may also find it helpful to display Math Talk Sentence Starters for students to use as they begin to participate in mathematical discourse. 

In her book Mathematical Mindsets, Jo Boaler has defined the following as the characteristics of rich mathematical tasks.

• Rich math tasks are open to encourage multiple methods, representations, and pathways

• Rich math tasks are inquiry based

• Rich math tasks allow students to experience the mathematics conceptually before procedures

• Rich math tasks have a visual component

• Rich math tasks are “low floor” and “high ceiling”

• Rich math tasks require students to convince, reason, or justify

Monongalia County Schools believes that students should have an opportunity to engage in rich math tasks to deepen their understanding about a concept, make connections between math concepts, critically reason about a problem, justify their thinking, and discuss their process with peers.  Monongalia County Schools has created a library of math tasks that can be used to supplement the adopted text.

Teachers who facilitate rich math tasks in their classroom provide students with opportunities for productive struggle, utilize questioning techniques to move learners forward during tasks, and encourage student engagement through critical thinking and discussion. 

Students in Monongalia County Schools experience classroom instruction through blended learning environments.  As such, teachers are encouraged to provide instruction consisting of a variety of learning modalities, including but not limited to, whole group direct instruction, activity-based discovery learning, collaborative small group tasks and projects, station work, and digital delivery.  

Due to the nature of mathematics, students should be encouraged to utilize paper and pencil (for example a spiral notebook or journal) when completing digital tasks in their online textbook, ALEKS personalized pathway, and iReady diagnostics.  Doing so may reinforce skills, discourage students from attempting to work out solutions mentally, and encourage students to display their thinking and justify their solutions.  Additionally, use of a notebook or journal can give teachers an opportunity to better assist students in identifying their mistakes or misconceptions.

Similarly, math notebooks/journals are recommended for student use to provide reference to concepts previously learned that may appear in later topics.  Middle school students require explicit teaching and modeling of appropriate note-taking and reference techniques.