Enriching mathematical learning experience using group tasks Yik Ching Lee (Josh), Matt Wilkins, Emily Saavedra Massey University

Group tasks as guided discovery Collaboration Guided instruction Teacher support Student responsibility You do together We do You do I do Independent practice discovery Modelled instruction

Why work in group? construct meaning through communications strengthen subject knowledge develop professional skills Image source: https://openclipart.org/detail/227550/students-group-work

Low-Threshold-High-Ceiling tasks Image modified from https://www.freepik.com/free-photos-vectors/swimming Relatively simple, yet challenging

L T H C Why LTHC tasks? meet the needs of a wide range of learners capacity to think, reason, and problem solve positive classroom culture motivate and challenge learners

How? “Enabling prompts” Image source: https://www.kisspng.com

How? “Extending prompts” Image source: https://www.vectorstock.com

Implementing LTHC tasks in classroom word problems small groups a summary activity Image source: https://www.vectorstock.com

Example of a LTHC task “Pete's Pastries sells doughnuts and cronuts. Tell Pete the best number of doughnuts and cronuts to make, to maximize his profit. Unfortunately Pete can't make, store, or afford an unlimited number of these yummy pastries, he has a number of constraints: 1. Only enough storage space to keep 140 pastries total. 2. He wants to make at least 36 cronuts since that allows him to fill his cronut display case. 3. Doughnuts cost $2 each to make, cronuts $5 each. He has $610 to buy the ingredients. 4. Pete works really hard, but even so, he only has 6 hours of time available per week to make pastries. Doughnuts require 3 minutes to make, cronuts 2 minutes.”  Profit is $3 per doughnut and $4 per cronut. So P = 3x + 4y Make y the subject, and draw the profit lines for a range of sensible P values to find the profit line that has at least one (x, y) point in the feasible region that is maximizing P. An example of one of the tasks which required algebra to model inequalities

Objective of the study y = mx + c words Image source: http://www.brocku.ca

The cohort pre-degree Foundation Mathematics 2 class PaCE, Massey University, Albany. international and domestic students.

Method Surveyed 29 students Overt observations

What do students think of group tasks? Image source: https://www.newlinkstraining.com 70% found group tasks useful. Students showed a high satisfactory level of learning.

Student feedback (Positive) “An activity to interact with classmates and being given a chance to talk about what we understand and what we don't.” Student A “Allow us to practice what we learned with another brain.” Student B “Useful when you are unsure about a topic and others in group can help.” Student C Image source: https://www.123rf.com

Social interaction and active learning Enthusiastic and active about sharing ideas Social interaction leads to enhanced knowledge Genuine learning via exchanging ideas. Image source: http://diysolarpanelsv.com

For low confident or average students Inclusive & address learner differences Opportunity to transform experience into knowledge A sense of achievement upon completing parts of group tasks

For high achieving students Active engagement Altruism Self-efficacy Positive behaviours Image source: https://www.vectorstock.com

Student feedback (Negative) “People work at different pace, hard to collaborate.” Student D “One person usually dominates, while others slack out.” Student E “Depends on group members, not all are engaged. Prefer individual task.” Student F Image source: https://www.vectorstock.com

Factors affecting the success of the use of group tasks heterogeneous group relatively ineffective group work learn about the progress of students to provide feedback. https://all-free-download.com

What is next? narratives performance measures students’ attitudes prior to the implementation Image source: https://www.vectorstock.com