ACE Mathematics Newsletter
3 - 8 Mathematics | OCT 2018 YEAR 3: VOL. 1
In this Edition:
Mathematics Instructional Block: Aggressive Monitoring
Instructional Planning Tools: Instructional Planning Calendars & Assessment of Course Performance (ACP) Exemplars
Instructional Trends in Mathematics: Embracing the Power of Productive Struggle in Math
Math Team Thursday: Recap October 18, 2018 Session
Upcoming Professional Development: Math Team Thursday
Announcements: ACE Website
As many of our campuses continue developing their systems for aggressively monitoring students' performance and comprehension, it is critical that we review both rationale and instructional benefits for implementing this practice.
Actively observing, interacting (checking for understanding) and gathering data of students' understanding and performance throughout a lesson.
- Raises the accountability factor in students.
- Teachers are able to receive and provide real-time feedback about errors and misconceptions.
The intent is to check students' independent work to determine whether they are learning what you are teaching.
Create & implement a monitoring pathway:
- Create a seating chart to monitor students most effectively.
- Monitor higher achievers first then proceed to struggling students.
Monitor the quality of student work:
- Check answers against your exemplar.
- Track correct and incorrect answers to class questions.
Pen in Hand: mark up student work as you circulate.
- Use a coding system to affirm correct answers.
- Cues students to revise answers, using minimal verbal intervention. (Name the error, ask them to fix it, tell them you will follow up.)
Instructional Planning Tools
The following tools can be found on the ACE website under Instructional Planning Tools.
Instructional Planning Calendars
When reviewing the Instructional Planning Calendars, pay close attention to the proposed unpacking of the targeted standards that support teaching using a conceptual trajectory of content development. Note the instructional resources section for suggested strategies, manipulatives, and anchor charts to incorporate into instruction. The links below can be used to access the grade-specific calendars.
Assessment of Course Performance (ACP) Exemplars
Assessment of Course Performance Sample Items are provided by the STEM Department, Mathematics, and mirror the student expectations that will be administered on the December assessments. The strategies pictured are recommended but are not the only strategies that can be used. A teacher’s tool box must be filled with multiple test-taking strategies that can be shared with students.
Productive struggle is a highly effective methodology when it comes to teaching math and other STEM related subjects. Used mostly in the primary level, it involves letting students deal with problems and puzzles on their own, even when they are a bit too advanced for them, and letting them figure out to how to solve them. This, which may seem counterintuitive, is actually intended to let students resort to their own creativity to find possible solutions to problems that do not necessarily have a single way to approach them.
Different studies have led to the conclusion that struggling to make sense of mathematics is an essential part of the learning process, and is the most efficient way to get students to really understand the topics at hand. Unfortunately, struggle is not often perceived as a positive and constructive part of the learning process and, rather, it is treated as failure both by the learner and the teacher. And with curriculums that are designed to move from one topic to the other, regardless of the students’ capacity to master a particular knowledge before moving on, are creating major problems in the study of this field.
Many math courses are taking a dubious approach in which the correct answer is valued more than reasoning and understanding, and where strict formulas are provided in a lecture-like manner, without giving students the possibility to discuss them or to fully understand why they work the way they do. According to some specialists, this leads to students who lack confidence in their abilities, and who – because of this insecurity – are reluctant to put the effort to understand. A problem which is worsened by popular beliefs like that you are either good in mathematics, or that you are not.
Productive Struggle is a methodology that was proposed to end this, and to foster true understanding of math related topics in students of all levels and ages, but especially among younger ones. The goal of this technique is to help students make sense of problems and persevere in solving them, no matter how difficult they find them to be. In order to apply this methodology, teachers present a problem to the class, and give individual students time to think it in on their own. These problems can be framed in any way, but according to recent research studies, problems that have a real-life feel to them are often more meaningful, as students can apply their personal experience, and feel more secure when working out the answer.
After giving students enough time to develop a strategy to resolve the problem and to try it out, fail, and start over, until they figure out an effective way to reach a solution, teachers gather students in small groups, where different solutions are meant to be compared, and used to come up with a better solution based on what the group learnt. Finally, the whole class is meant to discuss the problem, and all the proposed solutions. During the course of the exercises, teachers are not supposed to help students out other than encouraging them, or helping them identify the source of their struggle (are they having trouble identifying how to get started, or how to lay down a strategy? Or are they having a problem applying their line of thought?), or just by pointing out that difficulties are an essential part of learning, and that failing is ok so long as they try.
Only after the whole class has discussed the possible solutions and the different answers, teachers are allowed to draw a map to the solution, and to provide students with tools and tasks that may help them in the future. But, according to experts, it is important that they address that math is hard, and that it is supposed to feel complicated in order for it to be understood, as a means to downsize frustration and encourage students to keep trying.
Math Team Thursday
Math TEAM Thursday on October 18, 2018, focused on developing mathematical concepts through the learning progression of exposing students to concepts through concrete objects, pictorial representations and then abstract representations. Following the constructivist theory of learning that states a learner must construct their understanding of learning to truly own the learning, the three phases are:
· Concrete – Students interact with common objects as well as mathematics manipulatives to explore a concept.
· Pictorial – Students draw pictures that represent the manipulatives to eliminate the need for the actual objects and begin to move to the abstract.
· Abstract – Students represent a concept using words, symbols, and numbers.
Team leaders, classroom instructional coaches, and assistant participants engaged in exploring bundled student expectations from third grade involving fractions through a lesson using licorice that included all three phases of development.
Participants analyzed their grade-level student expectations from the 3rd six weeks Instructional planning calendar to determine where each SE fell along the conceptual spectrum. Using the same lens, participants were asked to decompose a student expectation to the level of specificity and implications for instruction.