WEBVTT

00:00:00.046 --> 00:00:03.706
[Music] Welcome to the overview

00:00:03.706 --> 00:00:06.046
on Facilitating Mathematical

00:00:06.046 --> 00:00:07.886
Problem Solving.

00:00:09.046 --> 00:00:10.856
Problem-solving skills are essential

00:00:10.856 --> 00:00:12.356
for students as they progress

00:00:12.356 --> 00:00:13.746
through the entire mathematics

00:00:13.746 --> 00:00:15.866
curriculum -- from early informal

00:00:15.866 --> 00:00:17.106
understanding through

00:00:17.106 --> 00:00:18.436
advanced mathematics.

00:00:18.646 --> 00:00:20.726
Students who learn early

00:00:20.726 --> 00:00:21.946
to analyze problems,

00:00:21.946 --> 00:00:23.946
follow a reasoning process,

00:00:23.946 --> 00:00:26.136
and construct arguments are better able

00:00:26.136 --> 00:00:28.156
to handle the complex reasoning involved

00:00:28.156 --> 00:00:30.806
in advanced mathematics.

00:00:30.806 --> 00:00:31.776
Unfortunately,

00:00:31.776 --> 00:00:33.516
international assessments show

00:00:33.516 --> 00:00:34.376
that elementary

00:00:34.376 --> 00:00:35.456
and middle school students

00:00:35.456 --> 00:00:37.046
in the United States are not

00:00:37.046 --> 00:00:38.776
as proficient in problem solving

00:00:38.816 --> 00:00:40.136
as students in many other

00:00:40.136 --> 00:00:41.566
industrialized nations.

00:00:41.606 --> 00:00:45.016
Mathematics textbooks often fall short

00:00:45.016 --> 00:00:46.786
in providing teachers and students

00:00:46.786 --> 00:00:47.956
with rich opportunities

00:00:47.956 --> 00:00:49.506
to practice problem solving.

00:00:50.246 --> 00:00:52.306
They may offer very limited guidance

00:00:52.386 --> 00:00:53.686
for teaching process skills

00:00:54.016 --> 00:00:55.736
and contain too few examples

00:00:55.736 --> 00:00:58.206
of problems, especially cognitively

00:00:58.206 --> 00:00:59.336
demanding problems.

00:01:01.116 --> 00:01:02.896
Problem solving involves more

00:01:02.896 --> 00:01:04.936
than word problems and means more

00:01:04.936 --> 00:01:07.276
than applying learned rules.

00:01:07.276 --> 00:01:09.196
It involves mathematical reasoning

00:01:09.296 --> 00:01:10.926
and using multiple strategies

00:01:10.926 --> 00:01:12.796
to solve a wide range of problems.

00:01:12.796 --> 00:01:15.526
To build students' skills,

00:01:15.836 --> 00:01:17.546
teachers should incorporate problem

00:01:17.546 --> 00:01:18.986
solving into their whole-class

00:01:18.986 --> 00:01:21.066
instruction on a daily basis --

00:01:21.066 --> 00:01:22.996
using a variety of both routine

00:01:22.996 --> 00:01:24.466
and non-routine problems.

00:01:24.466 --> 00:01:27.476
There are specific teaching practices

00:01:27.476 --> 00:01:28.846
that experts recommend

00:01:28.976 --> 00:01:30.596
to help engage students

00:01:30.596 --> 00:01:31.286
and improve their

00:01:31.286 --> 00:01:32.726
problem-solving abilities.

00:01:33.886 --> 00:01:35.816
Teachers need to take special care

00:01:35.816 --> 00:01:37.646
in selecting and preparing problems

00:01:37.706 --> 00:01:38.936
that will be the most effective

00:01:38.936 --> 00:01:41.116
in helping students understand a key

00:01:41.116 --> 00:01:42.496
mathematical concept

00:01:42.496 --> 00:01:44.526
or apply a particular strategy.

00:01:44.586 --> 00:01:47.546
Students should have the language skills

00:01:47.546 --> 00:01:49.276
and mathematical background knowledge

00:01:49.276 --> 00:01:50.696
that will allow them to focus

00:01:50.696 --> 00:01:52.096
on the reasoning required

00:01:52.096 --> 00:01:53.136
to solve problems.

00:01:53.976 --> 00:01:56.006
Teachers may need to rewrite problems

00:01:56.006 --> 00:01:58.356
by substituting contexts and words

00:01:58.356 --> 00:02:00.976
that are more familiar to students.

00:02:00.976 --> 00:02:03.256
Problems that are accessible are more

00:02:03.256 --> 00:02:05.606
likely to engage students and ensure

00:02:05.606 --> 00:02:07.416
that they understand what the problem

00:02:07.416 --> 00:02:08.036
is asking.

00:02:09.126 --> 00:02:10.936
Teachers can also focus students'

00:02:10.936 --> 00:02:12.986
attention on reasoning by reviewing

00:02:12.986 --> 00:02:14.976
in advance the mathematics concepts

00:02:14.976 --> 00:02:16.666
and skills that will be required

00:02:16.666 --> 00:02:17.726
to solve the problem.

00:02:18.826 --> 00:02:20.276
There are several instructional

00:02:20.336 --> 00:02:21.996
strategies that teachers can use

00:02:22.026 --> 00:02:23.726
to guide students as they learn how

00:02:23.726 --> 00:02:25.366
to tackle mathematics problems.

00:02:26.136 --> 00:02:28.946
These include: - using thinkalouds

00:02:29.036 --> 00:02:29.886
to guide students

00:02:29.886 --> 00:02:31.876
in creating visual representations

00:02:31.876 --> 00:02:33.836
of relevant information in the problem,

00:02:34.356 --> 00:02:35.546
- encouraging students

00:02:35.546 --> 00:02:37.076
to explore multiple ways

00:02:37.076 --> 00:02:39.026
to solve the problem, and -

00:02:39.026 --> 00:02:40.466
demonstrating how to break

00:02:40.466 --> 00:02:42.146
down the problem into steps

00:02:42.146 --> 00:02:43.376
that can then be expressed

00:02:43.376 --> 00:02:45.526
through formal mathematical notation.

00:02:46.956 --> 00:02:47.936
Students who learn

00:02:47.936 --> 00:02:49.766
to create visual representations

00:02:49.766 --> 00:02:50.936
of a problem's components

00:02:50.936 --> 00:02:52.966
and steps prior to translating them

00:02:52.966 --> 00:02:54.236
into equations tend

00:02:54.236 --> 00:02:56.276
to be more effective problem solvers.

00:02:57.246 --> 00:02:59.186
The most useful visuals are those

00:02:59.186 --> 00:03:00.846
that link the quantities in a problem

00:03:00.846 --> 00:03:02.736
to the mathematical operations needed

00:03:02.736 --> 00:03:03.886
to solve the problem.

00:03:04.646 --> 00:03:06.776
Teachers can talk students through how

00:03:06.776 --> 00:03:08.266
to present the problem's essential

00:03:08.266 --> 00:03:10.136
information in appropriate visuals,

00:03:10.176 --> 00:03:14.156
such as tables, number lines, graphs,

00:03:14.236 --> 00:03:17.276
strip diagrams, and so forth.

00:03:17.276 --> 00:03:18.546
Researchers recommend

00:03:18.546 --> 00:03:20.396
that students be explicitly taught

00:03:20.396 --> 00:03:22.016
that problems can be solved in more

00:03:22.016 --> 00:03:22.796
than one way.

00:03:22.796 --> 00:03:24.926
Students who practice multiple

00:03:24.986 --> 00:03:26.756
strategies and share their solutions

00:03:26.756 --> 00:03:27.786
with each other learn

00:03:27.786 --> 00:03:29.876
to become more flexible and efficient

00:03:29.876 --> 00:03:30.956
in problem solving.

00:03:31.886 --> 00:03:33.116
Encouraging students

00:03:33.116 --> 00:03:34.526
to compare different approaches

00:03:34.526 --> 00:03:36.646
to problems and explain their reasoning

00:03:36.646 --> 00:03:38.796
to each other strengthens the notion

00:03:38.796 --> 00:03:40.046
that there are multiple ways

00:03:40.106 --> 00:03:41.236
to approach problems.

00:03:41.446 --> 00:03:44.556
Students may prefer a more intuitive

00:03:44.556 --> 00:03:46.096
approach to problem solving.

00:03:46.836 --> 00:03:48.906
Teachers can build on that understanding

00:03:49.046 --> 00:03:50.766
by showing how to express problems

00:03:50.766 --> 00:03:52.306
through mathematical notation,

00:03:52.476 --> 00:03:54.366
including algebraic notation.

00:03:55.156 --> 00:03:56.806
While working through problem solving

00:03:56.806 --> 00:03:57.696
with students,

00:03:57.696 --> 00:03:59.326
teachers can take the opportunity

00:03:59.326 --> 00:04:01.076
to review or explain relevant

00:04:01.076 --> 00:04:02.386
mathematical concepts.

00:04:02.426 --> 00:04:06.036
Finally, teachers can help students

00:04:06.036 --> 00:04:08.036
monitor their thinking and reflect

00:04:08.036 --> 00:04:09.876
on the problem-solving process

00:04:09.876 --> 00:04:12.036
by using question prompts or a list

00:04:12.036 --> 00:04:14.346
of problem-solving steps.

00:04:14.346 --> 00:04:16.516
Students can be encouraged to reflect

00:04:16.516 --> 00:04:17.666
on their own processes

00:04:17.666 --> 00:04:18.946
and share them with others.

00:04:19.745 --> 00:04:21.116
When students discuss their

00:04:21.116 --> 00:04:22.646
problem-solving strategies

00:04:22.646 --> 00:04:23.306
with each other,

00:04:23.626 --> 00:04:25.156
they get valuable practice

00:04:25.156 --> 00:04:26.676
in explaining their reasoning

00:04:26.886 --> 00:04:28.826
and reinforce their understanding

00:04:28.826 --> 00:04:29.696
of the steps in the

00:04:29.696 --> 00:04:32.236
problem-solving process.

00:04:32.236 --> 00:04:33.556
There's a lot involved

00:04:33.556 --> 00:04:35.016
in helping students become better

00:04:35.016 --> 00:04:35.996
problem solvers: -

00:04:36.056 --> 00:04:38.526
carefully selecting problems, -

00:04:39.096 --> 00:04:40.986
using visual representations, -

00:04:41.596 --> 00:04:43.216
encouraging multiple approaches

00:04:43.216 --> 00:04:44.016
to problems, -

00:04:44.506 --> 00:04:46.176
teaching mathematical notation, -

00:04:46.176 --> 00:04:48.746
reflecting on the steps, and -

00:04:48.746 --> 00:04:50.416
debriefing strategies together.

00:04:51.206 --> 00:04:52.656
While teachers may not be able

00:04:52.656 --> 00:04:54.646
to incorporate all these recommendations

00:04:54.646 --> 00:04:56.666
at one time, they should all be

00:04:56.666 --> 00:04:58.616
considered when preparing whole-class

00:04:58.616 --> 00:04:59.746
mathematics lessons.

00:05:01.626 --> 00:05:03.776
You will find materials on this site

00:05:03.776 --> 00:05:04.926
to provide information

00:05:04.966 --> 00:05:05.706
about the teaching

00:05:05.706 --> 00:05:07.416
of mathematical problem solving.

00:05:08.246 --> 00:05:10.156
Each recommended practice includes

00:05:10.156 --> 00:05:11.386
background information,

00:05:11.666 --> 00:05:13.516
expert explanations of content

00:05:13.516 --> 00:05:15.296
and pedagogy, and examples

00:05:15.296 --> 00:05:16.796
of how teachers have implemented

00:05:16.796 --> 00:05:18.506
the practices.

00:05:18.506 --> 00:05:20.796
Begin with the multimedia overviews

00:05:20.796 --> 00:05:22.936
and expert interviews for each practice

00:05:22.936 --> 00:05:24.796
in the Learn What Works section.

00:05:25.746 --> 00:05:27.876
Watch teachers using the recommended

00:05:27.876 --> 00:05:29.016
teaching practices

00:05:29.016 --> 00:05:30.936
in the See How It Works section.

00:05:31.776 --> 00:05:34.196
Use the tools in the Do What Works

00:05:34.226 --> 00:05:36.386
section to conduct your own professional

00:05:36.386 --> 00:05:38.576
development, develop lessons,

00:05:38.576 --> 00:05:39.976
and review existing practices.

00:05:41.516 --> 00:05:44.500
[Music]