Environmental Literacy Education and Sustainable Development in Schools Based on Teaching Effectiveness

Through teaching effectiveness evaluation, educators can understand which environmental literacy education methods are effective and which need improvement, thereby optimizing teaching methods and improving teaching quality. This helps to assess students' learning outcomes in environmental literacy education, promptly discover students' knowledge gaps and needs, and provide targeted educational resources. The evaluation index system for the teaching effectiveness of environmental literacy education should comprehensively and multi-dimensionally evaluate students' environmental knowledge, skills, attitudes, and behavior. The index system constructed in this study is as follows:

Knowledge mastery:

a) Basic environmental knowledge: Understand basic concepts, principles, and policies and regulations in the environmental field.

b) Interdisciplinary knowledge: Understand geography, biology, chemistry, and other interdisciplinary knowledge related to environmental protection.

c) Environmental problem analysis: Possess the ability to analyze environmental problems and understand the causes and impacts of environmental issues.

Skill development:

a) Environmental protection skills: Master practical environmental protection skills, such as waste sorting, energy-saving emission reduction, and ecological restoration.

b) Problem-solving ability: Possess the ability to analyze, evaluate, and solve environmental protection problems.

c) Team collaboration and communication: Be able to play a role in the team and effectively communicate environmental awareness and perspectives with others.

Attitudes and awareness:

a) Environmental awareness: Possess a high level of environmental awareness, pay attention to environmental issues, and care about our planet.

b) Environmental responsibility: Possess a sense of social responsibility, actively participate in environmental protection activities, and contribute to environmental protection.

c) Self-reflection: Be able to reflect on one's behavior's impact on the environment and actively improve.

Practical behavior:

a) Environmental behavior: Actively participate in environmental protection actions in daily life, such as resource conservation and low-carbon living.

b) Social participation: Participate in environmental protection organizations and activities, promoting the development of environmental protection causes.

c) Knowledge dissemination: Spread environmental knowledge and concepts to others, raising others' environmental awareness.

This study evaluates teaching effectiveness of environmental literacy education based on fuzzy comprehensive evaluation. First, according to the evaluation index system of environmental literacy education teaching effectiveness, an evaluation factor set is constituted. A set of evaluation comments, such as excellent, good, average, and poor, is set for each evaluation factor, constituting a comment set. Let I represent the evaluation factor set of environmental literacy education teaching effectiveness, and I characterize the fuzzy set composed of various influencing factors affecting the teaching effectiveness of environmental literacy education, satisfying I=(i_u), u=1,2,...,b. Let C represent the comment set, characterizing the collection of evaluation results corresponding to each evaluation index given by the evaluator, satisfying C=(c_k), k=1,2,...,b.

According to the actual teaching situation, establish membership function relationships between each evaluation factor and the comments in the comment set, and construct a fuzzy relation matrix. The membership function is a value between 0 and 1, indicating the degree of membership of the evaluation factor on the comments. Let the membership relation between i_u in I and c_k in C be represented by e_uk, then:

$\begin{aligned} & e_{u k}=\left\{\begin{array}{l}1, z<s \\ \left(\frac{z-s}{n-s}\right)^k, s<z \leq n \\ 0, z>n\end{array}\right. \\ & e_{u k}=\left\{\begin{array}{l}1, z \geq s \\ \left(\frac{z-s}{n-s}\right)^k, n \leq z<s \\ 0, z<n\end{array}\right. \\ & e_{u k}=\left\{\begin{array}{l}0, z \leq s \\ \frac{z-s}{n-s}, s \leq z \leq n \\ 1, n \leq z \leq v \\ \frac{f-z}{f-v}, v<z \leq f \\ 0, z>f\end{array}\right.\end{aligned}$

$e_{\imath k}=\left\{\begin{array}{l}0, z \leq s \\ \frac{z-s}{n-s}, s<z \leq n \\ \frac{v-z}{v-n}, n \leq z \leq v \\ 0, z>v\end{array}\right.$              (1)

$E=\left[\begin{array}{cccc}e_{11} & e_{12} & \cdots & e_{1 b} \\ e_{21} & e_{22} & \cdots & e_{2 b} \\ \cdots & \cdots & \cdots & \cdots \\ e_{l 1} & e_{l 2} & \cdots & e_{l b}\end{array}\right]$              (2)

Assign weights to each evaluation factor according to the importance of the evaluation factors, forming a weight vector. Then, perform matrix operations on the fuzzy relation matrix and the weight vector to obtain the fuzzy evaluation vector. This study uses the analytic hierarchy process (AHP) to determine the weights of the indicators, and the second-level indicators of the index system need to undergo weight synthesis. Suppose the weight vector synthesized by the secondary indicators is represented by S, then the fuzzy evaluation vector N=S●E using the most widely used MM(●,+) logical operation model.

Based on the membership values in the fuzzy evaluation vector, apply the weighted average principle to calculate the comprehensive evaluation value of each evaluation factor. Finally, according to the comprehensive evaluation value, conduct an overall evaluation of the teaching effectiveness of environmental literacy education. To achieve the ranking and selection of the evaluation objects, further sum up the ranks of each level of the environmental literacy education teaching effectiveness evaluation index system based on the weighted average principle. Suppose the rank of environmental literacy education teaching effectiveness is represented by b, and the membership degree of the result vector belonging to the bth level is represented by n_b. The undetermined coefficient (j=1 or j=2) is represented by J, and in this study, 1 is taken. The percentile interval median of the bth level is represented by z_b. The fuzzy comprehensive evaluation result L of the teaching effectiveness of environmental literacy education can be obtained by calculating the following formula:

$L=\frac{\sum_1^b n_b^j \cdot z_b}{\sum_1^b n_b}$                    (3)

2.png

Figure 2. Algorithm flow of environmental literacy education resource recommendation for promoting sustainable school development

In order to obtain more accurate similarity calculation results, assume that the total number of environmental literacy education resource projects rated by student g and student f in the source domain is represented by U_gf, and the total number of educational resources evaluated by the two students in the source domain is represented by YTO. Introduce the following calculation:

$X S D(g, f)=\frac{\left|U_{g f}\right|}{Y_{T O}}$                         (8)

By multiplying Formula 1 and Formula 2, a more accurate similarity calculation result can be obtained:

$\begin{aligned} & \operatorname{SIM}_i(g, f)= \frac{\sum_{u \in U_g \cap U_f}\left(e_{g u}-\bar{e}_g\right) \times\left(e_{f i}-\bar{e}_f\right)}{\sqrt{\sum_{u \in U_g \cap U_f}\left(e_{g u}-\bar{e}_g\right)^2}} \times \frac{\left|U_{g f}\right|}{Y_{T O}} \quad \times \sqrt{\sum_{u \in U_g \cap U_f}\left(e_{f u}-\bar{e}_f\right)^2}\end{aligned}$                   (9)

One of the key steps in a recommendation system is predicting students' ratings of educational resources in the target domain. The significance of calculating target domain ratings lies in predicting students' ratings of educational resources in the target domain (environmental literacy education field) based on their ratings, interests, and knowledge in the source domain, as well as information from other similar students. If there are no similar student users in the source domain, the rating matrix needs to be filled. Assume that the value to be filled is represented by A_SC, the similarity value between students is represented by SIM_i(g,f), and the rating value of similar students for environmental literacy education resource projects in the target domain is represented by e. The following formula gives the predicted value of the target domain rating when the similarity is between [0.4,1].

$A_{S C}=S I M_i(g, f) \times e$                      (10)

Using the results of environmental literacy education teaching effectiveness evaluation as part of the students' latent features can help the recommendation system better understand students' needs and performance in environmental literacy education. This study divides the evaluation results into multiple dimensions (such as knowledge mastery, practical ability, attitude and values, etc.) and includes these dimensions in the students' latent feature vectors. In this way, when calculating similarity and predicting ratings, the recommendation system can fully consider students' teaching effectiveness evaluation results.

User latent feature sequencing refers to analyzing students' ratings and behavioral data in the source domain in the recommendation system, and mining students' latent features (such as interest preferences, knowledge structure, etc.). The significance of this step is to convert students' ratings and behavioral data into more easily understood and processed latent features, providing a basis for subsequent recommendation calculations. At the same time, by mining latent features, a better understanding of students' needs and interests can be achieved, thus providing more accurate environmental literacy education resource recommendations. Figure 3 shows an example of feature matrix update.

3.png

Figure 3. Schematic diagram of feature matrix update

In this study, the user feature matrix of students in the source domain and the feature matrix of environmental literacy education resource projects are generated based on the Funk-SVD model matrix decomposition, as well as the student user feature matrix and environmental literacy education resource project feature matrix in the target domain. Funk-SVD uses mean square error as the loss function, and the objective function is given by the following formula:

$\arg \min _{o^*, w^*} \sum_{(i, u) \in b}\left(e_{i u}-w_u^Y o_i\right)^2+\eta\left(\left\|o_i\right\|^2+\left\|w_u\right\|^2\right)$                  (11)

Assume that a hyperparameter is represented by η, the student user feature matrix is represented by O, and the environmental literacy education resource project feature matrix is represented by W. The derivatives of the above formula are:

$\frac{\partial K}{\partial O_i}=-2\left(e_{i u}-w_u^Y o_i\right) w_u+2 \eta o_i$                       (12)

$\frac{\partial K}{\partial w_u}=-2\left(e_{i u}-w_u^Y o_i\right) o_i+2 \eta w_u$                    (13)

The Funk-SVD model matrix decomposition algorithm uses gradient descent to solve parameters, and the iterative formulas for gradient descent are:

$o_i=o_i+\beta\left[\left(e_{i u}-w_u^T o_i\right) w_u-\eta o_i\right]$                    (14)

$w_u=w_u+\beta\left[\left(e_{i u}-w_u^T o_i\right) o_i-\eta w_u\right]$                 (15)

Through the above steps, the final O and W can be obtained.

The recommendation system needs to continuously update students' feature information based on new ratings and behavior data to maintain the timeliness and effectiveness of recommendation results. The significance of updating the student user feature matrix lies in adjusting and updating students' latent features and similarity information based on the latest ratings and behavior data in the source and target domains. This helps capture changes in student needs and interests, ensuring that the recommendation system can always provide suitable environmental literacy education resource recommendations for students.

In order to adjust the order of latent features in the source and target domains based on the similarity of students' latent features, it is necessary to establish a feature mapping relationship between the source and target domains for each student based on the calculated similarity. This can be achieved through maximum similarity matching or other matching algorithms. According to the feature mapping relationship, adjust the order of latent features in the student user feature matrix of the source and target domains to keep them consistent. Specifically, swap the rows in the target domain student user feature matrix to make it consistent with the order of the source domain student user feature matrix. After adjusting the order of latent features in the source and target domains, the recommendation model can be retrained to fully utilize the similarity information between the source and target domains during knowledge transfer and recommendation calculations.

Assuming that a certain latent feature of a student in the source domain is represented by YY_j, and a certain latent feature of a student in the target domain is represented by MBY_r. The cosine similarity calculation method shown in the following formula can be used to measure the similarity of students' latent features:

$S I M=\frac{Y Y_j M B Y_r}{\left\|Y Y_j\right\| \cdot\left\|M B Y_r\right\|}$                     (16)

Assuming that a certain latent feature of a student in the source domain is represented by YY_j, and a certain latent feature of a student in the target domain is represented by MBY_r.

After ordering the latent features, the student user feature matrices in the source and target domains are obtained. The next step is to update the target domain's student user feature matrix by applying the source domain's student user feature matrix, which facilitates knowledge transfer. This means that the rating, interest, and knowledge information of students in the source domain can be used to assist in the recommendation calculations in the target domain. This is particularly important for the target domain with insufficient rating information (cold start problem) and helps improve the accuracy of recommendations. Assume that the updated user feature of student f in the target domain is represented by MBY_f,qⁱ, and the number of environmental literacy education resource project ratings given by the student in the source domain is represented by B_u∈ae^a_f,u, satisfying B_u∈ae^a_f,u+B_u∈ae^a_f,u. The following update formula is then derived:

$\begin{aligned} & M B Y_{f, q}{ }^i=\frac{{ }_{u \in a}^B e_{f, u}^a}{\underset{u \in a}{B} e_{f, u}^a+\underset{u \in y}{B} e_{f, u}^y} \times Y Y_{f, q} +\frac{\underset{u \in y}{B} e_{f, u}^y}{\underset{u \in a}{B} e_{f, u}^a+\underset{u \in y}{B} e_{f, u}^y} \times M B Y_{f, q} \\ & \end{aligned}$                        (17)

$e=O W$                       (18)