As we began the year, we sought to identify skills that our twenty-first century learners would need for success, not only during their years at school, but beyond. Each group of learners is unique, but as we identified the strengths of our current students, we also began to wonder if there were specific areas of growth and learning that applied to many students within our classrooms. These musings became the focus of two specific inquiry projects throughout the year, focusing on numeracy and writing.
How can performance tasks or problem solving allow students to recognize and justify their work using specific criteria? Will students be able to communicate their learning using a variety of strategies to explain and justify their mathematical ideas and decisions?
How does using student generated goals improve the quality of student writing (conventions, detail, adjectives, sentence beginning)?
Children arrive at school with intuitive mathematical understandings. A teacher needs to connect with and build on those understandings through experiences that allow students to explore mathematics and communicate their ideas in a meaningful dialogue with their teacher and peers. Math is no longer about computations and algorithms. This past year, we implemented a variety of strategies that allowed students to find success in math at their own level. Our goal this year has been to help students become flexible in their thinking and to use a variety of different approaches to solve math word problems. In order to do this, we implemented specific approaches to use while working through a problem. By applying these approaches, we are aiming for an intentional shift of focus - transitioning from memorization and using only one formula to solve a problem, to be confident in using multiple strategies and sharing their reasoning. We flip the traditional pedagogy and start with the problem, see what we know and what we need to figure out, and then along the way introduce the skills and strategies that will help guide students to the be more flexible in their mathematical thinking.
"In my first work, I answered without knowing any strategy, then I started using CUBES. By doing so, I'm able to know what I will be solving, and I know what the question is asking. Evaluating and drawing helps the reader know what is going on and makes it easier to solve."
To explain their understanding of problem solving and performance tasks, our grade 4 and grade 7 students communicated math ideas and understanding in oral, written, and visual forms. We documented growth of students during this process. Teachers also recorded observations during group work, conferenced with individual students, and students reflected and self-assessed their own progress. Students focus was to recognize and use different approaches and strategies to solve problems.
The importance of problem-solving in learning mathematics comes from the belief that mathematics is primarily about reasoning, not memorization. Problem-solving allows students to develop understanding and explain the processes used to arrive at solutions, rather than remembering and applying a set of procedures Problem-solving in mathematics supports the development of:
The ability to think creatively, critically, and logically
The ability to structure and organize
The ability to process information
Enjoyment of an intellectual challenge
The skills to solve problems that help them to investigate and understand the world
A mathematical performance task includes learning activities and assessments that require students to produce a product that demonstrates their understanding and proficiency. This practice measures how well a student can apply or use what he or she knows, often in real-world situations.
Students are asked to do more than recall knowledge with performance tasks. They are asked to apply what they know to a new problem. These tasks typically don’t have one solution. Problems are open-ended and allow for different pathways to arrive at feasible solutions. Performance tasks enable teachers to gather evidence not just about what a student knows, but also what he or she can do with that. Rather than asking students to recall facts, performance tasks and word problems measure whether a student can apply his or her knowledge to a new problem.
This year a grade 4 class and grade 7 class worked on using problem solving strategies when trying to solve a math problem or a performance task. As a class we worked on going through problem solving steps and strategies to use when approaching a problem.
Students became more familiar with the four steps of problem solving: Understand, Execute, Plan and Review. By allowing our students to grapple with these challenging problems we are helping them acquire essential problem-solving skills and the confidence needed to successfully execute them.
Problem Solving Steps:
This is a time to think. You cannot solve a problem until you know what the problem is! Students are asked to read and re-read the problem. To further develop their understanding, students are asked to circle the numbers, underline the question, and box the key words. By using this visual technique, it helped students better understand the problem.
Now it’s time to decide on a plan of action! Students evaluate and choose a reasonable problem-solving strategy. Several strategies have been taught and are listed on anchor charts that they can refer to.
Now students understand the problem and have a plan to solve it. Now it’s time to dig in and get to work! Students employ their chosen strategy/strategies to solve. Here, students may draw a visual representation of the problem. As they work, they may need to revise their plan.
Students must always go back and check their work. Reviewing their work is just as important as the first 3 steps! Students are asked to reread the problem and review all their work. They may use estimation, inverse operations, or another strategy to help them review.
"I don't overthink the problem because I now follow the steps and feel confident."
After the end of our first Learning Sprint, we noticed that students were beginning to use the steps to solve a problem. Our next step was having students self-assess their own work in order to build confidence in their problem-solving abilities and justification of their work. At this point we tweaked the criteria so that it was student friendly and with more detailed descriptions, allowing students to further breakdown their approach. We discovered that this greatly improved students’ self-efficacy overall in the results.
"I feel I can organise my work better, and I understand the problem better if I use the flip chart."
How does using student generated goals improve the quality of student writing (conventions, detail, adjectives, sentence beginning)?
-do students do better with goal setting and self-reflection? If so, why?
-are students able to independently work on the skill and become self-motivated to achieve their goal? And how is this accomplished?
At every grade level, students engage in various writing practices for different audiences and purposes. They develop their communication skills by utilizing proper language conventions such as spelling, punctuation, and so on. As students’ progress through the grade levels, their writing skills evolve as they learn to craft logical sequences, incorporate details, and increase sentence complexity. Despite these improvements, students often require specific, measurable, achievable, and realistic writing goals to enhance their writing abilities. We wondered whether this approach would enhance students' self-confidence in writing. If students set writing goals collaboratively with their teacher and track progress over time, would this motivate them to achieve their goal? Throughout the year, students explore different writing components and language conventions through whole-class lessons and units. However, we questioned whether providing individual students with a tailored writing goal, such as using conventions effectively, including more details or adjectives, and diversifying sentence starters, would result in improved writing skills.
During our initial 4-week sprint in Term 2, we collaborated with 40 students ranging from grades 2-4 to successfully launch our writing portfolios. These included personalized writing goals as part of our effort to aid students in improving their writing skills in the areas of conventions, meaning, form, and style. By receiving comment-only feedback in small groups, students were able to identify their personal writing strengths and areas for improvement. They then established their own writing objectives, which they pursued during independent writing periods with the inclusion of different resources, such as comic-strip templates and brain maps, in their writing folders. These resources provided support to organize their ideas and create multiple drafts of personal narratives to select from.
“I like using writing goals because when I achieve it I think it makes my writing better and that makes me feel good."
Throughout the school year, our students were provided with personalized writing goals through the use of individual writing folders. Although different classes may have emphasized various skills as a group, our students engaged in small group writing workshops and one-on-one conferences to establish a specific, achievable writing goal for themselves during independent writing time. By participating in daily writing activities, the students were able to take ownership of their learning and development through focusing on their designated objective. Our hope was for students to see more substantial progress over the year by narrowing down their focus to one goal tailored to their individual writing needs. These writing folders also contained anchor charts and a rubric which aided in the students' self-reflection during each writing session. Ultimately, the writing folders served as a tool for the students to comprehend and achieve their writing goals
“I like our writing folders because it helps me notice things that I need to keep working on, and when I feel stuck I can just look back and remember.”
Student 1: “I like using the thesaurus to help me meet my writing goal. I am learning how to add ‘wow’ words so my writing is interesting.”
As the academic year progressed, our students engaged in two "sprints" of writing that were tailored to their individualized writing goals. Our initial sprint spanned from January to March, lasting six weeks, while our subsequent sprint transpired from April to May, also for six weeks. We made several noteworthy observations. First, our students' stamina and productivity improved. Initially, most of them found it challenging to write for the entire duration of the activity, which typically lasted for thirty minutes. However, with time, their writing endurance increased, leading to a significant rise in their output. This experience also helped build their confidence as they became more aware of their writing strengths. Additionally, we noticed our students became more self-motivated, frequently working on writing tasks beyond the classroom environment. They eagerly set new writing goals and showed great enthusiasm in achieving them. Interestingly, this self-reflection helped them identify areas that required improvement, notably, the need to edit their work. As teachers, we observed a remarkable sense of independence among our students as they accomplished their writing goals and continued to set newer ones.
Student 3: “I feel good when I meet my goals. It makes me happy that I actually improved on something. I’m proud of the wow words I used. I would look at a word and think about how I could change it to make it sound better.”
Moving forward, we will continue to provide explicit instruction on the problem-solving strategies and students will continue to work on self-assessing their work. We want students to extend their thinking by solving a problem using multiple strategies. In order to achieve this, we will use the 4 Quadrant math problem solving organizer. Students will work in groups on a problem using the method shown below. As a class we will model effective math strategies and techniques. We would also provide opportunities for students to practice their skills in groups. After students have completed their work, we will display and discuss one problem at a time. We will compare ways they solved problems, graphed, or drew problems, and their thinking behind the problem. This will allow all the students to really “see” other ways to solve the same problem.
This year we observed that students were intrinsically motivated to achieve their writing goals, which boosted their confidence and enabled them to reflect on their writing progress regularly. Weekly conferences with their teacher were instrumental in assisting students in determining the necessary next steps in their writing process, whereas peer editing sessions helped them to look for ways to improve their writing through feedback such as using descriptive language and engaging the readers' senses. The provided resources such as using a thesaurus, anchor charts, word walls, and word lists to help them with transitions and adding details to their writing have also assisted them in expanding their writing. For instance, a student shared how she could use words like "drowsy," "exhausted," and "weary" instead of merely saying "tired" based on the synonyms that she could use from the word bank handouts for emotions.
Student 2: “I have found I write more. It helps me keep track of my writing goals”
Moving forward, we will continue to provide explicit instruction on the writing process and types of writing, as well as model effective writing strategies and techniques. We would also provide opportunities for students to practice their writing skills in a variety of contexts and settings, including creative writing, research-based writing, and persuasive writing. We would also continue to incorporate peer review and feedback activities to help students learn to give and receive constructive criticism. Lastly, we would use assessment tools such as a checklist or rubric catered to individual writing goals to monitor and adjust our instruction as needed, and provide ongoing feedback to students and their families on their progress towards their writing goals. We aim to witness an improvement in students writing style and voice from its earliest draft, prior to revisions and edits. Our hope is that with individualized goals, students would enhance their unique writing style and observe their own implementation of new vocabularly. By implementing these steps and providing ongoing support, we are confident that our students' writing skills will continue to improve and flourish.
Student 4: “I am proud of myself because I can use 'wow' words instead of just using simple words. For example instead of saying big, I can say ‘huge’ or ‘gigantic’. My writing stamina has also improved when I focus".