In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…

Despite growing attention to identifying equitable teaching practices that provide all students opportunities to engage in mathematical thinking and reasoning (Tan and Kastberg 2017; NCTM 2014), students with disabilities have had limited opportunities to take on the role of doers of mathematics and to see themselves or have others see them as…

El Dorado Middle School, Kansas, is using MAP® Skills™ from NWEA® to ensure every single student is getting instruction where they need it most, and it is having a huge impact on student growth and achievement, including special education students. Besides empowering students to monitor their own learning, MAP Skills enables teachers to move…

Students learning math are expected to do more than just solve problems; they must also be able to demonstrate their thinking and share their ideas, both orally and in writing. As many classroom teachers have discovered, these can be challenging tasks for students. The good news is, mathematical communication can be taught and mastered. In…

Elementary school mathematics is increasingly recognized for its crucial role in developing the foundational skills and understandings for algebra. In this article, the author uses a lesson to introduce the concept of "rates"--comparing two different types and units of measure--and how to graph them. Described is the lesson and shared…

Students' experiences with statistics and data analysis in middle school are often limited to little more than making and interpreting graphs. Although students may develop fluency in statistical procedures and vocabulary, they frequently lack the skills necessary to apply statistical reasoning in situations other than clear-cut textbook examples.…

In grade 6, students should be able to "perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order" (p. 44). In grades 7 and 8, the rules of order of operations are used to simplify progressively complicated expressions and in…

For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

To succeed in college, career, and life, students need to become financially literate. But understanding the basics of a long-term investment or a short-term loan is not enough without the math skills to make financially sound choices. In the already full curriculum of middle schools today, how can teachers find room to include financial literacy?…

The tenth annual Boston Opportunity Agenda Report Card takes a closer look at the impact of two years of pandemic on the achievement of students on key indicators from kindergarten through college and adult education. It finds mixed results for Boston's public and public charter school students, with some areas seeing much larger changes triggered…

The ninth annual Boston Opportunity Agenda Report Card looks at how the pandemic has affected many of the indicators used to track how Boston students are doing in education from early childhood through adulthood, as well as tracking the landscape of the Opportunity Agenda's efforts to strengthen the education pipeline. This report card contains…

The purpose of this report is to describe the technical qualities of the 2018-2019 operational administration of the English language arts/literacy (ELA/L) and mathematics summative assessments in grades 3 through 8 and high school. The ELA/L assessments focus on reading and comprehending a range of sufficiently complex texts independently and…

The purpose of this report is to describe the technical qualities of the 2018-2019 operational administration of the English language arts/literacy (ELA/L) and mathematics assessments in grades 3 through 8 and high school. New Meridian, in coordination with multiple states and vendors, developed an alternate form of the summative assessment to…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…