More About MathsRepublic's Problem-based Lessons

Students should not just learn about mathematics, they should do mathematics.

This can be defined as engaging in the mathematical practices: making sense of problems, reasoning abstractly and quantitatively, making arguments and critiquing the reasoning of others, modelling with mathematics, making appropriate use of tools, attending to precision in their use of language, looking for and making use of structure, and expressing regularity in repeated reasoning.

The purpose of the Lessons available to Teachers after Registering for a Free Trial (www.MathsRepublic.com.au) is to impact student learning and achievement.

First, we define the attitudes and beliefs about mathematics and mathematics learning we want to cultivate in students, and what mathematics students should know and be able to do.

Attitudes and Beliefs We Want to Cultivate

Many people think that mathematical knowledge and skills exclusively belong to “maths people.”

Research shows however, that students who believe that hard work is more important than innate talent learn more mathematics.

We want students to believe anyone can do mathematics and that persevering will result in understanding and success. We want students to develop a “productive disposition—[the] habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.”

Conceptual understanding: Students need to understand the why behind the how in mathematics. Concepts build on experience with concrete contexts. Students should access these concepts from a number of perspectives in order to see maths as more than a set of disconnected procedures.

Procedural fluency: We view procedural fluency as solving problems expected by the standards with speed, accuracy, and flexibility.

Application: Application means applying mathematical or statistical concepts and skills to a novel mathematical or real-world context.

These three aspects of mathematical proficiency are interconnected: procedural fluency is supported by understanding, and deep understanding often requires procedural fluency. In order to be successful in applying mathematics, students must both understand and be able to do the mathematics.

What T&L should look like

How teachers should teach depends on what we want students to learn?

To understand what teachers need to know and be able to do, we need to understand how students develop the different (but intertwined) strands of mathematical proficiency, and what kind of instructional moves support that development.

Principles for Mathematics Teaching and Learning

Active learning is best: Students learn best and retain what they learn better by solving problems. Often, mathematics instruction is shaped by the belief that if teachers tell students how to solve problems and then students practice, students will learn how to do mathematics.

Our signature mathematical language routines (MLRs) offer detailed guidance for developing students into mathematical thinkers. Facilitate and assess students’ ability to communicate mathematical thinking verbally, visually, and in writing.

Every lesson plan contains topic-specific professional learning resources. Our materials speak intelligently and professionally to educators, meeting teachers where they are in their practice and advancing them.

Whether it’s for below-benchmark students or accelerated learners, MathsRepublic’s Lessons provide content-specific resources within lessons, from warm-up to cool down.

Discussion-filled classrooms beget deeper learning. Our materials encourage student communication and the development of problem-solving and reasoning skills.

Teachers Love the ‘Anticipated Misconceptions’

Educators can easily prepare to recognize, analyse, and respond to common student struggles thanks to the scaffolding provided with each lesson.

Each course contains nine units. Each of the first eight are anchored by a few big ideas in grade-level mathematics. Units contain between 11 and 23 lesson plans.

Each unit has a diagnostic assessment for the beginning of the unit (Check Your Readiness) and an end-of-unit assessment. Longer units also have a mid-unit assessment. The last unit in each course is structured differently, and contains optional lessons that help students apply and tie together big ideas from the year.

The time estimates in these materials refer to instructional time. Each lesson plan is designed to fit within a class period that is around an hour long. Some lessons contain optional activities that provide additional scaffolding or practice for teachers to use at their discretion.

Students can work solely with printed tasks distributed by their teacher. Later when all students have access to an appropriate device, students will be able to view look at the Task Statements on that device and write their responses in their workbook.

Teachers can access the teacher materials either in print or in a browser.

A classroom with a digital projector is recommended for Teachers to project the Student Task Statements.

Many activities are written in a card sort, matching, or info gap format that requires teachers to provide students with a set of cards or slips of paper that have been photocopied and cut up ahead of time.

Teachers might stock up on two sizes of resealable plastic bags: sandwich size and a larger size. For a given activity, one set of cards can go in each small bag, and then the small bags for one class can be placed in a large bag.

If these are labelled and stored in an organized manner, it can facilitate preparing ahead of time and re-using card sets between classes. Additionally, if possible, it is often helpful to print the slips for different parts of an activity on different color paper.

This helps facilitate quickly sorting the cards between classes.