Dúvida no Ex. 12 da Aula 2 - Cadastro de produtos

Estou encontrando um problema na hora de inserir o produto no banco, segue o erro:

GRAVE: Servlet.service() for servlet [dispatcher] in context with path [/novacasadocodigo] threw exception [Request processing failed; nested exception is java.lang.NullPointerException] with root cause
java.lang.NullPointerException
    at br.com.novacasadocodigo.controller.ProdutosController.gravar(ProdutosController.java:23)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at org.springframework.web.method.support.InvocableHandlerMethod.invoke(InvocableHandlerMethod.java:215)
    at org.springframework.web.method.support.InvocableHandlerMethod.invokeForRequest(InvocableHandlerMethod.java:132)
    at org.springframework.web.servlet.mvc.method.annotation.ServletInvocableHandlerMethod.invokeAndHandle(ServletInvocableHandlerMethod.java:104)
    at org.springframework.web.servlet.mvc.method.annotation.RequestMappingHandlerAdapter.invokeHandleMethod(RequestMappingHandlerAdapter.java:781)
    at org.springframework.web.servlet.mvc.method.annotation.RequestMappingHandlerAdapter.handleInternal(RequestMappingHandlerAdapter.java:721)
    at org.springframework.web.servlet.mvc.method.AbstractHandlerMethodAdapter.handle(AbstractHandlerMethodAdapter.java:83)
    at org.springframework.web.servlet.DispatcherServlet.doDispatch(DispatcherServlet.java:943)
    at org.springframework.web.servlet.DispatcherServlet.doService(DispatcherServlet.java:877)
    at org.springframework.web.servlet.FrameworkServlet.processRequest(FrameworkServlet.java:961)
    at org.springframework.web.servlet.FrameworkServlet.doPost(FrameworkServlet.java:863)
    at javax.servlet.http.HttpServlet.service(HttpServlet.java:650)
    at org.springframework.web.servlet.FrameworkServlet.service(FrameworkServlet.java:837)
    at javax.servlet.http.HttpServlet.service(HttpServlet.java:731)
    at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:303)
    at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
    at org.apache.tomcat.websocket.server.WsFilter.doFilter(WsFilter.java:52)
    at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:241)
    at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:208)
    at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:218)
    at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:122)
    at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:505)
    at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:169)
    at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:103)
    at org.apache.catalina.valves.AccessLogValve.invoke(AccessLogValve.java:956)
    at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:116)
    at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:442)
    at org.apache.coyote.http11.AbstractHttp11Processor.process(AbstractHttp11Processor.java:1082)
    at org.apache.coyote.AbstractProtocol$AbstractConnectionHandler.process(AbstractProtocol.java:623)
    at org.apache.tomcat.util.net.JIoEndpoint$SocketProcessor.run(JIoEndpoint.java:316)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at org.apache.tomcat.util.threads.TaskThread$WrappingRunnable.run(TaskThread.java:61)
    at java.lang.Thread.run(Unknown Source)

ProdutoController

package br.com.novacasadocodigo.controller;

import org.springframework.stereotype.Controller;
import org.springframework.web.bind.annotation.RequestMapping;

import br.com.novacasadocodigo.models.Produto;
import br.com.novacasadocoidgo.dao.ProdutoDAO;



@Controller
public class ProdutosController {

    private ProdutoDAO produtoDao;

    @RequestMapping("/produtos/form")
    public String form(){
        return "produtos/form";
    }

    @RequestMapping("/produtos")
    public String gravar(Produto produto){
        produtoDao.gravar(produto);
        return "produtos/ok";
    }
}

JPAConfiguration

package br.com.novacasadocodigo.conf;

import java.util.Properties;

import org.springframework.context.annotation.Bean;
import org.springframework.jdbc.datasource.DriverManagerDataSource;
import org.springframework.orm.jpa.JpaVendorAdapter;
import org.springframework.orm.jpa.LocalContainerEntityManagerFactoryBean;
import org.springframework.orm.jpa.vendor.HibernateJpaVendorAdapter;
import org.springframework.transaction.annotation.EnableTransactionManagement;

@EnableTransactionManagement
public class JPAConfiguration {


    @Bean
    public LocalContainerEntityManagerFactoryBean entityManagerFactory(){
        LocalContainerEntityManagerFactoryBean factoryBean = new LocalContainerEntityManagerFactoryBean();

        JpaVendorAdapter vendor = new HibernateJpaVendorAdapter();
        factoryBean.setJpaVendorAdapter(vendor);

        DriverManagerDataSource dataSource = new DriverManagerDataSource();
        dataSource.setUsername("root");
        dataSource.setPassword("mtw003");
        dataSource.setUrl("jdbc:mysql://localhost/novacasadocodigo");
        dataSource.setDriverClassName("com.mysql.jdbc.Driver");

        factoryBean.setDataSource(dataSource);

        Properties props = new Properties();
        props.setProperty("hibernate.dialect", "org.hibernate.dialect.MySQL5Dialect");
        props.setProperty("hibernate.show_sql", "true");
        props.setProperty("hibernate.hbm2ddl.auto", "update");

        factoryBean.setJpaProperties(props);
        factoryBean.setPackagesToScan("br.com.novacasadocodigo.models");

        return factoryBean;

    }
}

Produto

package br.com.novacasadocodigo.models;

import javax.persistence.Entity;
import javax.persistence.GeneratedValue;

import javax.persistence.GenerationType;
import javax.persistence.Id;

@Entity
public class Produto {
    @Id 
    @GeneratedValue(strategy=GenerationType.IDENTITY)
    private int id;
    private String titulo;
    private String descricao;
    private int paginas;


    public int getId() {
        return id;
    }
    public void setId(int id) {
        this.id = id;
    }
    public String getTitulo() {
        return titulo;
    }
    public void setTitulo(String titulo) {
        this.titulo = titulo;
    }
    public String getDescricao() {
        return descricao;
    }
    public void setDescricao(String descricao) {
        this.descricao = descricao;
    }
    public int getPaginas() {
        return paginas;
    }
    public void setPaginas(int paginas) {
        this.paginas = paginas;
    }


}

ProdutoDAO

package br.com.novacasadocoidgo.dao;

import javax.persistence.EntityManager;
import javax.persistence.PersistenceContext;

import org.springframework.stereotype.Repository;
import org.springframework.transaction.annotation.Transactional;

import br.com.novacasadocodigo.models.Produto;

@Repository
@Transactional
public class ProdutoDAO {

    @PersistenceContext
    private EntityManager maneger;

    public void gravar(Produto produto){
        maneger.persist(produto);
    }
}